;;;                 COPYRIGHT NOTICE
;;;  
;;;  Copyright (C) 2007-2016 Mario Rodriguez Riotorto
;;;  
;;;  This program is free software; you can redistribute
;;;  it and/or modify it under the terms of the
;;;  GNU General Public License as published by
;;;  the Free Software Foundation; either version 2 
;;;  of the License, or (at your option) any later version. 
;;;  
;;;  This program is distributed in the hope that it
;;;  will be useful, but WITHOUT ANY WARRANTY;
;;;  without even the implied warranty of MERCHANTABILITY
;;;  or FITNESS FOR A PARTICULAR PURPOSE. See the 
;;;  GNU General Public License for more details at
;;;  http://www.gnu.org/copyleft/gpl.html

;;; This is a maxima-gnuplot interface.

;;; Visit
;;; http://tecnostats.net/Maxima/gnuplot
;;; for examples

;;; For questions, suggestions, bugs and the like, feel free
;;; to contact me at
;;; riotorto @@@ yahoo DOT com


;; use $draw_version to save package version
;; and to know whether the package was loaded
($put '$gnuplot 1 '$version); to be removed in the future
(defvar $draw_version 2)



(defvar *windows-OS* (string= *autoconf-windows* "true") )

(defmacro write-font-type ()
   '(if (string= (get-option '$font) "")
      ""
      (format nil "font '~a,~a'" (get-option '$font) (get-option '$font_size))))


;; one-window multiplot: consecutive calls
;; to draw allways plot on the same window
(defvar *multiplot-is-active* nil)
(defun $multiplot_mode (term)
  (when (not *windows-OS*)
    (case term
      ($screen
        ($multiplot_mode '$none)
        (send-gnuplot-command
          (format nil "set terminal x11 dashed ~a~%set multiplot~%" (write-font-type)))
        (setf *multiplot-is-active* t))
      ($wxt
        ($multiplot_mode '$none)
        (send-gnuplot-command
          (format nil "set terminal wxt dashed ~a~%set multiplot~%" (write-font-type)))
        (setf *multiplot-is-active* t))
      ($qt
        ($multiplot_mode '$none)
       (send-gnuplot-command
         (format nil "set terminal qt dashed ~a~%set multiplot~%" (write-font-type)))
       (setf *multiplot-is-active* t))
      ($none
        (send-gnuplot-command
          (format nil "unset multiplot~%"))
        (setf *multiplot-is-active* nil))
      (otherwise
        (merror "draw: ~M is not recognized as a multiplot mode" term)))))



;; This function is called from the graphic objects constructors
;; (points, rectangle, etc.). When a new object is created, and if
;; the user hasn't especified an x or y range, ranges are computed
;; automaticallly by calling this function. There is a trick so
;; that object constructors know if they can modify global variables
;; xrange and yrange; if these lists are of length 2, it means that
;; it was a user selection and they can't be altered; if they are of
;; length 3 (with a dummy 0), object constructors should make the necessary changes
;; to fit the objects in the window; if they are nil, default
;; value, constructors are also allowed to make changes.
(defmacro update-range (axi vmin vmax)
   `(case (length (get-option ,axi))
          (0 (setf (gethash ,axi *gr-options*) (list ,vmin ,vmax 0)))
          (3 (setf (gethash ,axi *gr-options*) (list (min ,vmin (first  (get-option ,axi)))
                                           (max ,vmax (second (get-option ,axi)))
                                           0))) ))

(defun update-ranges-2d (xmin xmax ymin ymax)
   (if (get-option '$xaxis_secondary)
      (update-range '$xrange_secondary xmin xmax)
      (update-range '$xrange xmin xmax))
   (if (get-option '$yaxis_secondary)
      (update-range '$yrange_secondary ymin ymax)
      (update-range '$yrange ymin ymax)) )

(defun update-ranges-3d (xmin xmax ymin ymax zmin zmax)
   (update-ranges-2d xmin xmax ymin ymax)
   (update-range '$zrange zmin zmax))

(defmacro check-extremes-x ()
  '(when (numberp xx)
    (when (< xx xmin) (setf xmin xx))
    (when (> xx xmax) (setf xmax xx))))

(defmacro check-extremes-y ()
  '(when (numberp yy)
    (when (< yy ymin) (setf ymin yy))
    (when (> yy ymax) (setf ymax yy))))

(defmacro check-extremes-z ()
  '(when (numberp zz)
    (when (< zz zmin) (setf zmin zz))
    (when (> zz zmax) (setf zmax zz))))

;; Controls whether the actual graphics object must
;; be plotted against the primary or the secondary axes,
;; both horizontal and vertical. Secondary axes in 3D
;; are not yet supported.
(defun axes-to-plot ()
   (format nil "~a~a"
           (if (get-option '$xaxis_secondary)
               "x2"
               "x1")
           (if (get-option '$yaxis_secondary)
               "y2"
               "y1")))

(defstruct gr-object
   name command groups points)

(defun make-obj-title (str)
  (if (> (length str) 80)
      (concatenate 'string "t '" (subseq str 0 75) " ...'"))
      (concatenate 'string "t '" str "'"))





;; Object: 'errors'
;; Usage:
;;     errors([[x1,y1,...], [x2,y2,...], [x3,y3,...],...])
;; Options:
;;     error_type
;;     points_joined
;;     line_width
;;     key
;;     line_type
;;     color
;;     fill_density
;;     xaxis_secondary
;;     yaxis_secondary
(defun errors (arg)
  (let ((etype  (get-option '$error_type))
        (joined (get-option '$points_joined))
        element-size
        pts pltcmd grouping xmin xmax ymin ymax with)
    (if (and ($listp arg)
             (every #'$listp (rest arg)))
        (setf element-size (length (cdadr arg)))
        (merror "draw (errors object): incorrect input format"))
    (unless (every #'(lambda (z) (= element-size ($length z))) (rest arg))
      (merror "draw (errors object): lists of different sizes"))
    ; create plot command
    (cond ((and (eql etype '$x)
                (or (= element-size 3)
                    (= element-size 4)))
             (if (null joined)
               (setf with "xerrorbars")
               (setf with "xerrorlines"))  )
          ((and (eql etype '$y)
                (or (= element-size 3)
                    (= element-size 4)))
             (if (null joined)
               (setf with "yerrorbars")
               (setf with "yerrorlines"))  )
          ((and (eql etype '$xy)
                (or (= element-size 4)
                    (= element-size 6)))
             (if (null joined)
               (setf with "xyerrorbars")
               (setf with "xyerrorlines"))  )
          ((and (eql etype '$boxes)
                (or (= element-size 4)
                    (= element-size 6)))
             (setf with "boxxyerrorbars") )
          (t
             (merror "draw (errors object): incompatibility with option error_type")))

    (setf grouping `((,element-size 0)))
    (setf pltcmd
          (format nil
                  " ~a w ~a ~a lw ~a lt ~a lc ~a axis ~a"
                  (make-obj-title (get-option '$key))
                  with
                  (if (eql etype '$boxes)  ; in case of boxes, should they be filled?
                      (format nil "fs solid ~a"
                              (get-option '$fill_density))
                      "")
                  (get-option '$line_width)
                  (get-option '$line_type)
                  (hex-to-rgb (get-option '$color))
                  (axes-to-plot)))
    (setf pts (map 'list #'rest (rest ($float arg))))
    (let ((x (map 'list #'first  pts))
          (y (map 'list #'second pts)))
      (setf xmin ($tree_reduce 'min (cons '(mlist simp) x))
            xmax ($tree_reduce 'max (cons '(mlist simp) x))
            ymin ($tree_reduce 'min (cons '(mlist simp) y))
            ymax ($tree_reduce 'max (cons '(mlist simp) y))))
    (update-ranges-2d xmin xmax ymin ymax)
    (make-gr-object
       :name 'errors
       :command pltcmd
       :groups grouping
       :points (list (make-array (* element-size (length pts))
                                 :element-type 'flonum
                                 :initial-contents (flatten pts)))) ))



     


;; Object: 'points'
;; Usage:
;;     points([[x1,y1], [x2,y2], [x3,y3],...])
;;     points([x1,x2,x3,...], [y1,y2,y3,...])
;;     points([y1,y2,y3,...]), abscissas are automatically chosen: 1,2,3,...
;;     points(matrix), one-column, one-row, two-column or two-row matrix
;;     points(array1d)
;;     points(array1d, array1d)
;;     points(array2d), two-column or two-row array
;; Options:
;;     point_size
;;     point_type
;;     points_joined
;;     line_width
;;     key
;;     line_type
;;     color
;;     xaxis_secondary
;;     yaxis_secondary
;;     transform
(defun points-command ()
  (let ((pj (get-option '$points_joined))
        (ps (get-option '$point_size))
        (pt (get-option '$point_type)) )
    (cond
      ((null pj) ; draws isolated points
         (format nil " ~a w p ps ~a pt ~a lc ~a axis ~a"
                 (make-obj-title (get-option '$key))
                 ps
                 pt
                 (hex-to-rgb (get-option '$color))
                 (axes-to-plot)))
      ((and (eq pj t) (or (= ps 0.0) (= pt 0)) ) ; draws joined points without symbols
         (format nil " ~a w l lw ~a lt ~a lc ~a axis ~a"
                 (make-obj-title (get-option '$key))
                 (get-option '$line_width)
                 (get-option '$line_type)
                 (hex-to-rgb (get-option '$color))
                 (axes-to-plot)))
      ((eq pj t) ; draws joined points
         (format nil " ~a w lp ps ~a pt ~a lw ~a lt ~a lc ~a axis ~a"
                 (make-obj-title (get-option '$key))
                 ps
                 pt
                 (get-option '$line_width)
                 (get-option '$line_type)
                 (hex-to-rgb (get-option '$color))
                 (axes-to-plot)))
      (t  ; draws impulses
         (format nil " ~a w i lw ~a lt ~a lc ~a axis ~a"
                 (make-obj-title (get-option '$key))
                 (get-option '$line_width)
                 pt
                 (hex-to-rgb (get-option '$color))
                 (axes-to-plot))))) )

(defun points-array-2d (arg)
   (let ((xmin most-positive-double-float)
         (xmax most-negative-double-float)
         (ymin most-positive-double-float)
         (ymax most-negative-double-float)
         (pos -1)
         (dim (array-dimensions arg))
         n xx yy pts twocolumns)
      (cond
         ((and (= (length dim) 2)   ; two-column array
               (= (cadr dim) 2))
            (setf n (car dim))
            (setf twocolumns t))
         ((and (= (length dim) 2)   ; two-row array
               (= (car dim) 2))
            (setf n (cadr dim))
            (setf twocolumns nil))
         (t (merror "draw (points2d): bad 2d array input format")))
      (setf pts (make-array (* 2 n) :element-type 'flonum))
      (loop for k below n do
         (if twocolumns
            (setf xx ($float (aref arg k 0))
                  yy ($float (aref arg k 1)))
            (setf xx ($float (aref arg 0 k))
                  yy ($float (aref arg 1 k))))
         (transform-point 2)
         (check-extremes-x)
         (check-extremes-y)
         (setf (aref pts (incf pos)) xx)
         (setf (aref pts (incf pos)) yy))
      (update-ranges-2d xmin xmax ymin ymax)
      (make-gr-object
         :name 'points
         :command (points-command)
         :groups '((2 0)) ; numbers are sent to gnuplot in groups of 2
         :points (list pts))))

(defun points-array-1d (arg1 &optional (arg2 nil))
   (let ((xmin most-positive-double-float)
         (xmax most-negative-double-float)
         (ymin most-positive-double-float)
         (ymax most-negative-double-float)
         (pos -1)
         (dim (array-dimensions arg1))
         n x y xx yy pts)
      (cond
         ((and (null arg2)
               (= (length dim) 1))  ; y format
            (setf n (car dim))
            (setf x (make-array n
                                :element-type 'flonum
                                :initial-contents (loop for k from 1 to n collect ($float k)) ))
            (setf y (make-array n
                                :element-type 'flonum
                                :initial-contents (loop for k below n collect ($float (aref arg1 k))))))
         ((and (arrayp arg2)   ; xx yy format
               (= (length dim) 1)
               (equal dim (array-dimensions arg2)))
            (setf n (car dim))
            (setf x arg1
                  y arg2))
         (t (merror "draw (points2d): bad 1d array input format")))
      (setf pts (make-array (* 2 n) :element-type 'flonum))
      (loop for k below n do
         (setf xx ($float (aref x k))
               yy ($float (aref y k)))
         (transform-point 2)
         (check-extremes-x)
         (check-extremes-y)
         (setf (aref pts (incf pos)) xx)
         (setf (aref pts (incf pos)) yy))
      (update-ranges-2d xmin xmax ymin ymax)
      (make-gr-object
         :name 'points
         :command (points-command)
         :groups '((2 0)) ; numbers are sent to gnuplot in groups of 2
         :points (list pts))))

(defun points-list (arg1 &optional (arg2 nil))
   (let (x y xmin xmax ymin ymax pts)
      (cond 
            ((and ($listp arg1)
                  (null arg2)
                  (every #'$listp (rest arg1)))     ; xy format
               (let ((tmp (mapcar #'rest (rest arg1))))
                  (setf x (map 'list #'$float (map 'list #'first tmp))
                        y (map 'list #'$float (map 'list #'second tmp)))) )
            ((and ($matrixp arg1)
                  (= (length (cadr arg1)) 3)
                  (null arg2))                 ; two-column matrix
               (let ((tmp (mapcar #'rest (rest arg1))))
                  (setf x (map 'list #'$float (map 'list #'first tmp))
                        y (map 'list #'$float (map 'list #'second tmp)) ) ) )
            ((and ($listp arg1)
                  (null arg2)
                  (notany #'$listp (rest arg1)))   ; y format
               (setf x (loop for xx from 1 to (length (rest arg1)) collect ($float xx))
                     y (map 'list #'$float (rest arg1))))
            ((and ($matrixp arg1)
                  (= (length (cadr arg1)) 2)
                  (null arg2))                 ; one-column matrix
               (setf x (loop for xx from 1 to (length (rest arg1)) collect ($float xx))
                     y (map 'list #'$float (map 'list #'second (rest arg1)))))
            ((and ($matrixp arg1)
                  (= ($length arg1) 1)
                  (null arg2))                 ; one-row matrix
               (setf x (loop for xx from 1 to (length (cdadr arg1)) collect ($float xx))
                     y (map 'list #'$float (cdadr arg1))))
            ((and ($listp arg1)
                  ($listp arg2)
                  (= (length arg1) (length arg2)))  ; xx yy format
               (setf x (map 'list #'$float (rest arg1))
                     y (map 'list #'$float (rest arg2))))
            ((and ($matrixp arg1)
                  (= ($length arg1) 2)
                  (null arg2))            ; two-row matrix
               (setf x (map 'list #'$float (cdadr arg1))
                     y (map 'list #'$float (cdaddr arg1))))
            (t (merror "draw (points2d): incorrect input format")))
      (transform-lists 2)
      (setf xmin ($tree_reduce 'min (cons '(mlist simp) x))
            xmax ($tree_reduce 'max (cons '(mlist simp) x))
            ymin ($tree_reduce 'min (cons '(mlist simp) y))
            ymax ($tree_reduce 'max (cons '(mlist simp) y)) )
      (setf pts (make-array (* 2 (length x)) :element-type 'flonum
                                             :initial-contents (mapcan #'list x y)))
      ;; update x-y ranges if necessary
      (update-ranges-2d xmin xmax ymin ymax)
      (make-gr-object
         :name 'points
         :command (points-command)
         :groups '((2 0)) ; numbers are sent to gnuplot in groups of 2
         :points (list pts) ) ))

(defun points (arg1 &optional (arg2 nil))
   (if (arrayp arg1)
      (if (= (length (array-dimensions arg1)) 2)
         (points-array-2d arg1)
         (points-array-1d arg1 arg2))
      (points-list arg1 arg2)))







;; Object: 'points3d'
;; Usage:
;;     points([[x1,y1,z1], [x2,y2,z2], [x3,y3,z3],...])
;;     points([x1,x2,x3,...], [y1,y2,y3,...], [z1,z2,z3,...])
;;     points(matrix), three-column or three-row matrix
;;     points(array2d),  three-column or three-row array
;;     points(array1d, array1d, array1d, array1d)
;; Options:
;;     point_size
;;     point_type
;;     points_joined
;;     line_width
;;     key
;;     line_type
;;     color
;;     enhanced3d
;;     transform
(defun points3d-command ()
  (let ((pj (get-option '$points_joined))
        (ps (get-option '$point_size))
        (pt (get-option '$point_type))
        (pal (if (> *draw-enhanced3d-type* 0)
                 "palette"
                 (hex-to-rgb (get-option '$color)) )))
    (cond
      ((null pj) ; draws isolated points
         (format nil " ~a w p ps ~a pt ~a lc ~a"
                 (make-obj-title (get-option '$key))
                 ps
                 pt
                 pal ))
      ((and (eq pj t) (or (= ps 0.0) (= pt 0)) ) ; draws joined points without symbols
         (format nil " ~a w l lw ~a lt ~a lc ~a "
                 (make-obj-title (get-option '$key))
                 (get-option '$line_width)
                 (get-option '$line_type)
                 (hex-to-rgb (get-option '$color))))
      ((eq pj t) ; draws joined points
         (format nil " ~a w lp ps ~a pt ~a lw ~a lt ~a lc ~a"
                 (make-obj-title (get-option '$key))
                 ps
                 pt
                 (get-option '$line_width)
                 (get-option '$line_type)
                 pal ))
      (t  ; draws impulses
         (format nil " ~a w i lw ~a lt ~a lc ~a"
                 (make-obj-title (get-option '$key))
                 (get-option '$line_width)
                 (get-option '$line_type)
                 pal )))))

(defun points3d (arg1 &optional (arg2 nil) (arg3 nil))
   (let (pts x y z xmin xmax ymin ymax zmin zmax ncols col)
      (check-enhanced3d-model "points" '(0 1 3))
      (cond (($listp arg1)   ; list input
               (cond ((and (every #'$listp (rest arg1))   ; xyz format
                           (null arg2)
                           (null arg3))
                        (let ((tmp (mapcar #'rest (rest arg1))))
                        (setf x (map 'list #'$float (map 'list #'first tmp))
                              y (map 'list #'$float (map 'list #'second tmp))
                              z (map 'list #'$float (map 'list #'third tmp)) ) ) )
                     ((and ($listp arg2)                  ; xx yy zz format
                           ($listp arg3)
                           (= (length arg1) (length arg2) (length arg3)))
                        (setf x (map 'list #'$float (rest arg1))
                              y (map 'list #'$float (rest arg2))
                              z (map 'list #'$float (rest arg3)) )) 
                     (t (merror "draw (points3d): bad list input format"))))
            (($matrixp arg1)   ; matrix input
               (cond ((and (= (length (cadr arg1)) 4)     ; three-column matrix
                           (null arg2)
                           (null arg3))
                        (let ((tmp (mapcar #'rest (rest arg1))))
                        (setf x (map 'list #'$float (map 'list #'first tmp))
                              y (map 'list #'$float (map 'list #'second tmp))
                              z (map 'list #'$float (map 'list #'third tmp)) ) ) )
                     ((and (= ($length arg1) 3)           ; three-row matrix
                           (null arg2)
                           (null arg3))
                        (setf x (map 'list #'$float (cdadr arg1))
                              y (map 'list #'$float (cdaddr arg1))
                              z (map 'list #'$float (cdaddr (rest arg1)) ) ) )
                     (t (merror "draw (points3d): bad matrix input format"))))
            ((arrayp arg1)   ; array input
               (let ((dim (array-dimensions arg1))) 
               (cond ((and (= (length dim) 2)   ; three-row array
                           (= (first dim) 3)
                           (null arg2)
                           (null arg3))
                        (setf x (loop for k from 0 below (second dim)
                                    collect ($float (aref arg1 0 k)))
                              y (loop for k from 0 below (second dim)
                                    collect ($float (aref arg1 1 k)))
                              z (loop for k from 0 below (second dim)
                                    collect ($float (aref arg1 2 k))) ))
                     ((and (= (length dim) 2)   ; three-column array
                           (= (second dim) 3)
                           (null arg2)
                           (null arg3))
                        (setf x (loop for k from 0 below (first dim)
                                    collect ($float (aref arg1 k 0)))
                              y (loop for k from 0 below (first dim)
                                    collect ($float (aref arg1 k 1)))
                              z (loop for k from 0 below (first dim)
                                    collect ($float (aref arg1 k 2))) ))
                     ((and (= (length dim) 1)   ; three 1d arrays
                           (arrayp arg2)
                           (arrayp arg3)
                           (equal dim (array-dimensions arg2))
                           (equal dim (array-dimensions arg3)))
                        (setf x (map 'list #'$float arg1)
                              y (map 'list #'$float arg2)
                              z (map 'list #'$float arg3) ) )
                     (t (merror "draw (points3d): bad array input format")) ) ) )
            (t (merror "draw (points3d): bad input format")))
      (transform-lists 3)
      ; set pm3d colors
      (cond ((= *draw-enhanced3d-type* 0)
                (setf ncols 3)
                (setf pts (make-array (* ncols (length x))
                                      :element-type 'flonum
                                      :initial-contents (mapcan #'list x y z))))
            ((= *draw-enhanced3d-type* 1)
                (setf col (loop for k from 1 to (length x)
                                collect (funcall *draw-enhanced3d-fun* k)))
                (setf ncols 4)
                (setf pts (make-array (* ncols (length x))
                                      :element-type 'flonum
                                      :initial-contents (mapcan #'list x y z col))))
            ((= *draw-enhanced3d-type* 3)
                (setf col (mapcar #'(lambda (xx yy zz) (funcall *draw-enhanced3d-fun* xx yy zz)) x y z))
                (setf ncols 4)
                (setf pts (make-array (* ncols (length x))
                                      :element-type 'flonum
                                      :initial-contents (mapcan #'list x y z col)))) )
      (setf xmin ($tree_reduce 'min (cons '(mlist simp) x))
            xmax ($tree_reduce 'max (cons '(mlist simp) x))
            ymin ($tree_reduce 'min (cons '(mlist simp) y))
            ymax ($tree_reduce 'max (cons '(mlist simp) y))
            zmin ($tree_reduce 'min (cons '(mlist simp) z))
            zmax ($tree_reduce 'max (cons '(mlist simp) z)) )
      ;; update x-y-y ranges if necessary
      (update-ranges-3d xmin xmax ymin ymax zmin zmax)
      (make-gr-object
         :name 'points
         :command (points3d-command)
         :groups `((,ncols 0)) ; numbers are sent to gnuplot in groups of 4 or 3 
                               ; (depending on colored 4th dimension or not), without blank lines
         :points (list pts) )  ))






;; Object: 'polygon'
;; Usage:
;;     polygon([[x1,y1], [x2,y2], [x3,y3],...])
;;     polygon([x1,x2,x3,...], [y1,y2,y3,...])
;; Options:
;;     transparent
;;     fill_color
;;     border
;;     line_width
;;     line_type
;;     color
;;     key
;;     xaxis_secondary
;;     yaxis_secondary
;;     transform
(defun polygon (arg1 &optional (arg2 nil))
   (if (and (get-option '$transparent)
            (not (get-option '$border)))
       (merror "draw (polygon): transparent is true and border is false; this is not consistent"))
   (let (pltcmd pts grps x y xmin xmax ymin ymax)
      (cond ((and ($listp arg1)
                  (every #'$listp (rest arg1))
                  (null arg2) )                    ; xy format
               (let ((tmp (mapcar #'rest (rest arg1))))
                  (setf x (map 'list #'(lambda (z) ($float (first z))) tmp)
                        y (map 'list #'(lambda (z) ($float (second z))) tmp) ) )  )
            ((and ($listp arg1)
                  ($listp arg2)
                  (= (length arg1) (length arg2)))  ; xx yy format
               (setf x (map 'list #'$float (rest arg1))
                     y (map 'list #'$float (rest arg2))) )
            (t (merror "draw (polygon): bad input format"))  )
      (transform-lists 2)
      (setf xmin ($tree_reduce 'min (cons '(mlist simp) x))
            xmax ($tree_reduce 'max (cons '(mlist simp) x))
            ymin ($tree_reduce 'min (cons '(mlist simp) y))
            ymax ($tree_reduce 'max (cons '(mlist simp) y)) )
      ;; update x-y ranges if necessary
      (update-ranges-2d xmin xmax ymin ymax)
      (cond
         ((get-option '$transparent)  ; if transparent, draw only the border
             (setf pltcmd (format nil " ~a  w l lw ~a lt ~a lc ~a axis ~a"
                                      (make-obj-title (get-option '$key))
                                      (get-option '$line_width)
                                      (get-option '$line_type)
                                      (hex-to-rgb (get-option '$color))
                                      (axes-to-plot)))
             (setf grps '((2 0)))  ; numbers are sent to gnuplot in groups of 2
             (setf pts (list (make-array (+ (* 2 (length x)) 2)
                                         :element-type 'flonum
                                         :initial-contents (append (mapcan #'list x y)
                                                                   (list (first x) (first y))) )) ) )
         ((not (get-option '$border)) ; no transparent, no border
             (setf pltcmd (format nil " ~a w filledcurves lc ~a axis ~a"
                                      (make-obj-title (get-option '$key))
                                      (hex-to-rgb (get-option '$fill_color))
                                      (axes-to-plot)))
             (setf grps '((2 0)))  ; numbers are sent to gnuplot in groups of 2
             (setf pts (list (make-array (* 2 (length x))
                                         :element-type 'flonum
                                         :initial-contents (mapcan #'list x y)) ) ))
         (t ; no transparent with border
             (setf pltcmd (list (format nil " ~a w filledcurves lc ~a axis ~a"
                                        (make-obj-title (get-option '$key))
                                        (hex-to-rgb (get-option '$fill_color))
                                        (axes-to-plot))
                                (format nil " t '' w l lw ~a lt ~a lc ~a axis ~a"
                                        (get-option '$line_width)
                                        (get-option '$line_type)
                                        (hex-to-rgb (get-option '$color))
                                        (axes-to-plot))))
             (setf grps '((2 0) (2 0)))  ; both sets of vertices (interior and border)
                                     ; are sent to gnuplot in groups of 2
             (setf pts (list (make-array (* 2 (length x))
                                         :element-type 'flonum
                                         :initial-contents (mapcan #'list x y))
                             (make-array (+ (* 2 (length x)) 2)
                                         :element-type 'flonum
                                         :initial-contents (append (mapcan #'list x y)
                                                                   (list (first x) (first y))))))))
      (make-gr-object
         :name   'polygon
         :command pltcmd
         :groups  grps
         :points  pts )))







;; Object: 'triangle'
;; Usage:
;;     triangle([x1,y1], [x2,y2], [x3,y3])
;; Options:
;;     transparent
;;     fill_color
;;     border
;;     line_width
;;     line_type
;;     color
;;     key
;;     xaxis_secondary
;;     yaxis_secondary
;;     transform
(defun triangle (arg1 arg2 arg3)
   (if (or (not ($listp arg1))
           (not (= ($length arg1) 2))
           (not ($listp arg2))
           (not (= ($length arg2) 2))
           (not ($listp arg3))
           (not (= ($length arg3) 2)))
       (merror "draw2d (triangle): vertices are not correct"))
   (let* ((x1 ($float (cadr arg1)))
          (y1 ($float (caddr arg1)))
          (x2 ($float (cadr arg2)))
          (y2 ($float (caddr arg2)))
          (x3 ($float (cadr arg3)))
          (y3 ($float (caddr arg3)))
          (grobj (polygon `((mlist simp)
                            ((mlist simp) ,x1 ,y1)
                            ((mlist simp) ,x2 ,y2)
                            ((mlist simp) ,x3 ,y3)
                            ((mlist simp) ,x1 ,y1)))))
      (setf (gr-object-name grobj) 'triangle)
      grobj))






;; Object: 'quadrilateral'
;; Usage:
;;     quadrilateral([x1,y1], [x2,y2], [x3,y3], [x4,y4])
;; Options:
;;     transparent
;;     fill_color
;;     border
;;     line_width
;;     line_type
;;     color
;;     key
;;     xaxis_secondary
;;     yaxis_secondary
;;     transform
(defun quadrilateral (arg1 arg2 arg3 arg4)
   (if (or (not ($listp arg1))
           (not (= ($length arg1) 2))
           (not ($listp arg2))
           (not (= ($length arg2) 2))
           (not ($listp arg3))
           (not (= ($length arg3) 2))
           (not ($listp arg4))
           (not (= ($length arg4) 2)))
       (merror "draw2d (quadrilateral): vertices are not correct"))
   (let* ((x1 ($float (cadr arg1)))
          (y1 ($float (caddr arg1)))
          (x2 ($float (cadr arg2)))
          (y2 ($float (caddr arg2)))
          (x3 ($float (cadr arg3)))
          (y3 ($float (caddr arg3)))
          (x4 ($float (cadr arg4)))
          (y4 ($float (caddr arg4)))
          (grobj (polygon `((mlist simp)
                            ((mlist simp) ,x1 ,y1)
                            ((mlist simp) ,x2 ,y2)
                            ((mlist simp) ,x3 ,y3)
                            ((mlist simp) ,x4 ,y4)
                            ((mlist simp) ,x1 ,y1)))))
      (setf (gr-object-name grobj) 'quadrilateral)
      grobj))







;; Object: 'rectangle'
;; Usage:
;;     rectangle([x1,y1], [x2,y2]), being [x1,y1] & [x2,y2] opposite vertices
;; Options:
;;     transparent
;;     fill_color
;;     border
;;     line_width
;;     line_type
;;     color
;;     key
;;     xaxis_secondary
;;     yaxis_secondary
;;     transform
(defun rectangle (arg1 arg2)
   (if (or (not ($listp arg1))
           (not (= ($length arg1) 2))
           (not ($listp arg2))
           (not (= ($length arg2) 2)))
       (merror "draw2d (rectangle): vertices are not correct"))
   (let* ((x1 ($float (cadr arg1)))
          (y1 ($float (caddr arg1)))
          (x2 ($float (cadr arg2)))
          (y2 ($float (caddr arg2)))
          (grobj (polygon `((mlist simp)
                            ((mlist simp) ,x1 ,y1)
                            ((mlist simp) ,x2 ,y1)
                            ((mlist simp) ,x2 ,y2)
                            ((mlist simp) ,x1 ,y2)
                            ((mlist simp) ,x1 ,y1)))))
      (setf (gr-object-name grobj) 'rectangle)
      grobj))







;; Object: 'ellipse'
;; Usage:
;;     ellipse(xc, yc, a, b, ang1 ang2)
;; Options:
;;     nticks
;;     transparent
;;     fill_color
;;     border
;;     line_width
;;     line_type
;;     key
;;     color
;;     xaxis_secondary
;;     yaxis_secondary
;;     transform
(defun ellipse (xc yc a b ang1 ang2)
  (if (and (get-option '$transparent)
           (not (get-option '$border)))
      (merror "draw2d (ellipse): transparent is true and border is false; this is not consistent"))
  (let ((fxc ($float xc))
        (fyc ($float yc))
        (fa ($float a))
        (fb ($float b))
        (fang1 ($float ang1))
        (fang2 ($float ang2))
        (nticks (get-option '$nticks))
        (xmin most-positive-double-float)
        (xmax most-negative-double-float)
        (ymin most-positive-double-float)
        (ymax most-negative-double-float)
        (result nil)
        pts grps tmin tmax eps xx yy tt pltcmd)
    (when (or (notevery #'floatp (list fxc fyc fa fb fang1 fang2))
              (<= fa 0.0)
              (<= fb 0.0))
       (merror "draw (ellipse): illegal argument(s)"))
    ; degrees to radians
    (setf fang1 (* 0.017453292519943295 fang1)
          fang2 (* 0.017453292519943295 fang2))
    (setf tmin (min fang1 (+ fang1 fang2))
          tmax (max fang1 (+ fang1 fang2))
          eps (/ (- tmax tmin) (- nticks 1)))
    (setf tt tmin)
    (loop
      (setf xx (+ fxc (* fa (cos tt))))
      (setf yy (+ fyc (* fb (sin tt))))
      (transform-point 2)
      (check-extremes-x)
      (check-extremes-y)
      (setf result (append (list xx yy) result))
      (if (>= tt tmax) (return))
      (setf tt (+ tt eps))
      (if (>= tt tmax) (setq tt tmax)) )
    (when (> *draw-transform-dimensions* 0)
      (let ((xold fxc)
            (yold fyc))
        (setf fxc (funcall *draw-transform-f1* xold yold)
              fyc (funcall *draw-transform-f2* xold yold))) )
    ; update x-y ranges if necessary
    (setf xmin (min fxc xmin)
          xmax (max fxc xmax)
          ymin (min fyc ymin)
          ymax (max fyc ymax))
    (update-ranges-2d xmin xmax ymin ymax)
    (cond
       ((get-option '$transparent)  ; if transparent, draw only the border
           (setf pltcmd (format nil " ~a w l lw ~a lt ~a lc ~a axis ~a"
                                    (make-obj-title (get-option '$key))
                                    (get-option '$line_width)
                                    (get-option '$line_type)
                                    (hex-to-rgb (get-option '$color))
                                    (axes-to-plot)))
           (setf grps '((2 0)))
           (setf pts `( ,(make-array (length result) :element-type 'flonum
                                                    :initial-contents result)))  )
       ((not (get-option '$border)) ; no transparent, no border
           (setf pltcmd (format nil " ~a w filledcurves xy=~a,~a lc ~a axis ~a"
                                    (make-obj-title (get-option '$key))
                                    fxc fyc
                                    (hex-to-rgb (get-option '$fill_color))
                                    (axes-to-plot)))
           (setf grps '((2 0)))
           (setf pts `( ,(make-array (length result) :element-type 'flonum
                                                    :initial-contents result)))  )
       (t ; no transparent with border
             (setf pltcmd (list (format nil " ~a w filledcurves xy=~a,~a lc ~a axis ~a"
                                            (make-obj-title (get-option '$key))
                                            fxc fyc
                                            (hex-to-rgb (get-option '$fill_color))
                                            (axes-to-plot))
                                (format nil " t '' w l lw ~a lt ~a lc ~a axis ~a"
                                            (get-option '$line_width)
                                            (get-option '$line_type)
                                            (hex-to-rgb (get-option '$color))
                                            (axes-to-plot))))
           (setf grps '((2 0) (2 0)))
           (setf pts (list (make-array (length result) :element-type 'flonum
                                                       :initial-contents result)
                           (make-array (length result) :element-type 'flonum
                                                       :initial-contents result)))  ))
    (make-gr-object
       :name    'ellipse
       :command pltcmd
       :groups  grps
       :points  pts ) ))








;; Object: 'label'
;; Usage in 2d:
;;     label([string1,xx1,y1],[string2,xx2,y2],...)
;; Usage in 3d:
;;     label([string1,x1,y1,z1],[string2,x2,y2,z2],...)
;; Options:
;;     label_alignment
;;     label_orientation
;;     color
;;     xaxis_secondary
;;     yaxis_secondary

(defun replace-substring (string part replacement)
    (with-output-to-string (out)
      (loop with part-length = (length part)
            for old-pos = 0 then (+ pos part-length)
            for pos = (search part string
                              :start2 old-pos
                              :test #'char=)
            do (write-string string out
                             :start old-pos
                             :end (or pos (length string)))
            when pos do (write-string replacement out)
            while pos)))

(defun label (&rest lab)
  (let ((n (length lab))
        (result nil)
        is2d)
    (cond ((= n 0)
            (merror "draw (label): no arguments in object labels"))
          ((every #'$listp lab)
            (cond ((every #'(lambda (z) (= 3 ($length z))) lab)   ; labels in 2d
                    (setf is2d t))
                  ((every #'(lambda (z) (= 4 ($length z))) lab)   ; labels in 3d
                    (setf is2d nil))
                  (t
                    (merror "draw (label): arguments of not equal length")))
            (cond (is2d
                    (let (fx fy text)
                      (dolist (k lab)
                        (setf fx   ($float ($second k))
                              fy   ($float ($third k))
                              ; backslashes are replaced by double backslashes to allow LaTeX code in labels.
                              text (format nil "\"~a\"" (replace-substring ($first k) "\\" "\\\\")))
                        (if (or (not (floatp fx)) 
                                (not (floatp fy)))
                            (merror "draw (label): non real 2d coordinates"))
                        (update-ranges-2d fx fx fy fy)
                        (setf result (append (list fx fy text) result)))))
                  (t ; labels in 3d
                    (let (fx fy fz text)
                      (dolist (k lab)
                        (setf fx   ($float ($second k))
                              fy   ($float ($third k))
                              fz   ($float ($fourth k))
                              text (format nil "\"~a\"" ($first k)) )
                        (if (or (not (floatp fx)) 
                                (not (floatp fy))
                                (not (floatp fz)))
                            (merror "draw (label): non real 3d coordinates"))
                        (update-ranges-3d fx fx fy fy fz fz)
                        (setf result (append (list fx fy fz text) result)))))) )
          (t (merror "draw (label): illegal arguments")))
    (make-gr-object
       :name 'label
       :command (format nil " t '' w labels ~a ~a tc ~a ~a"
                              (case (get-option '$label_alignment)
                                 ($center "center")
                                 ($left   "left")
                                 ($right  "right"))
                              (case (get-option '$label_orientation)
                                 ($horizontal "norotate")
                                 ($vertical  "rotate"))
                              (hex-to-rgb (get-option '$color))
                              (if is2d
                                 (format nil "axis ~a" (axes-to-plot))
                                 "") )
       :groups (if is2d '((3 0)) '((4 0)))
       :points (list (make-array (length result) :initial-contents result))) ))







;; Object: 'bars'
;;     bars([x1,h1,w1],[x2,h2,w2],...), x, height and width 
;; Options:
;;     key
;;     fill_color
;;     fill_density
;;     line_width
;;     xaxis_secondary
;;     yaxis_secondary
(defun bars (&rest boxes)
  (let ((n (length boxes))
        (count -1)
        (xmin most-positive-double-float)
        (xmax most-negative-double-float)
        (ymin most-positive-double-float)
        (ymax most-negative-double-float)
        result x h w w2)
    (when (= n 0) 
      (merror "draw2d (bars): no arguments in object bars"))
    (when (not (every #'(lambda (z) (and ($listp z) (= 3 ($length z)))) boxes))
      (merror "draw2d (bars): arguments must be lists of length three"))
    (setf result (make-array (* 3 n) :element-type 'flonum))
    (dolist (k boxes)
       (setf x ($float ($first k))
             h ($float ($second k))
             w ($float ($third k)))
       (setf w2 (/ w 2))
       (setf (aref result (incf count)) x
             (aref result (incf count)) h
             (aref result (incf count)) w)
       (setf xmin (min xmin (- x w2))
             xmax (max xmax (+ x w2))
             ymin (min ymin h)
             ymax (max ymax h)) )
    (update-ranges-2d xmin xmax ymin ymax)
    (make-gr-object
       :name 'bars
       :command (format nil " ~a w boxes fs solid ~a lw ~a lc ~a axis ~a"
                            (make-obj-title (get-option '$key))
                            (get-option '$fill_density)
                            (get-option '$line_width)
                            (hex-to-rgb (get-option '$fill_color))
                            (axes-to-plot) )
       :groups '((3 0))  ; numbers are sent to gnuplot in groups of 3, without blank lines
       :points (list (make-array (length result) :initial-contents result))) ))








;; Object: 'vector'
;; Usage:
;;     vector([x,y], [dx,dy]), represents vector from [x,y] to [x+dx,y+dy]
;; Options:
;;     head_both
;;     head_length
;;     head_angle
;;     head_type
;;     line_width
;;     line_type
;;     key
;;     color
;;     unit_vectors
;;     xaxis_secondary
;;     yaxis_secondary
(defun vect (arg1 arg2)
   (if (or (not ($listp arg1))
           (not (= ($length arg1) 2))
           (not ($listp arg2))
           (not (= ($length arg2) 2)))
       (merror "draw (vector): coordinates are not correct"))
   (let* ((x ($float (cadr arg1)))
          (y ($float (caddr arg1)))
          (dx ($float (cadr arg2)))
          (dy ($float (caddr arg2)))
          xdx ydy)
      (when (and (get-option '$unit_vectors)
                 (or (/= dx 0) (/= dy 0)))
         (let ((module (sqrt (+ (* dx dx) (* dy dy)))))
            (setf dx (/ dx module)
                  dy (/ dy module)  )))
      (setf xdx ($float (+ x dx))
            ydy ($float (+ y dy)))
      (update-ranges-2d (min x xdx) (max x xdx) (min y ydy) (max y ydy))
      (make-gr-object
         :name 'vector
         :command (format nil " ~a w vect ~a size ~a, ~a ~a lw ~a lt ~a lc ~a axis ~a"
                              (make-obj-title (get-option '$key))
                              (if (get-option '$head_both) "heads" "head")
                              (get-option '$head_length)
                              (get-option '$head_angle)
                              (case (get-option '$head_type)
                                 ($filled   "filled")
                                 ($empty    "empty")
                                 ($nofilled "nofilled"))
                              (get-option '$line_width)
                              (get-option '$line_type)
                              (hex-to-rgb (get-option '$color))
                              (axes-to-plot) )
         :groups '((4 0))
         :points `(,(make-array 4 :element-type 'flonum
                                  :initial-contents (list x y dx dy))) ) ))







;; Object: 'vector3d'
;; Usage:
;;     vector([x,y,z], [dx,dy,dz]), represents vector from [x,y,z] to [x+dx,y+dy,z+dz]
;; Options:
;;     head_both
;;     head_length
;;     head_angle
;;     head_type
;;     line_width
;;     line_type
;;     key
;;     color
;;     unit_vectors
(defun vect3d (arg1 arg2)
   (if (or (not ($listp arg1))
           (not (= ($length arg1) 3))
           (not ($listp arg2))
           (not (= ($length arg2) 3)))
       (merror "draw (vector): coordinates are not correct"))
   (let* ((x ($float (cadr arg1)))
          (y ($float (caddr arg1)))
          (z ($float (cadddr arg1)))
          (dx ($float (cadr arg2)))
          (dy ($float (caddr arg2)))
          (dz ($float (cadddr arg2)))
          xdx ydy zdz )
      (when (and (get-option '$unit_vectors)
                 (or (/= dx 0) (/= dy 0) (/= dz 0)))
         (let ((module (sqrt (+ (* dx dx) (* dy dy) (* dz dz)))))
            (setf dx (/ dx module)
                  dy (/ dy module)
                  dz (/ dz module)  )))
      (setf xdx ($float (+ x dx))
            ydy ($float (+ y dy))
            zdz ($float (+ z dz)) )
      (update-ranges-3d (min x xdx) (max x xdx) (min y ydy) (max y ydy) (min z zdz) (max z zdz))
      (make-gr-object
         :name 'vector
         :command (format nil " ~a w vect ~a size ~a, ~a ~a lw ~a lt ~a lc ~a"
                              (make-obj-title (get-option '$key))
                              (if (get-option '$head_both) "heads" "head")
                              (get-option '$head_length)
                              (get-option '$head_angle)
                              (case (get-option '$head_type)
                                 ($filled   "filled")
                                 ($empty    "empty")
                                 ($nofilled "nofilled"))
                              (get-option '$line_width)
                              (get-option '$line_type)
                              (hex-to-rgb (get-option '$color)) )
         :groups '((6 0))
         :points `(,(make-array 6 :element-type 'flonum
                                  :initial-contents (list x y z dx dy dz))) ) ))








;; Object: 'explicit'
;; Usage:
;;     explicit(fcn,var,minval,maxval)
;; Options:
;;     nticks
;;     adapt_depth
;;     line_width
;;     line_type
;;     color
;;     filled_func
;;     fill_color
;;     key
;;     xaxis_secondary
;;     yaxis_secondary
(defun explicit (fcn var minval maxval)
  (let* ((nticks (get-option '$nticks))
         (depth (get-option '$adapt_depth))
         ($numer t)
         (xmin ($float minval))
         (xmax ($float maxval))
         (x-step (/ (- xmax xmin) ($float nticks) 2))
         (ymin most-positive-double-float)
         (ymax most-negative-double-float)
         (*plot-realpart* *plot-realpart*)
         x-samples y-samples yy result pltcmd result-array)
    (when (< xmax xmin)
       (merror "draw2d (explicit): illegal range"))
    (setq *plot-realpart* (get-option '$draw_realpart))
    (setq fcn (coerce-float-fun fcn `((mlist) ,var)))
    (when (get-option '$logx)
      (setf xmin (log xmin))
      (setf xmax (log xmax))
      (setf x-step (/ (- xmax xmin) ($float nticks) 2)))
    (flet ((fun (x)
               (let ((y (if (get-option '$logx)
                            (funcall fcn (exp x))
                            (funcall fcn x))))
                 (if (and (get-option '$logy)
                          (numberp y))
                     (if (> y 0)
                       (log y)
                       (merror "draw2d (explicit): logarithm of negative number"))
                     y))))
      (dotimes (k (1+ (* 2 nticks)))
        (let ((x (+ xmin (* k x-step))))
          (push x x-samples)
          (push (fun x) y-samples)))
      (setf x-samples (nreverse x-samples))
      (setf y-samples (nreverse y-samples))
      ;; For each region, adaptively plot it.
      (do ((x-start x-samples (cddr x-start))
           (x-mid (cdr x-samples) (cddr x-mid))
           (x-end (cddr x-samples) (cddr x-end))
           (y-start y-samples (cddr y-start))
           (y-mid (cdr y-samples) (cddr y-mid))
           (y-end (cddr y-samples) (cddr y-end)))
          ((null x-end))
        ;; The region is x-start to x-end, with mid-point x-mid.
        (let ((sublst (adaptive-plot #'fun (car x-start) (car x-mid) (car x-end)
                                           (car y-start) (car y-mid) (car y-end)
                                           depth 1e-5)))
          (when (notevery #'(lambda (x) (or (numberp x) (eq x t) (eq x nil))) sublst)
            (let ((items sublst) (item 'nil))
	      ;; Search for the item in sublist that is the undefined variable
	      (while items
		(when (not (or (numberp (car items))
                               (eq (car items) t)
                               (eq (car items) nil)))
		    (setq item (car items)) )
		(setq items (cdr items)) )
	      (merror "draw2d (explicit): non defined variable in term: ~M" item) ) )

          (when (not (null result))
            (setf sublst (cddr sublst)))
          (do ((lst sublst (cddr lst)))
              ((null lst) 'done)
            (setf result (cons (if (and (get-option '$logy) (numberp (second lst)))
                                 (exp (second lst))
                                 (second lst))
                               result)) 
            (setf result (cons (if (and (get-option '$logx) (numberp (first lst)))
                                 (exp (first lst))
                                 (first lst))
                               result)) ) )))

    ; reset x extremes to original values
    (when (get-option '$logx)
      (setf xmin (exp xmin))
      (setf xmax (exp xmax)))

    (cond ((null (get-option '$filled_func))
             (cond
               ((> *draw-transform-dimensions* 0)
                  ; With geometric transformation.
                  ; When option filled_func in not nil,
                  ; geometric transformation is ignored
                  (setf result-array (make-array (length result)))
                  (setf xmin most-positive-double-float
                        xmax most-negative-double-float)
                  (let (xold yold x y (count -1))
                    (do ((lis result (cddr lis)))
                        ((null lis))
                      (setf xold (first lis)
                            yold (second lis))
                      (setf x (funcall *draw-transform-f1* xold yold)
                            y (funcall *draw-transform-f2* xold yold))
                      (if (> x xmax) (setf xmax x))
                      (if (< x xmin) (setf xmin x))
                      (if (> y ymax) (setf ymax y))
                      (if (< y ymin) (setf ymin y))
                      (setf (aref result-array (incf count)) x)
                      (setf (aref result-array (incf count)) y)  )  ) )
               (t
                  ; No geometric transformation invoked.
                  (do ((y (cdr result) (cddr y)))
                      ((null y))
                    (setf yy (car y))
                    (check-extremes-y))
                  (setf result-array (make-array (length result)
                                                 :initial-contents result))))
             (update-ranges-2d xmin xmax ymin ymax)
             (setf pltcmd (format nil " ~a w l lw ~a lt ~a lc ~a axis ~a"
                                      (make-obj-title (get-option '$key))
                                      (get-option '$line_width)
                                      (get-option '$line_type)
                                      (hex-to-rgb (get-option '$color))
                                      (axes-to-plot)))
             (make-gr-object
                :name   'explicit
                :command pltcmd
                :groups '((2 0))  ; numbers are sent to gnuplot in groups of 2
                :points  (list result-array )) )
          ((equal (get-option '$filled_func) t)
             (do ((y (cdr result) (cddr y)))
                 ((null y))
                (setf yy (car y))
                (check-extremes-y))
             (update-ranges-2d xmin xmax ymin ymax)
             (setf result-array (make-array (length result)
                                            :element-type 'flonum 
                                            :initial-contents result))
             (setf pltcmd (format nil " ~a w filledcurves x1 lc ~a axis ~a"
                                      (make-obj-title (get-option '$key))
                                      (hex-to-rgb (get-option '$fill_color))
                                      (axes-to-plot)))
             (make-gr-object
                :name   'explicit
                :command pltcmd
                :groups '((2 0))  ; numbers are sent to gnuplot in groups of 2
                :points  (list result-array )))
          (t
             (let (fcn2 yy2 (count -1))
                (setf result-array (make-array (* (/ (length result) 2) 3)
                                               :element-type 'flonum))
                (setq fcn2 (coerce-float-fun (get-option '$filled_func) `((mlist), var)))
                (flet ((fun (x) (funcall fcn2 x)))
                  (do ((xx result (cddr xx)))
                    ((null xx))
                    (setf yy  (second xx)
                          yy2 (fun (first xx)))
                    (setf ymax (max ymax yy yy2)
                          ymin (min ymin yy yy2))
                    (setf (aref result-array (incf count)) (first xx)
                          (aref result-array (incf count)) yy
                          (aref result-array (incf count)) yy2) )  ))
             (update-ranges-2d xmin xmax ymin ymax)
             (setf pltcmd (format nil " ~a w filledcurves lc ~a axis ~a"
                                      (make-obj-title (get-option '$key))
                                      (hex-to-rgb (get-option '$fill_color))
                                      (axes-to-plot)  ))
             (make-gr-object
                :name   'explicit
                :command pltcmd
                :groups '((3 0))  ; numbers are sent to gnuplot in groups of 3
                :points  (list result-array))))  ))







;; Object: 'region'
;; Usage:
;;     region(ineq,x-var,x-minval,x-maxval,y-var,y-minval,y-maxval)
;; Options:
;;     fill_color
;;     key
;;     x_voxel
;;     y_voxel
(defmacro build-polygon (coord)
  (let ((len (1- (length coord))))
    `(push (make-array ,len :element-type 'flonum :initial-contents ,coord) pts)))

(defun region (ineq x-var x-minval x-maxval y-var y-minval y-maxval)
  (let* ((nx (get-option '$x_voxel))
         (ny (get-option '$y_voxel))
         (xmin ($float x-minval))
         (xmax ($float x-maxval))
         (ymin ($float y-minval))
         (ymax ($float y-maxval))
         (dx (/ (- xmax xmin) nx))
         (dy (/ (- ymax ymin) ny))
         (err (* 0.02 (min dx dy)))
         (xarr (make-array (list (1+ nx) (1+ ny)) :element-type 'flonum))
         (yarr (make-array (list (1+ nx) (1+ ny)) :element-type 'flonum))
         (barr (make-array (list (1+ nx) (1+ ny)) :element-type 'boolean))
         (pts '())
         pltcmd grouping x y)

    (when (not (subsetp (rest ($listofvars ineq)) (list x-var y-var)))
       (merror "draw2d (region): non defined variable"))

    ; build 2d arrays: x, y and boolean
    (labels ((fun (xx yy)  ; evaluates boolean expression
                  (is-boole-check 
                    (simplify
                      ($substitute
                        (list '(mlist)
                              (list '(mequal) x-var xx)
                              (list '(mequal) y-var yy))
                        ineq))))
             (bipart (xx1 yy1 xx2 yy2) ; bipartition, (xx1, yy1) => T, (xx2, yy2) => NIL
                     (let ((xm (* 0.5 (+ xx1 xx2)))
                           (ym (* 0.5 (+ yy1 yy2))))
                       (cond
                         ((< (+ (* (- xx2 xx1) (- xx2 xx1))
                                (* (- yy2 yy1) (- yy2 yy1)))
                             (* err err))
                            (list xm ym))
                         ((fun xm ym)
                            (bipart xm ym xx2 yy2))
                         (t
                            (bipart xx1 yy1 xm ym)) ))  ))
      ; fill arrays
      (loop for i to nx do
        (loop for j to ny do
          (setf x (+ xmin (* i dx)))
          (setf y (+ ymin (* j dy)))
          (setf (aref xarr i j) x)
          (setf (aref yarr i j) y)
          (setf (aref barr i j) (fun x y))))
      ; check vertices of rectangles and cuts
      (loop for i below nx do
        (loop for j below ny do
          (let ((x1 (aref xarr i j))            ; SW point
                (y1 (aref yarr i j))
                (b1 (aref barr i j))
                (x2 (aref xarr (1+ i) j))       ; SE point
                (y2 (aref yarr (1+ i) j))
                (b2 (aref barr (1+ i) j))
                (x3 (aref xarr (1+ i) (1+ j)))  ; NE point
                (y3 (aref yarr (1+ i) (1+ j)))
                (b3 (aref barr (1+ i) (1+ j)))
                (x4 (aref xarr i (1+ j)))       ; NW point
                (y4 (aref yarr i (1+ j)))
                (b4 (aref barr i (1+ j)))
                pa pb pc)    ; pa and pb are frontier points

            (cond ((and b1 b2 b3 b4)
                     (build-polygon (list x1 y1 x2 y2 x3 y3 x4 y4)))
                  ((and b1 b2 b3)
                     (setf pa (bipart x3 y3 x4 y4)
                           pb (bipart x1 y1 x4 y4))
                     (build-polygon (list x1 y1 x2 y2 x3 y3 (first pa) (second pa) (first pb) (second pb))))
                  ((and b4 b1 b2)
                     (setf pa (bipart x2 y2 x3 y3)
                           pb (bipart x4 y4 x3 y3))
                     (build-polygon (list x4 y4 x1 y1 x2 y2 (first pa) (second pa) (first pb) (second pb))))
                  ((and b3 b4 b1)
                     (setf pa (bipart x1 y1 x2 y2)
                           pb (bipart x3 y3 x2 y2))
                     (build-polygon (list x3 y3 x4 y4 x1 y1 (first pa) (second pa) (first pb) (second pb))))
                  ((and b2 b3 b4)
                     (setf pa (bipart x4 y4 x1 y1)
                           pb (bipart x2 y2 x1 y1))
                     (build-polygon (list x2 y2 x3 y3 x4 y4 (first pa) (second pa) (first pb) (second pb))))
                  ((and b2 b3)
                     (setf pa (bipart x3 y3 x4 y4)
                           pb (bipart x2 y2 x1 y1))
                     (build-polygon (list x2 y2 x3 y3 (first pa) (second pa) (first pb) (second pb))))
                  ((and b4 b1)
                     (setf pa (bipart x1 y1 x2 y2)
                           pb (bipart x4 y4 x3 y3))
                     (build-polygon (list x4 y4 x1 y1 (first pa) (second pa) (first pb) (second pb))))
                  ((and b3 b4)
                     (setf pa (bipart x4 y4 x1 y1)
                           pb (bipart x3 y3 x2 y2))
                     (build-polygon (list x3 y3 x4 y4 (first pa) (second pa) (first pb) (second pb))))
                  ((and b1 b2)
                     (setf pa (bipart x2 y2 x3 y3)
                           pb (bipart x1 y1 x4 y4))
                     (build-polygon (list x1 y1 x2 y2 (first pa) (second pa) (first pb) (second pb))))
                  (b1
                     (setf pa (bipart x1 y1 x2 y2)
                           pb (bipart x1 y1 x3 y4)
                           pc (bipart x1 y1 x4 y4))
                     (build-polygon (list x1 y1 (first pa) (second pa) (first pb) (second pb)(first pc) (second pc))))
                  (b2
                     (setf pa (bipart x2 y2 x3 y3)
                           pb (bipart x2 y2 x4 y4)
                           pc (bipart x2 y2 x1 y1))
                     (build-polygon (list x2 y2 (first pa) (second pa) (first pb) (second pb) (first pc) (second pc))))
                  (b3
                     (setf pa (bipart x3 y3 x4 y4)
                           pb (bipart x3 y3 x1 y1)
                           pc (bipart x3 y3 x2 y2))
                     (build-polygon (list x3 y3 (first pa) (second pa) (first pb) (second pb) (first pc) (second pc))))
                  (b4
                     (setf pa (bipart x4 y4 x1 y1)
                           pb (bipart x4 y4 x2 y2)
                           pc (bipart x4 y4 x3 y3))
                     (build-polygon (list x4 y4 (first pa) (second pa) (first pb) (second pb) (first pc) (second pc)))) )))))

    ; list of commands
    (setf pltcmd
          (cons (format nil " ~a w filledcurves lc ~a axis ~a"
                        (make-obj-title (get-option '$key))
                        (hex-to-rgb (get-option '$fill_color))
                        (axes-to-plot))
                (make-list (- (length pts) 1)
                           :initial-element (format nil " t '' w filledcurves lc ~a axis ~a"
                                              (hex-to-rgb (get-option '$fill_color))
                                              (axes-to-plot) ))))
    (update-ranges-2d xmin xmax ymin ymax)
    (setf grouping
          (make-list (length pts)
                     :initial-element '(2 0)))
    (make-gr-object
       :name    'region
       :command pltcmd
       :groups  grouping
       :points  pts)    ))








;; Object: 'implicit'
;; Usage:
;;     implicit(fcn,x-var,x-minval,x-maxval,y-var,y-minval,y-maxval)
;; Options:
;;     ip_grid
;;     ip_grid_in
;;     line_width
;;     line_type
;;     key
;;     color
;;     xaxis_secondary
;;     yaxis_secondary
;; Note: taken from implicit_plot.lisp

;; returns elements at odd positions
(defun x-elements (list)
  (if (endp list) list
      (list* (first list) (x-elements (rest (rest list))))))

;; returns elements at even positions
(defun y-elements (list)
  (x-elements (rest list)))

(defvar pts ())

(defun contains-zeros (i j sample)
  (not (and (> (* (aref sample i j) (aref sample (1+ i)     j  )) 0)
	    (> (* (aref sample i j) (aref sample     i  (1+ j) )) 0)
	    (> (* (aref sample i j) (aref sample (1+ i) (1+ j) )) 0) )))

(defun sample-data (expr xmin xmax ymin ymax sample grid)
  (let* ((xdelta (/ (- xmax xmin) ($first grid)))
	 (ydelta (/ (- ymax ymin) ($second grid)))
	 (epsilon #+gcl (float 1/1000000) #-gcl 1e-6))
    (do ((x-val xmin (+ x-val xdelta))
	 (i 0 (1+ i)))
	((> i ($first grid)))
      (do ((y-val ymin (+ y-val ydelta))
	   (j 0 (1+ j)))
	  ((> j ($second grid)))
	(let ((fun-val (funcall expr x-val y-val)))
          (when (and (not (floatp fun-val)) (not (eq fun-val t)))
                (merror "draw2d (implicit): non defined variable in condition ~M=0" fun-val))
	  (if (or (eq fun-val t) (>= fun-val epsilon))
	      (setf (aref sample i j) 1)
	      (setf (aref sample i j) -1)))))))

(defun draw-print-segment (points xmin xdelta ymin ydelta)
  (let* ((point1 (car points)) (point2 (cadr points))
	 (x1 (coerce (+ xmin (/ (* xdelta (+ (car point1) (caddr point1))) 2)) 'flonum) )
	 (y1 (coerce (+ ymin (/ (* ydelta (+ (cadr point1) (cadddr point1))) 2)) 'flonum) )
	 (x2 (coerce (+ xmin (/ (* xdelta (+ (car point2) (caddr point2))) 2)) 'flonum) )
	 (y2 (coerce (+ ymin (/ (* ydelta (+ (cadr point2) (cadddr point2))) 2)) 'flonum) ))
     (setq pts (nconc (list x1 y1 x2 y2) pts))))	

(defun draw-print-square (xmin xmax ymin ymax sample grid)
  (let* ((xdelta (/ (- xmax xmin) ($first grid)))
	 (ydelta (/ (- ymax ymin) ($second grid))))
    (do ((i 0 (1+ i)))
	((= i ($first grid)))
      (do ((j 0 (1+ j)))
	  ((= j ($second grid)))
	(if (contains-zeros i j sample)
	    (let ((points ()))
	      (if (< (* (aref sample i j) (aref sample (1+ i) j)) 0)
		  (setq points (cons `(,i ,j ,(1+ i) ,j) points)))
	      (if (< (* (aref sample (1+ i) j) (aref sample (1+ i) (1+ j))) 0)
		  (setq points (cons `(,(1+ i) ,j ,(1+ i) ,(1+ j)) points)))
	      (if (< (* (aref sample i (1+ j)) (aref sample (1+ i) (1+ j))) 0)
		  (setq points (cons `(,i ,(1+ j) ,(1+ i) ,(1+ j)) points)))
	      (if (< (* (aref sample i j) (aref sample i (1+ j))) 0)
		  (setq points (cons `(,i ,j ,i ,(1+ j)) points)))
	      (draw-print-segment points xmin xdelta ymin ydelta)) )))))

(defun imp-pl-prepare-factor (expr)
  (cond 
    ((or ($numberp expr) (atom expr))
     expr)
    ((eq (caar expr) 'mexpt)
     (cadr expr))
    (t
     expr)))

(defun imp-pl-prepare-expr (expr)
  (let ((expr1 ($factor (m- ($rhs expr) ($lhs expr)))))
    (cond ((or ($numberp expr) (atom expr1)) expr1)
	  ((eq (caar expr1) 'mtimes)
	   `((mtimes simp factored 1)
	     ,@(mapcar #'imp-pl-prepare-factor (cdr expr1))))
	  ((eq (caar expr) 'mexpt)
	   (imp-pl-prepare-factor expr1))
	  (t
	   expr1))))

(defun implicit (expr x xmin xmax y ymin ymax)
  (let* (($numer t) ($plot_options $plot_options)
         (pts ())
         (expr (m- ($rhs expr) ($lhs expr)))
         (ip-grid (get-option '$ip_grid))
         (ip-grid-in (get-option '$ip_grid_in))
         e pltcmd 
         (xmin ($float xmin))
         (xmax ($float xmax))
         (ymin ($float ymin))
         (ymax ($float ymax))
         (xdelta (/ (- xmax xmin) ($first ip-grid)))
         (ydelta (/ (- ymax ymin) ($second ip-grid)))
         (sample (make-array `(,(1+ ($first ip-grid))
			       ,(1+ ($second ip-grid)))))
	 (ssample (make-array `(,(1+ ($first ip-grid-in))
				,(1+ ($second ip-grid-in))))) )

    (setq e (coerce-float-fun (imp-pl-prepare-expr expr)
			      `((mlist simp)
				,x ,y)))
    (update-ranges-2d xmin xmax ymin ymax)
    (sample-data e xmin xmax ymin ymax sample ip-grid)
    (do ((i 0 (1+ i)))
	((= i ($first ip-grid)))
      (do ((j 0 (1+ j)))
	  ((= j ($second ip-grid)))
	(if (contains-zeros i j sample)
	    (let* ((xxmin (+ xmin (* i xdelta)))
		   (xxmax (+ xxmin xdelta))
		   (yymin (+ ymin (* j ydelta)))
		   (yymax (+ yymin ydelta)))
	      (sample-data e xxmin xxmax yymin yymax
			   ssample ip-grid-in)
	      (draw-print-square xxmin xxmax yymin yymax
			    ssample ip-grid-in) )) ))

    ; geometric transformation
    (when (> *draw-transform-dimensions* 0)
      (let ((x (x-elements pts))
            (y (y-elements pts))
            xmin xmax ymin ymax)
        (transform-lists 2)
        (setf xmin ($tree_reduce 'min (cons '(mlist simp) x))
              xmax ($tree_reduce 'max (cons '(mlist simp) x))
              ymin ($tree_reduce 'min (cons '(mlist simp) y))
              ymax ($tree_reduce 'max (cons '(mlist simp) y)) )
        (update-ranges-2d xmin xmax ymin ymax)
        (setf pts
          (loop
            collect (car x)
            collect (car y)
            do (setf x (cdr x))
               (setf y (cdr y))
            when (null x) do (loop-finish) ))) )

    (setf pltcmd (format nil " ~a w l lw ~a lt ~a lc ~a axis ~a"
                              (make-obj-title (get-option '$key))
                              (get-option '$line_width)
                              (get-option '$line_type)
                              (hex-to-rgb (get-option '$color))
                              (axes-to-plot)))
    (make-gr-object
       :name   'implicit
       :command pltcmd
       :groups '((2 2))
       :points  `(,(make-array (length pts) :element-type 'flonum
                                            :initial-contents pts)) ) ))






;; Object: 'implicit3d'
;; Usage:
;;     implicit(expr,x,xmin,xmax,y,ymin,ymax,z,zmin,zmax)
;; Options:
;;     key
;;     x_voxel
;;     y_voxel
;;     z_voxel
;;     line_width
;;     line_type
;;     color
;;     enhanced3d
;;     wired_surface
;; Some functions and macros are defined in grcommon.lisp
(defun implicit3d (expr par1 xmin xmax par2 ymin ymax par3 zmin zmax)
  (let ((xmin ($float xmin))
        (xmax ($float xmax))
        (ymin ($float ymin))
        (ymax ($float ymax))
        (zmin ($float zmin))
        (zmax ($float zmax))
        (pts '())
        (grouping '())
        pltcmd ncols vertices)
    (when (not (subsetp (rest ($listofvars expr)) (list par1 par2 par3)))
       (merror "draw3d (implicit): non defined variable"))
    (check-enhanced3d-model "implicit" '(0 3 99))
    (when (= *draw-enhanced3d-type* 99)
       (update-enhanced3d-expression (list '(mlist) par1 par2 par3)))
    (setf ncols (if (= *draw-enhanced3d-type* 0) 3 4))

    (setf vertices (find-triangles expr par1 xmin xmax par2 ymin ymax par3 zmin zmax))
    (when (null vertices)
      (merror "draw3d (implicit): no surface within these ranges"))
    (update-ranges-3d xmin xmax ymin ymax zmin zmax)
    (setf pltcmd
          (cons (format nil " ~a w ~a lw ~a lt ~a lc ~a"
                        (make-obj-title (get-option '$key))
                        (if (equal (get-option '$enhanced3d) '$none) "l" "pm3d")
                        (get-option '$line_width)
                        (get-option '$line_type)
                        (hex-to-rgb (get-option '$color)))
                (make-list (- (/ (length vertices) 3) 1)
                           :initial-element (format nil " t '' w ~a lw ~a lt ~a lc ~a"
                                              (if (equal (get-option '$enhanced3d) '$none) "l" "pm3d")
                                              (get-option '$line_width)
                                              (get-option '$line_type)
                                              (hex-to-rgb (get-option '$color)) ))))
    (do ((v vertices (cdddr v)))
        ((null v) 'done)
      (case ncols
        (3 (push (make-array 12 :element-type 'flonum
                                :initial-contents (flatten (list (first v) (second v) (first v) (third v))))
                 pts))
        (4 (let (v1 v2 v3
                 color1 color2 color3)
             (setf v1 (first v)
                   v2 (second v)
                   v3 (third v))
             (setf color1 (funcall *draw-enhanced3d-fun* (car v1) (cadr v1) (caddr v1))
                   color2 (funcall *draw-enhanced3d-fun* (car v2) (cadr v2) (caddr v2))
                   color3 (funcall *draw-enhanced3d-fun* (car v3) (cadr v3) (caddr v3)) )
             (push (make-array 16 :element-type 'flonum
                                  :initial-contents (flatten (list v1 color1 v2 color2 v1 color1 v3 color3)))
                    pts))) )
      (push `(,ncols 2)
            grouping) )
    (make-gr-object
       :name    'implicit
       :command pltcmd
       :groups  grouping
       :points  pts)))







;; Object: 'explicit3d'
;; Usage:
;;     explicit(fcn,par1,minval1,maxval1,par2,minval2,maxval2)
;; Options:
;;     xu_grid
;;     yv_grid
;;     line_type
;;     line_width
;;     color
;;     key
;;     enhanced3d
;;     wired_surface
;;     surface_hide
;;     transform
(defun explicit3d (fcn par1 minval1 maxval1 par2 minval2 maxval2)
  (let* ((xu_grid (get-option '$xu_grid))
         (yv_grid (get-option '$yv_grid))
         (fminval1 ($float minval1))
         (fminval2 ($float minval2))
         (fmaxval1 ($float maxval1))
         (fmaxval2 ($float maxval2))
         (epsx (/ (- fmaxval1 fminval1) xu_grid))
         (epsy (/ (- fmaxval2 fminval2) yv_grid))
         (xx 0.0) (uu 0.0)
         (yy 0.0) (vv 0.0)
         (zz 0.0)
         (xmin most-positive-double-float)
         (xmax most-negative-double-float)
         (ymin most-positive-double-float)
         (ymax most-negative-double-float)
         (zmin most-positive-double-float)
         (zmax most-negative-double-float)
         (*plot-realpart* *plot-realpart*)
         (nx (+ xu_grid 1))
         (ny (+ yv_grid 1))
         ($numer t)
         (count -1)
         ncols result)
    (when (not (subsetp (rest ($listofvars fcn)) (list par1 par2)))
            (let ((items (rest ($listofvars fcn))) (item 'nil))
	      ;; Search for the item in sublist that is the undefined variable
	      (while items
		(if
		    (
		     not
		     (subsetp (list (car items)) (list par1 par2))
		     )
		    (setq item (car items))
		  )
		(setq items (cdr items))
		)
	      (merror "draw3d (explicit): non defined variable in term ~M" item)
	      )
	    )
    (setq *plot-realpart* (get-option '$draw_realpart))
    (check-enhanced3d-model "explicit" '(0 2 3 99))
    (when (= *draw-enhanced3d-type* 99)
       (update-enhanced3d-expression (list '(mlist) par1 par2)))
    (setq fcn (coerce-float-fun fcn `((mlist) ,par1 ,par2)))
    (setf ncols (if (= *draw-enhanced3d-type* 0) 3 4))
    (setf result (make-array (* ncols nx ny)))
    (loop for j below ny
           initially (setf vv fminval2)
           do (setf uu fminval1)
           (loop for i below nx
                  do
                  (setf xx uu
                        yy vv)
                  (setf zz (funcall fcn xx yy))
                  (transform-point 3)
                  (when (> *draw-transform-dimensions* 0)
                    (check-extremes-x) 
                    (check-extremes-y))
                  (check-extremes-z)
                  (setf (aref result (incf count)) xx
                        (aref result (incf count)) yy
                        (aref result (incf count)) zz)
                  ; check texture model
                  (case *draw-enhanced3d-type*
                    ((2 99) (setf (aref result (incf count)) (funcall *draw-enhanced3d-fun* xx yy)))
                    (3  (setf (aref result (incf count)) (funcall *draw-enhanced3d-fun* xx yy zz))) )
                  (setq uu (+ uu epsx)))
           (setq vv (+ vv epsy)))
    (when (> *draw-transform-dimensions* 0)
      (setf fminval1 xmin
            fmaxval1 xmax
            fminval2 ymin
            fmaxval2 ymax))
    (update-ranges-3d fminval1 fmaxval1 fminval2 fmaxval2 zmin zmax)
    (make-gr-object
       :name   'explicit
       :command (format nil " ~a w ~a lw ~a lt ~a lc ~a"
                            (make-obj-title (get-option '$key))
                            (if (> *draw-enhanced3d-type* 0) "pm3d" "l")
                            (get-option '$line_width)
                            (get-option '$line_type)
                            (hex-to-rgb (get-option '$color)))
       :groups `((,ncols ,nx))
       :points  (list result))))








;; Object: 'elevation_grid'
;; Usage:
;;     elevation_grid(mat,x0,y0,width,height)
;; Options:
;;     line_type
;;     line_width
;;     color
;;     key
;;     enhanced3d
;;     wired_surface
;;     transform
(defun elevation_grid (mat x0 y0 width height)
  (let ( (fx0 ($float x0))
         (fy0 ($float y0))
         (fwidth ($float width))
         (fheight ($float height))
         (xmin most-positive-double-float)
         (xmax most-negative-double-float)
         (ymin most-positive-double-float)
         (ymax most-negative-double-float)
         (zmin most-positive-double-float)
         (zmax most-negative-double-float)
         ncols-file result nrows ncols)
    (check-enhanced3d-model "elevation_grid" '(0 2 3))
    (cond (($matrixp mat)
             (let ((xi 0.0)
                   (yi (+ fy0 fheight))
                   (xx 0.0)
                   (yy 0.0)
                   (zz 0.0)
                   (count -1)
                   dx dy)
                (setf ncols (length (cdadr mat))
                      nrows (length (cdr mat)))
                (setf dx (/ fwidth (1- ncols))
                      dy (/ fheight (1- nrows)))
                (setf ncols-file (if (= *draw-enhanced3d-type* 0) 3 4))
                (setf result (make-array (* ncols nrows ncols-file) :element-type 'flonum))
                (loop for row on (cdr mat) by #'cdr do
                   (setf xi fx0)
                   (loop for col on (cdar row) by #'cdr do
                      (setf xx xi
                            yy yi)
                      (setf zz ($float (car col)))
                      (transform-point 3)
                      (when (> *draw-transform-dimensions* 0) 
                        (check-extremes-x)
                        (check-extremes-y))
                      (check-extremes-z)
                      (setf (aref result (incf count)) xx
                            (aref result (incf count)) yy
                            (aref result (incf count)) zz)
                      ; check texture model
                      (case *draw-enhanced3d-type*
                        (2 (setf (aref result (incf count)) (funcall *draw-enhanced3d-fun* xx yy)))
                        (3 (setf (aref result (incf count)) (funcall *draw-enhanced3d-fun* xx yy zz))) )
                      (setf xi (+ xi dx)))
                   (setf yi (- yi dy)))))
          (t
             (merror "draw3d (elevation_grid): Argument not recognized")))
    (when (= *draw-transform-dimensions* 0)
       (setf xmin fx0
             xmax (+ fx0 fwidth)
             ymin fy0
             ymax (+ fy0 fheight)))
    (update-ranges-3d xmin xmax ymin ymax zmin zmax)
    (make-gr-object
       :name   'elevation_grid
       :command (format nil " ~a w ~a lw ~a lt ~a lc ~a"
                            (make-obj-title (get-option '$key))
                            (if (> *draw-enhanced3d-type* 0) "pm3d" "l")
                            (get-option '$line_width)
                            (get-option '$line_type)
                            (hex-to-rgb (get-option '$color)))
       :groups `((,ncols-file ,ncols))
       :points  (list result)) ))








;; Object: 'mesh'
;; Usage:
;;     mesh([[x_11,y_11,z_11], ...,[x_1n,y_1n,z_1n]],
;;          [[x_21,y_21,z_21], ...,[x_2n,y_2n,z_2n]], 
;;          ...,
;;          [[x_m1,y_m1,z_m1], ...,[x_mn,y_mn,z_mn]])
;; Options:
;;     line_type
;;     line_width
;;     color
;;     key
;;     enhanced3d
;;     wired_surface
;;     transform
(defun mesh (&rest row)
  (let (result xx yy zz
        (xmin most-positive-double-float)
        (xmax most-negative-double-float)
        (ymin most-positive-double-float)
        (ymax most-negative-double-float)
        (zmin most-positive-double-float)
        (zmax most-negative-double-float)
        m n ncols-file col-num row-num
        (count -1))
    (cond
      ; let's see if the user wants to use mesh in the old way,
      ; what we now call elevation_grid
      ((and (= (length row) 5)
            ($matrixp (first row)))
        (print "Warning: Seems like you want to draw an elevation_grid object...")
        (print "         Please, see documentation for object elevation_grid.")
        (apply #'elevation_grid row))
      (t
        (check-enhanced3d-model "mesh" '(0 2 3))
        (when (or (< (length row) 2)
                  (not (every #'$listp row)))
          (merror "draw3d (mesh): Arguments must be two or more lists"))
        (setf ncols-file (if (= *draw-enhanced3d-type* 0) 3 4))
        (setf m (length row)
              n ($length (first row)))
        (setf result (make-array (* m n ncols-file) :element-type 'flonum))
        (setf row-num 0)
        (dolist (r row)
          (incf row-num)
          (setf col-num 0)
          (dolist (c (rest r))
            (incf col-num)
            (setf xx ($float ($first c))
                  yy ($float ($second c))
                  zz ($float ($third c)))
            (transform-point 3)
            (check-extremes-x)
            (check-extremes-y)
            (check-extremes-z)
            (setf (aref result (incf count)) xx
                  (aref result (incf count)) yy
                  (aref result (incf count)) zz)
            ; check texture model
            (case *draw-enhanced3d-type*
              (2 (setf (aref result (incf count)) (funcall *draw-enhanced3d-fun* row-num col-num)))
              (3 (setf (aref result (incf count)) (funcall *draw-enhanced3d-fun* xx yy zz))))  )   )
        (update-ranges-3d xmin xmax ymin ymax zmin zmax)
        (make-gr-object
          :name   'mesh
          :command (format nil " ~a w ~a lw ~a lt ~a lc ~a"
                           (make-obj-title (get-option '$key))
                           (if (> *draw-enhanced3d-type* 0) "pm3d" "l")
                           (get-option '$line_width)
                           (get-option '$line_type)
                           (hex-to-rgb (get-option '$color)))
          :groups `((,ncols-file ,n))
          :points  (list result))))))







;; Object: 'triangle3d'
;; Usage:
;;     triangle([x1,y1,z1], [x2,y2,z2], [x3,y3,z3])
;; Options:
;;     line_type
;;     line_width
;;     color
;;     key
;;     enhanced3d
;;     transform
(defun triangle3d (arg1 arg2 arg3)
   (if (or (not ($listp arg1))
           (not (= ($length arg1) 3))
           (not ($listp arg2))
           (not (= ($length arg2) 3))
           (not ($listp arg3))
           (not (= ($length arg3) 3)))
       (merror "draw3d (triangle): vertices are not correct"))
   (let* ((x1 ($float (cadr arg1)))
          (y1 ($float (caddr arg1)))
          (z1 ($float (cadddr arg1)))
          (x2 ($float (cadr arg2)))
          (y2 ($float (caddr arg2)))
          (z2 ($float (cadddr arg2)))
          (x3 ($float (cadr arg3)))
          (y3 ($float (caddr arg3)))
          (z3 ($float (cadddr arg3)))
          (grobj (mesh `((mlist simp)
                            ((mlist simp) ,x1 ,y1 ,z1)
                            ((mlist simp) ,x1 ,y1 ,z1) )

                       `((mlist simp)
                            ((mlist simp) ,x2 ,y2 ,z2)
                            ((mlist simp) ,x3 ,y3 ,z3) ) )))
      (setf (gr-object-name grobj) 'triangle)
      grobj))







;; Object: 'quadrilateral3d'
;; Usage:
;;     quadrilateral([x1,y1,z1], [x2,y2,z2], [x3,y3,z3], [x4,y4,z4])
;; Options:
;;     line_type
;;     line_width
;;     color
;;     key
;;     enhanced3d
;;     transform
(defun quadrilateral3d (arg1 arg2 arg3 arg4)
   (if (or (not ($listp arg1))
           (not (= ($length arg1) 3))
           (not ($listp arg2))
           (not (= ($length arg2) 3))
           (not ($listp arg3))
           (not (= ($length arg3) 3))
           (not ($listp arg4))
           (not (= ($length arg4) 3)))
       (merror "draw3d (quadrilateral): vertices are not correct"))
   (let* ((x1 ($float (cadr arg1)))
          (y1 ($float (caddr arg1)))
          (z1 ($float (cadddr arg1)))
          (x2 ($float (cadr arg2)))
          (y2 ($float (caddr arg2)))
          (z2 ($float (cadddr arg2)))
          (x3 ($float (cadr arg3)))
          (y3 ($float (caddr arg3)))
          (z3 ($float (cadddr arg3)))
          (x4 ($float (cadr arg4)))
          (y4 ($float (caddr arg4)))
          (z4 ($float (cadddr arg4)))
          (grobj (mesh `((mlist simp)
                         ((mlist simp) ,x1 ,y1 ,z1)
                         ((mlist simp) ,x2 ,y2 ,z2))
                       `((mlist simp)
                         ((mlist simp) ,x3 ,y3 ,z3)
                         ((mlist simp) ,x4 ,y4 ,z4)))))
      (setf (gr-object-name grobj) 'quadrilateral)
      grobj))







;; Object: 'parametric'
;; Usage:
;;     parametric(xfun,yfun,par,parmin,parmax)
;; Options:
;;     nticks
;;     line_width
;;     line_type
;;     key
;;     color
;;     xaxis_secondary
;;     yaxis_secondary
;;     transform
;; Note: similar to draw2d-parametric in plot.lisp
(defun parametric (xfun yfun par parmin parmax)
  (let* ((nticks (get-option '$nticks))
         ($numer t)
         (tmin ($float parmin))
         (tmax ($float parmax))
         (xmin most-positive-double-float)
         (xmax most-negative-double-float)
         (ymin most-positive-double-float)
         (ymax most-negative-double-float)
         (*plot-realpart* *plot-realpart*)
         (tt ($float parmin))
         (eps (/ (- tmax tmin) (- nticks 1)))
         result f1 f2 xx yy)
    (when (< tmax tmin)
       (merror "draw2d (parametric): illegal range"))
    (when (not (subsetp (append (rest ($listofvars xfun)) (rest ($listofvars yfun))) (list par)))
       (merror "draw2d (parametric): non defined variable"))
    (setq *plot-realpart* (get-option '$draw_realpart))
    (setq f1 (coerce-float-fun xfun `((mlist), par)))
    (setq f2 (coerce-float-fun yfun `((mlist), par)))
    (setf result
       (loop
          do (setf xx ($float (funcall f1 tt)))
             (setf yy ($float (funcall f2 tt)))
             (transform-point 2)
             (check-extremes-x)
             (check-extremes-y)
          collect xx
          collect yy
          when (>= tt tmax) do (loop-finish)
          do (setq tt (+ tt eps))
             (if (>= tt tmax) (setq tt tmax)) ))
    ; update x-y ranges if necessary
    (update-ranges-2d xmin xmax ymin ymax)
    (make-gr-object
       :name 'parametric
       :command (format nil " ~a w l lw ~a lt ~a lc ~a axis ~a"
                            (make-obj-title (get-option '$key))
                            (get-option '$line_width)
                            (get-option '$line_type)
                            (hex-to-rgb (get-option '$color))
                            (axes-to-plot))
       :groups '((2 0))
       :points `(,(make-array (length result) :initial-contents result)))   ) )







;; Object: 'polar'
;; Usage:
;;     polar(radius,ang,minang,maxang)
;; Options:
;;     nticks
;;     line_width
;;     line_type
;;     key
;;     color
;;     xaxis_secondary
;;     yaxis_secondary
;; This object is constructed as a parametric function
(defun polar (radius ang minang maxang)
  (let ((grobj (parametric `((mtimes simp) ,radius ((%cos simp) ,ang))
                            `((mtimes simp) ,radius ((%sin simp) ,ang))
                            ang minang maxang)))
    (setf (gr-object-name grobj) 'polar)
    grobj ))







;; Object: 'spherical'
;; Usage:
;;     spherical(radius,az,minazi,maxazi,zen,minzen,maxzen)
;; Options:
;;     xu_grid
;;     yv_grid
;;     line_type
;;     color
;;     key
;;     enhanced3d
;;     wired_surface
;; This object is constructed as a parametric surface in 3d.
;; Functions are defined in format r=r(azimuth,zenith),
;; where, normally, azimuth is an angle in [0,2*%pi] and zenith in [0,%pi]
(defun spherical (radius azi minazi maxazi zen minzen maxzen)
  (let ((grobj (parametric_surface
                     `((mtimes simp) ,radius ((%sin simp) ,zen) ((%cos simp) ,azi))
                     `((mtimes simp) ,radius ((%sin simp) ,zen) ((%sin simp) ,azi))
                     `((mtimes simp) ,radius ((%cos simp) ,zen))
                     azi minazi maxazi
                     zen minzen maxzen)))
    (setf (gr-object-name grobj) 'spherical)
    grobj ))








;; Object: 'cylindrical'
;; Usage:
;;     cylindrical(r,z,minz,maxz,azi,minazi,maxazi)
;; Options:
;;     xu_grid
;;     yv_grid
;;     line_type
;;     color
;;     key
;;     enhanced3d
;;     wired_surface
;; This object is constructed as a parametric surface in 3d.
;; Functions are defined in format z=z(radius,azimuth), where,
;; normally, azimuth is an angle in [0,2*%pi] and r any real
(defun cylindrical (r z minz maxz azi minazi maxazi)
  (let ((grobj (parametric_surface
                     `((mtimes simp) ,r ((%cos simp) ,azi))
                     `((mtimes simp) ,r ((%sin simp) ,azi))
                     z 
                     z minz maxz
                     azi minazi maxazi)))
    (setf (gr-object-name grobj) 'cylindrical)
    grobj ))








;; Object: 'parametric3d'
;; Usage:
;;     parametric(xfun,yfun,zfun,par1,parmin,parmax)
;; Options:
;;     nticks
;;     line_width
;;     line_type
;;     color
;;     key
;;     enhanced3d
;;     surface_hide
;;     transform
(defun parametric3d (xfun yfun zfun par1 parmin parmax)
  (let* ((nticks (get-option '$nticks))
         ($numer t)
         (tmin ($float parmin))
         (tmax ($float parmax))
         (xmin most-positive-double-float)
         (xmax most-negative-double-float)
         (ymin most-positive-double-float)
         (ymax most-negative-double-float)
         (zmin most-positive-double-float)
         (zmax most-negative-double-float)
         (*plot-realpart* *plot-realpart*)
         (tt tmin)
         (eps (/ (- tmax tmin) (- nticks 1)))
         (count -1)
         ncols result f1 f2 f3 xx yy zz)
     (when (not (subsetp (rest ($append ($listofvars xfun) ($listofvars yfun) ($listofvars zfun))) (list par1)))
        (merror "draw3d (parametric): non defined variable"))
    (setq *plot-realpart* (get-option '$draw_realpart))
    (check-enhanced3d-model "parametric" '(0 1 3 99))
    (when (= *draw-enhanced3d-type* 99)
       (update-enhanced3d-expression (list '(mlist) par1)))
    (if (< tmax tmin)
       (merror "draw3d (parametric): illegal range"))
    (setq f1 (coerce-float-fun xfun `((mlist) ,par1)))
    (setq f2 (coerce-float-fun yfun `((mlist) ,par1)))
    (setq f3 (coerce-float-fun zfun `((mlist) ,par1)))
    (setf ncols (if (= *draw-enhanced3d-type* 0) 3 4))
    (setf result (make-array (* ncols nticks)))
    (dotimes (k nticks)
      (setf xx (funcall f1 tt))
      (setf yy (funcall f2 tt))
      (setf zz (funcall f3 tt))
      (transform-point 3)
      (check-extremes-x)
      (check-extremes-y)
      (check-extremes-z)
      (setf (aref result (incf count)) xx)
      (setf (aref result (incf count)) yy)
      (setf (aref result (incf count)) zz)
      ; check texture model
      (case *draw-enhanced3d-type*
        ((1 99) (setf (aref result (incf count)) (funcall *draw-enhanced3d-fun* tt)))
        (3      (setf (aref result (incf count)) (funcall *draw-enhanced3d-fun* xx yy zz))))
      (setf tt (+ tt eps)) )
    ; update x-y ranges if necessary
    (update-ranges-3d xmin xmax ymin ymax zmin zmax)
    (make-gr-object
       :name 'parametric
       :command (format nil " ~a w l lw ~a lt ~a lc ~a"
                            (make-obj-title (get-option '$key))
                            (get-option '$line_width)
                            (get-option '$line_type)
                            (if (> *draw-enhanced3d-type* 0)
                                "palette"
                                (hex-to-rgb (get-option '$color))) )
       :groups `((,ncols 0))
       :points (list result) )) )








;; Object: 'parametric_surface'
;; Usage:
;;     parametric_surface(xfun,yfun,zfun,par1,par1min,par1max,par2,par2min,par2max)
;; Options:
;;     xu_grid
;;     yv_grid
;;     line_type
;;     line_width
;;     color
;;     key
;;     enhanced3d
;;     wired_surface
;;     surface_hide
;;     transform
(defun parametric_surface (xfun yfun zfun par1 par1min par1max par2 par2min par2max)
  (let* ((ugrid (get-option '$xu_grid))
         (vgrid (get-option '$yv_grid))
         ($numer t)
         (umin ($float par1min))
         (umax ($float par1max))
         (vmin ($float par2min))
         (vmax ($float par2max))
         (xmin most-positive-double-float)
         (xmax most-negative-double-float)
         (ymin most-positive-double-float)
         (ymax most-negative-double-float)
         (zmin most-positive-double-float)
         (zmax most-negative-double-float)
         (*plot-realpart* *plot-realpart*)
         (ueps (/ (- umax umin) (- ugrid 1)))
         (veps (/ (- vmax vmin) (- vgrid 1)))
         (nu (+ ugrid 1))
         (nv (+ vgrid 1))
         (count -1)
         ncols result f1 f2 f3 xx yy zz uu vv)
     (when (not (subsetp (rest ($append ($listofvars xfun) ($listofvars yfun) ($listofvars zfun))) (list par1 par2)))
        (merror "draw3d (parametric_surface): non defined variable"))
    (setq *plot-realpart* (get-option '$draw_realpart))
    (check-enhanced3d-model "parametric_surface" '(0 2 3 99))
    (when (= *draw-enhanced3d-type* 99)
       (update-enhanced3d-expression (list '(mlist) par1 par2)))
    (if (or (< umax umin)
            (< vmax vmin))
       (merror "draw3d (parametric_surface): illegal range"))
    (setq f1 (coerce-float-fun xfun `((mlist) ,par1 ,par2)))
    (setq f2 (coerce-float-fun yfun `((mlist) ,par1 ,par2)))
    (setq f3 (coerce-float-fun zfun `((mlist) ,par1 ,par2)))
    (setf ncols (if (= *draw-enhanced3d-type* 0) 3 4))
    (setf result (make-array (* ncols nu nv)))
    (loop for j below nv
           initially (setq vv vmin)
           do (setq uu umin)
           (loop for i below nu
                  do
                  (setf xx (funcall f1 uu vv))
                  (setf yy (funcall f2 uu vv))
                  (setf zz (funcall f3 uu vv))
                  (transform-point 3)
                  (check-extremes-x)
                  (check-extremes-y)
                  (check-extremes-z)
                  (setf (aref result (incf count)) xx)
                  (setf (aref result (incf count)) yy)
                  (setf (aref result (incf count)) zz)
                  ; check texture model
                  (case *draw-enhanced3d-type*
                    ((2 99) (setf (aref result (incf count)) (funcall *draw-enhanced3d-fun* uu vv)))
                    (3      (setf (aref result (incf count)) (funcall *draw-enhanced3d-fun* xx yy zz))) )
                  (setq uu (+ uu ueps))
                  (if (> uu umax) (setf uu umax)))
           (setq vv (+ vv veps))
           (if (> vv vmax) (setf vv vmax)))
    ; update x-y-z ranges if necessary
    (update-ranges-3d xmin xmax ymin ymax zmin zmax)
    (make-gr-object
       :name 'parametric_surface
       :command (format nil " ~a w ~a lw ~a lt ~a lc ~a"
                            (make-obj-title (get-option '$key))
                            (if (> *draw-enhanced3d-type* 0) "pm3d" "l")
                            (get-option '$line_width)
                            (get-option '$line_type)
                            (hex-to-rgb (get-option '$color)))
       :groups `((,ncols ,nu)) ; ncols is 4 or 3, depending on colored 4th dimension or not
       :points (list result))))







;; Object: 'tube'
;; Usage:
;;     tube(xfun,yfun,zfun,rad,par1,parmin,parmax)
;; Options:
;;     xu_grid
;;     yv_grid
;;     line_type
;;     line_width
;;     color
;;     key
;;     enhanced3d
;;     wired_surface
;;     surface_hide
;;     transform
(defmacro check-tube-extreme (ex cx cy cz circ)
    `(when (equal (nth ,ex (get-option '$capping)) t)
       (let ((cxx ,cx)
             (cyy ,cy)
             (czz ,cz))
          (when (> *draw-transform-dimensions* 0)
            (setf cxx (funcall *draw-transform-f1* ,cx ,cy ,cz)
                  cyy (funcall *draw-transform-f2* ,cx ,cy ,cz)
                  czz (funcall *draw-transform-f3* ,cx ,cy ,cz)))
          (case *draw-enhanced3d-type*
            (0      (setf ,circ (list cxx cyy czz)))
            ((1 99) (setf ,circ (list cxx cyy czz (funcall *draw-enhanced3d-fun* tt))))
            (3      (setf ,circ (list cxx cyy czz (funcall *draw-enhanced3d-fun* cxx cyy czz)))))
          (dotimes (k vgrid)
            (setf result (append result ,circ))))))

(defun tube (xfun yfun zfun rad par1 parmin parmax)
  (let* ((ugrid (get-option '$xu_grid))
         (vgrid (get-option '$yv_grid))
         ($numer t)
         (tmin ($float parmin))
         (tmax ($float parmax))
         (vmax 6.283185307179586) ; = float(2*%pi)
         (xmin most-positive-double-float)
         (xmax most-negative-double-float)
         (ymin most-positive-double-float)
         (ymax most-negative-double-float)
         (zmin most-positive-double-float)
         (zmax most-negative-double-float)
         (teps (/ (- tmax tmin) (- ugrid 1)))
         (veps (/ vmax (- vgrid 1)))
         (tt tmin)
         ncols circ result
         f1 f2 f3 radius
         cx cy cz nx ny nz
         ux uy uz vx vy vz
         xx yy zz module r vv rcos rsin
         cxold cyold czold
         uxold uyold uzold ttnext)
    (when (< tmax tmin)
       (merror "draw3d (tube): illegal range"))
    (when (not (subsetp (rest ($append ($listofvars xfun) ($listofvars yfun)
                                       ($listofvars zfun) ($listofvars rad)))
                        (list par1)))
       (merror "draw3d (tube): non defined variable"))
    (check-enhanced3d-model "tube" '(0 1 3 99))
    (when (= *draw-enhanced3d-type* 99)
       (update-enhanced3d-expression (list '(mlist) par1)))
    (setq f1 (coerce-float-fun xfun `((mlist) ,par1)))
    (setq f2 (coerce-float-fun yfun `((mlist) ,par1)))
    (setq f3 (coerce-float-fun zfun `((mlist) ,par1)))
    (setf ncols (if (= *draw-enhanced3d-type* 0) 3 4))
    (setf radius
          (coerce-float-fun rad `((mlist) ,par1)))
    (loop do
      ; calculate center and radius of circle
      (cond
        ((= tt tmin)  ; 1st iteration
           (setf cx (funcall f1 tt)
                 cy (funcall f2 tt)
                 cz (funcall f3 tt)
                 ttnext (+ tt teps))
           (check-tube-extreme 1 cx cy cz circ)
           (setf nx (- (funcall f1 ttnext) cx)
                 ny (- (funcall f2 ttnext) cy)
                 nz (- (funcall f3 ttnext) cz)))
        (t  ; all next iterations along the parametric curve
           (setf cxold cx
                 cyold cy
                 czold cz)
           (setf cx (funcall f1 tt)
                 cy (funcall f2 tt)
                 cz (funcall f3 tt))
           (setf nx (- cx cxold)
                 ny (- cy cyold)
                 nz (- cz czold))))
      (setf r (funcall radius tt))
      ; calculate the unitary normal vector      
      (setf module (sqrt (+ (* nx nx) (* ny ny) (* nz nz))))
      (setf nx (/ nx module)
            ny (/ ny module)
            nz (/ nz module))
      ; calculate unitary vector perpendicular to n=(nx,ny,nz)
      ; ux.nx+uy.ny+uz.nz=0 => ux=-t(ny+nz)/nx, uy=uz=t
      ; let's take t=1
      (cond
        ((= nx 0.0)
           (setf ux 1.0 uy 0.0 uz 0.0))
        ((= ny 0.0)
           (setf ux 0.0 uy 1.0 uz 0.0))
        ((= nz 0.0)
           (setf ux 0.0 uy 0.0 uz 1.0))
        (t  ; all other cases
           (setf ux (- (/ (+ ny nz) nx))
                 uy 1.0
                 uz 1.0)))
      (setf module (sqrt (+ (* ux ux) (* uy uy) (* uz uz))))
      (setf ux (/ ux module)
            uy (/ uy module)
            uz (/ uz module))
      (when (and (> tt tmin)
                 (< (+ (* uxold ux)
                       (* uyold uy)
                       (* uzold uz))
                    0))
        (setf ux (- ux)
              uy (- uy)
              uz (- uz)))
      (setf uxold ux
            uyold uy
            uzold uz)
      ; vector v = n times u
      (setf vx (- (* ny uz) (* nz uy))
            vy (- (* nz ux) (* nx uz))
            vz (- (* nx uy) (* ny ux)))
      ; parametric equation of the circumference of radius
      ; r and centered at c=(cx,cy,cz):
      ; x(t) = c + r(cos(t)u + sin(t)v),
      ; for t in (0, 2*%pi)
      (setf vv 0.0)
      (setf circ '())
      (loop for i below vgrid do
        (setf rcos (* r (cos vv))
              rsin (* r (sin vv)))
        (setf xx (+ cx (* rcos ux) (* rsin vx))
              yy (+ cy (* rcos uy) (* rsin vy))
              zz (+ cz (* rcos uz) (* rsin vz)))
        (transform-point 3)
        (check-extremes-x)
        (check-extremes-y)
        (check-extremes-z)
        ; check texture model
        (case *draw-enhanced3d-type*
          (0      (setf circ (cons (list xx yy zz) circ)))
          ((1 99) (setf circ (cons (list xx yy zz (funcall *draw-enhanced3d-fun* tt)) circ)))
          (3      (setf circ (cons (list xx yy zz (funcall *draw-enhanced3d-fun* xx yy zz)) circ))))
        (setf vv (+ vv veps))
        (when (> vv vmax) (setf vv vmax))  ) ; loop for
      (setf result (append result (apply #'append circ)))
      when (>= tt tmax) do (loop-finish)
      do (setf tt (+ tt teps))
         (when (> tt tmax) (setf tt tmax))  ) ; loop do
      (check-tube-extreme 2 cx cy cz circ)
    ; update x-y-z ranges
    (update-ranges-3d xmin xmax ymin ymax zmin zmax)
    (make-gr-object
       :name 'tube
       :command (format nil " ~a w ~a lw ~a lt ~a lc ~a"
                            (make-obj-title (get-option '$key))
                            (if (> *draw-enhanced3d-type* 0) "pm3d" "l")
                            (get-option '$line_width)
                            (get-option '$line_type)
                            (hex-to-rgb (get-option '$color)))
       :groups `((,ncols ,vgrid))
       :points `(,(make-array (length result) :element-type 'flonum
                                              :initial-contents result)))))







;; Object: 'image'
;; Usages:
;;     image(matrix_of_numbers,x0,y0,width,height)
;;     image(matrix_of_[r,g,b],x0,y0,width,height)
;;     image(picture_object,x0,y0,width,height)
;; Options:
;;     colorbox
;;     palette
(defun image (mat x0 y0 width height)
  (let ( (fx0 ($float x0))
         (fy0 ($float y0))
         (fwidth ($float width))
         (fheight ($float height))
         result nrows ncols dx dy n)
    (cond (($matrixp mat)
             (setf nrows (length (cdr mat))
                   ncols (length (cdadr mat)))
             (setf dx (/ fwidth ncols)
                   dy (/ fheight nrows))
             (if (not ($listp (cadadr mat)))  ; it's a matrix of reals
                 (setf n 3)   ; 3 numbers to be sent to gnuplot: x,y,value
                 (setf n 5))  ; 5 numbers to be sent: x,y,r,g,b
             (case n
               (3 (setf result (make-array (* 3 nrows ncols) :element-type 'flonum))
                  (let ((yi (+ fy0 height (* dy -0.5)))
                        (counter -1)
                         xi)
                     (loop for row on (cdr mat) by #'cdr do
                       (setf xi (+ fx0 (* dx 0.5)))
                       (loop for col on (cdar row) by #'cdr do
                         (setf (aref result (incf counter)) xi
                               (aref result (incf counter)) yi
                               (aref result (incf counter)) ($float (car col)))
                         (setf xi (+ xi dx)))
                       (setf yi (- yi dy)) )))
               (5 (setf result (make-array (* 5 nrows ncols) :element-type 'flonum))
                  (let ((yi (+ fy0 height (* dy -0.5)))
                        (counter -1)
                         xi colors)
                     (loop for row on (cdr mat) by #'cdr do
                       (setf xi (+ fx0 (* dx 0.5)))
                       (loop for col on (cdar row) by #'cdr do
                         (setf colors (cdar col))
                         (setf (aref result (incf counter)) xi
                               (aref result (incf counter)) yi
                               (aref result (incf counter)) ($float (car colors))
                               (aref result (incf counter)) ($float (cadr colors))
                               (aref result (incf counter)) ($float (caddr colors)))
                         (setf xi (+ xi dx)))
                       (setf yi (- yi dy)) )))))
          (($picturep mat)
             (setf nrows (nth 3 mat)   ; picture height
                   ncols (nth 2 mat))  ; picture width
             (setf dx (/ fwidth ncols)
                   dy (/ fheight nrows))
             (if (equal (nth 1 mat) '$level)  ; gray level picture
                 (setf n 3)   ; 3 numbers to be sent to gnuplot: x,y,value
                 (setf n 5))  ; 5 numbers to be sent: x,y,r,g,b
             (setf result (make-array (* n nrows ncols) :element-type 'flonum))
             (let ((yi (+ fy0 height (* dy -0.5)))
                   (count1 -1)
                   (count2 -1)
                   xi)
                (loop for r from 0 below nrows do
                  (setf xi (+ fx0 (* dx 0.5)))
                  (loop for c from 0 below ncols do
                    (setf (aref result (incf count1)) xi)
                    (setf (aref result (incf count1)) yi)
                    (loop for q from 3 to n do
                      (setf (aref result (incf count1))
                            ($float (aref (nth 4 mat) (incf count2)))))
                    (setf xi (+ xi dx)))
                  (setf yi (- yi dy)))))
          (t
             (merror "draw2d (image): Argument not recognized")))
    ; update x-y ranges if necessary
    (update-ranges-2d fx0 (+ fx0 fwidth) fy0 (+ fy0 fheight))
    (make-gr-object
       :name 'image
       :command (case n
                   (3 (format nil " t '' w image"))
                   (5 (format nil " t '' w rgbimage")))
       :groups (case n
                   (3 '((3 0)))   ; numbers are sent to gnuplot in gropus of 3, no blank lines
                   (5 '((5 0))  ))  ; numbers in groups of 5, no blank lines
       :points (list result)) ) )






(defmacro write-palette-code ()
  '(let ((pal (get-option '$palette)))
     (cond
       ((equal pal '$gray)
          (format nil "set palette gray~%"))
       ((equal pal '$color)
          (format nil "set palette rgbformulae 7,5,15~%"))
       ((and (listp pal)
             (= (length pal) 3)
             (every #'(lambda (x) (and (integerp x) (<= (abs x) 36))) pal) )
          (format nil "set palette rgbformulae ~a,~a,~a~%"
                  (car pal) (cadr pal) (caddr pal)))
       ((and (listp pal)
             (every #'(lambda (x) (and (listp x) (= (length x) 3))) pal) )
          (let (triplete
                (n (length pal)))
            (with-output-to-string (stream)
              (format stream "set palette defined ( \\~%")
              (dotimes (k n)
                (setf triplete (nth k pal))
                (format stream "  ~a ~a ~a ~a "
                        k (car triplete) (cadr triplete) (caddr triplete))
                (if (= (1+ k) n)
                  (format stream ")~%")
                  (format stream ", \\~%") )))))
       (t
          (merror "draw: illegal palette description")))))



(defvar *2d-graphic-objects* (make-hash-table))

; table of basic 2d graphic objects
(setf (gethash '$points        *2d-graphic-objects*) 'points
      (gethash '$errors        *2d-graphic-objects*) 'errors
      (gethash '$polygon       *2d-graphic-objects*) 'polygon
      (gethash '$ellipse       *2d-graphic-objects*) 'ellipse
      (gethash '$triangle      *2d-graphic-objects*) 'triangle
      (gethash '$rectangle     *2d-graphic-objects*) 'rectangle
      (gethash '$quadrilateral *2d-graphic-objects*) 'quadrilateral
      (gethash '$region        *2d-graphic-objects*) 'region
      (gethash '$explicit      *2d-graphic-objects*) 'explicit
      (gethash '$implicit      *2d-graphic-objects*) 'implicit
      (gethash '$parametric    *2d-graphic-objects*) 'parametric
      (gethash '$vector        *2d-graphic-objects*) 'vect
      (gethash '$label         *2d-graphic-objects*) 'label
      (gethash '$bars          *2d-graphic-objects*) 'bars
      (gethash '$polar         *2d-graphic-objects*) 'polar
      (gethash '$image         *2d-graphic-objects*) 'image
      (gethash '%points        *2d-graphic-objects*) 'points
      (gethash '%errors        *2d-graphic-objects*) 'errors
      (gethash '%polygon       *2d-graphic-objects*) 'polygon
      (gethash '%ellipse       *2d-graphic-objects*) 'ellipse
      (gethash '%triangle      *2d-graphic-objects*) 'triangle
      (gethash '%rectangle     *2d-graphic-objects*) 'rectangle
      (gethash '%quadrilateral *2d-graphic-objects*) 'quadrilateral
      (gethash '%region        *2d-graphic-objects*) 'region
      (gethash '%explicit      *2d-graphic-objects*) 'explicit
      (gethash '%implicit      *2d-graphic-objects*) 'implicit
      (gethash '%parametric    *2d-graphic-objects*) 'parametric
      (gethash '%vector        *2d-graphic-objects*) 'vect
      (gethash '%label         *2d-graphic-objects*) 'label
      (gethash '%bars          *2d-graphic-objects*) 'bars
      (gethash '%polar         *2d-graphic-objects*) 'polar
      (gethash '%image         *2d-graphic-objects*) 'image )

(defun make-scene-2d (args)
   (let ((objects nil)
         plotcmd largs aux)
      (ini-gr-options)
      (ini-local-option-variables)
      (user-defaults)
      (setf largs (listify-arguments args))
      ; update option values and detect objects to be plotted
      (dolist (x largs)
         (cond ((equal ($op x) "=")
                   (update-gr-option ($lhs x) ($rhs x)))
               ((not (null (gethash (setf aux (caar x)) *2d-graphic-objects*)))
                  (setf objects
                         (append
                            objects 
                            (list (apply (gethash aux *2d-graphic-objects*) (rest x))))))
               (t (merror "draw: 2D graphic object not recognized, ~M" aux))))
      ; save in plotcmd the gnuplot preamble
      (setf plotcmd
         (concatenate 'string
            (unless (or *multiplot-is-active*
                        (member (get-option '$terminal) '($eps $epslatex $epslatex_standalone)))
               (format nil "set obj 1 fc rgb '~a' fs solid 1.0 noborder ~%"
                       (get-option '$background_color)) )
            (if (equal (get-option '$proportional_axes) '$none)
               (format nil "set size noratio~%")
               (format nil "set size ratio -1~%") )
            ; this let statement is to prevent error messages from gnuplot when
            ; the amplitude of the ranges equals zero
            (let ((xi (first  (get-option '$xrange)))
                  (xf (second (get-option '$xrange)))
                  (yi (first  (get-option '$yrange)))
                  (yf (second (get-option '$yrange)))
                  (x2i (first  (get-option '$xrange_secondary)))
                  (x2f (second (get-option '$xrange_secondary)))
                  (y2i (first  (get-option '$yrange_secondary)))
                  (y2f (second (get-option '$yrange_secondary))) )
               (when (and (get-option '$xrange) (near-equal xi xf))
                  (setf xi (- xi 0.01)
                        xf (+ xf 0.01)))
               (when (and (get-option '$xrange_secondary) (near-equal x2i x2f))
                  (setf x2i (- x2i 0.01)
                        x2f (+ x2f 0.01)))
               (when (and (get-option '$yrange) (near-equal yi yf))
                  (setf yi (- yi 0.01)
                        yf (+ yf 0.01)))
               (when (and (get-option '$yrange_secondary) (near-equal y2i y2f))
                  (setf y2i (- y2i 0.01)
                        y2f (+ y2f 0.01)))
               (format nil "~a~a~a~a"
                       (if (get-option '$xrange)
                         (format nil "set xrange [~a:~a]~%" xi xf)
                         "")
                       (if (get-option '$xrange_secondary)
                         (format nil "set x2range [~a:~a]~%" x2i x2f)
                         "")
                       (if (get-option '$yrange)
                         (format nil "set yrange [~a:~a]~%" yi yf)
                         "")
                       (if (get-option '$yrange_secondary)
                         (format nil "set y2range [~a:~a]~%" y2i y2f)
                         "") ) )
            (if (get-option '$cbrange)
               (format nil "set cbrange [~a:~a]~%"
                  (first (get-option '$cbrange))
                  (second (get-option '$cbrange)))
               (format nil "set cbrange [*:*]~%") )
            (if (get-option '$logx)
               (format nil "set logscale x~%")
               (format nil "unset logscale x~%"))
            (if (get-option '$logx_secondary)
               (format nil "set logscale x2~%")
               (format nil "unset logscale x2~%"))
            (if (get-option '$logy)
               (format nil "set logscale y~%")
               (format nil "unset logscale y~%"))
            (if (get-option '$logy_secondary)
               (format nil "set logscale y2~%")
               (format nil "unset logscale y2~%"))
            (if (get-option '$logcb)
               (format nil "set logscale cb~%")
	      (format nil "unset logscale cb~%") )
	    
	    ( if (equal (car (get-option '$grid)) 0)
		(format nil "unset grid~%")
	        (format nil "set grid xtics ytics mxtics mytics~%set mxtics ~a~%set mytics ~d~%"
		      (car  (get-option '$grid))
		      (cadr (get-option '$grid))
		      )
	      )
		   
            (format nil "set title '~a'~%"  (get-option '$title))
            (format nil "set xlabel '~a'~%" (get-option '$xlabel))
            (format nil "set x2label '~a'~%" (get-option '$xlabel_secondary))
            (format nil "set ylabel '~a'~%" (get-option '$ylabel))
            (format nil "set y2label '~a'~%" (get-option '$ylabel_secondary))
            (let ((suma 0))
              (if (get-option '$axis_bottom)  (setf suma (+ suma 1)))
              (if (get-option '$axis_left) (setf suma (+ suma 2)))
              (if (get-option '$axis_top) (setf suma (+ suma 4)))
              (if (get-option '$axis_right) (setf suma (+ suma 8)))
              (format nil "set border ~a~%" suma) )
            (if (get-option '$key_pos)
              (format nil "set key ~a~%" (get-option '$key_pos))
              (format nil "set key top right~%") )
            (if (get-option '$xaxis)
               (format nil "set xzeroaxis lw ~a lt ~a lc ~a~%"
                           (get-option '$xaxis_width)
                           (get-option '$xaxis_type)
                           (hex-to-rgb (get-option '$xaxis_color)) )
               (format nil "unset xzeroaxis~%"))
            (if (get-option '$yaxis)
               (format nil "set yzeroaxis lw ~a lt ~a lc ~a~%"
                           (get-option '$yaxis_width)
                           (get-option '$yaxis_type)
                           (hex-to-rgb (get-option '$yaxis_color)) )
               (format nil "unset yzeroaxis~%"))
            (if (null (get-option '$xtics_secondary))
               (format nil "unset x2tics~%set xtics nomirror~%")
               (format nil "set x2tics ~a ~a ~a~%"
                       (if (get-option '$xtics_secondary_rotate) "rotate" "norotate")
                       (if (get-option '$xtics_secondary_axis) "axis" "border")
                       (get-option '$xtics_secondary)))
            (if (null (get-option '$xtics))
               (format nil "unset xtics~%")
               (format nil "set xtics ~a ~a ~a~%" 
                       (if (get-option '$xtics_rotate) "rotate" "norotate")
                       (if (get-option '$xtics_axis) "axis" "border")
                       (get-option '$xtics)))
            (if (null (get-option '$ytics_secondary))
               (format nil "unset y2tics~%set ytics nomirror~%")
               (format nil "set ytics nomirror~%set y2tics ~a ~a ~a~%"
                       (if (get-option '$ytics_secondary_rotate) "rotate" "norotate")
                       (if (get-option '$ytics_secondary_axis) "axis" "border")
                       (get-option '$ytics_secondary)))
            (if (null (get-option '$ytics))
               (format nil "unset ytics~%")
               (format nil "set ytics ~a ~a ~a~%"
                       (if (get-option '$ytics_rotate) "rotate" "norotate")
                       (if (get-option '$ytics_axis) "axis" "border")
                       (get-option '$ytics)))
            (if (null (get-option '$cbtics))
               (format nil "unset cbtics~%")
               (format nil "set cbtics ~a~%" (get-option '$cbtics) ))
            (if (get-option '$colorbox)
               (format nil "set colorbox~%")
               (format nil "unset colorbox~%"))
            (format nil "set cblabel '~a'~%" 
                        (if (stringp (get-option '$colorbox))
                          (get-option '$colorbox)
                          ""))
            (write-palette-code)
            (if (not (string= (get-option '$user_preamble) ""))
               (format nil "~a~%" (get-option '$user_preamble))) ) )
      ; scene allocation
      (setf *allocations* (cons (get-option '$allocation) *allocations*))
      ; scene description: (dimensions, gnuplot preamble in string format, list of objects)
      (list
         2       ; it's a 2d scene
         plotcmd ; gnuplot preamble
         objects ; list of objects to be plotted
         )))






(defvar *3d-graphic-objects* (make-hash-table))

; table of basic 3d graphic objects
(setf (gethash '$points             *3d-graphic-objects*) 'points3d
      (gethash '$elevation_grid     *3d-graphic-objects*) 'elevation_grid
      (gethash '$mesh               *3d-graphic-objects*) 'mesh
      (gethash '$triangle           *3d-graphic-objects*) 'triangle3d
      (gethash '$quadrilateral      *3d-graphic-objects*) 'quadrilateral3d
      (gethash '$explicit           *3d-graphic-objects*) 'explicit3d
      (gethash '$implicit           *3d-graphic-objects*) 'implicit3d
      (gethash '$parametric         *3d-graphic-objects*) 'parametric3d
      (gethash '$vector             *3d-graphic-objects*) 'vect3d
      (gethash '$label              *3d-graphic-objects*) 'label
      (gethash '$parametric_surface *3d-graphic-objects*) 'parametric_surface
      (gethash '$tube               *3d-graphic-objects*) 'tube
      (gethash '$spherical          *3d-graphic-objects*) 'spherical
      (gethash '$cylindrical        *3d-graphic-objects*) 'cylindrical
      (gethash '%points             *3d-graphic-objects*) 'points3d
      (gethash '%elevation_grid     *3d-graphic-objects*) 'elevation_grid
      (gethash '%mesh               *3d-graphic-objects*) 'mesh
      (gethash '%triangle           *3d-graphic-objects*) 'triangle3d
      (gethash '%quadrilateral      *3d-graphic-objects*) 'quadrilateral3d
      (gethash '%explicit           *3d-graphic-objects*) 'explicit3d
      (gethash '%implicit           *3d-graphic-objects*) 'implicit3d
      (gethash '%parametric         *3d-graphic-objects*) 'parametric3d
      (gethash '%vector             *3d-graphic-objects*) 'vect3d
      (gethash '%label              *3d-graphic-objects*) 'label
      (gethash '%parametric_surface *3d-graphic-objects*) 'parametric_surface
      (gethash '%tube               *3d-graphic-objects*) 'tube
      (gethash '%spherical          *3d-graphic-objects*) 'spherical
      (gethash '%cylindrical        *3d-graphic-objects*) 'cylindrical  )

;; This function builds a 3d scene by calling the 
;; graphic objects constructors.
(defun make-scene-3d (args)
   (let ((objects nil)
         plotcmd largs aux)
      (ini-gr-options)
      (ini-local-option-variables)
      (user-defaults)
      (setf largs (listify-arguments args))
      ; update option values and detect objects to be plotted
      (dolist (x largs)
         (cond ((equal ($op x) "=")
                  (update-gr-option ($lhs x) ($rhs x)))
               ((not (null (gethash (setf aux (caar x)) *3d-graphic-objects*)))
                  (setf objects
                         (append
                            objects 
                            (list (apply (gethash aux *3d-graphic-objects*) (rest x))))))
               (t (merror "draw: 3D graphic object not recognized, ~M" aux) )))
      ; save in plotcmd the gnuplot preamble
      (setf plotcmd
         (concatenate 'string
            (format nil "set style rectangle fillcolor rgb '~a' fs solid 1.0 noborder~%"
                        (get-option '$background_color)) ; background rectangle
            ; this let statement is to prevent error messages in gnuplot when
            ; the amplitude of the ranges equals zero
            (let ((xi (first  (get-option '$xrange)))
                  (xf (second (get-option '$xrange)))
                  (yi (first  (get-option '$yrange)))
                  (yf (second (get-option '$yrange)))
                  (zi (first  (get-option '$zrange)))
                  (zf (second (get-option '$zrange))))
               (when (near-equal xi xf)
                  (setf xi (- xi 0.01)
                        xf (+ xf 0.01)))
               (when (near-equal yi yf)
                  (setf yi (- yi 0.01)
                        yf (+ yf 0.01)))
               (when (near-equal zi zf)
                  (setf zi (- zi 0.01)
                        zf (+ zf 0.01)))
               (format nil "set xrange [~a:~a]~%set yrange [~a:~a]~%set zrange [~a:~a]~%"
                           xi xf yi yf zi zf))
            (if (get-option '$cbrange)
               (format nil "set cbrange [~a:~a]~%" 
                  (first (get-option '$cbrange))
                  (second (get-option '$cbrange)) )
               (format nil "set cbrange [*:*]~%") )
            (case (get-option '$contour)
               ($surface (format nil "set contour surface;set cntrparam levels ~a~%"
                                      (get-option '$contour_levels) ))
               ($base    (format nil "set contour base;set cntrparam levels ~a~%"
                                      (get-option '$contour_levels) ))
               ($both    (format nil "set contour both;set cntrparam levels ~a~%"
                                      (get-option '$contour_levels) ))
               ($map     (format nil "set contour base~%unset surface~%set cntrparam levels ~a~%"
                                      (get-option '$contour_levels))) )
            (format nil "set title '~a'~%"  (get-option '$title))
            (format nil "set xlabel '~a'~%" (get-option '$xlabel))
            (format nil "set ylabel '~a'~%" (get-option '$ylabel))
            (if (< (length (get-option '$zlabel)) 5)
               (format nil "set zlabel '~a'~%" (get-option '$zlabel))
               (format nil "set zlabel '~a' rotate~%" (get-option '$zlabel)) )
            (format nil "set datafile missing 'NIL'~%")
            (if (get-option '$logx)
               (format nil "set logscale x~%")
               (format nil "unset logscale x~%"))
            (if (get-option '$logy)
               (format nil "set logscale y~%")
               (format nil "unset logscale y~%"))
            (if (get-option '$logz)
               (format nil "set logscale z~%")
               (format nil "unset logscale z~%"))
            (if (get-option '$key_pos)
               (format nil "set key ~a~%" (get-option '$key_pos))
               (format nil "set key top center~%") )
            (if (get-option '$logcb)
               (format nil "set logscale cb~%")
               (format nil "unset logscale cb~%") )
	    (if (equal (car (get-option '$grid)) 0)
		(format nil "unset grid~%")
	        (format nil "set grid xtics ytics ztics mxtics mytics mztics~%set mxtics ~a~%set mytics ~d~%"
		      (car  (get-option '$grid))
		      (cadr (get-option '$grid))
		      )
	      )
            (if (get-option '$xaxis)
               (format nil "set xzeroaxis lw ~a lt ~a lc ~a~%"
                           (get-option '$xaxis_width)
                           (get-option '$xaxis_type)
                           (hex-to-rgb (get-option '$xaxis_color)) )
               (format nil "unset xzeroaxis~%"))
            (if (get-option '$yaxis)
               (format nil "set yzeroaxis lw ~a lt ~a lc ~a~%"
                           (get-option '$yaxis_width)
                           (get-option '$yaxis_type)
                           (hex-to-rgb (get-option '$yaxis_color)) )
               (format nil "unset yzeroaxis~%"))
            (if (get-option '$zaxis)
               (format nil "set zzeroaxis lw ~a lt ~a lc ~a~%"
                           (get-option '$zaxis_width)
                           (get-option '$zaxis_type)
                           (hex-to-rgb (get-option '$zaxis_color)))
               (format nil "unset zzeroaxis~%"))
            (if (null (get-option '$xtics))
               (format nil "unset xtics~%")
               (format nil "set xtics ~a ~a ~a~%" 
                       (if (get-option '$xtics_rotate) "rotate" "norotate")
                       (if (get-option '$xtics_axis) "axis" "border")
                       (get-option '$xtics)))
            (if (null (get-option '$ytics))
               (format nil "unset ytics~%")
               (format nil "set ytics ~a ~a ~a~%"
                       (if (get-option '$ytics_rotate) "rotate" "norotate")
                       (if (get-option '$ytics_axis) "axis" "border")
                       (get-option '$ytics)))
            (if (null (get-option '$ztics))
               (format nil "unset ztics~%")
               (format nil "set ztics ~a ~a ~a~%"
                       (if (get-option '$ztics_rotate) "rotate" "norotate")
                       (if (get-option '$ztics_axis) "axis" "border")
                       (get-option '$ztics)))
            (if (null (get-option '$cbtics))
               (format nil "unset cbtics~%")
               (format nil "set cbtics ~a~%"
                       (get-option '$cbtics)) )
            (if (or (eql (get-option '$contour) '$map)
                    (eql (get-option '$view) '$map) )
               (format nil "set view map~%~a~%"
                            (if (equal (get-option '$proportional_axes) '$none)
                               "set size noratio"
                               "set size ratio -1") )
               (format nil "set view ~a, ~a, 1, 1~%~a~%"
                            (first  (get-option '$view))
                            (second (get-option '$view))
                            (case (get-option '$proportional_axes)
                               ($xy       "set view equal xy" )
                               ($xyz      "set view equal xyz")
                               (otherwise ""))))
            (if (not (get-option '$axis_3d))
                (format nil "set border 0~%unset xtics~%unset ytics~%unset ztics~%"))
            (when (not (null (get-option '$enhanced3d)))
              (if (null (get-option '$wired_surface))
                (format nil "set pm3d at s ~a explicit~%" (get-option '$interpolate_color))
                (format nil "set style line 1 lt 1 lw 1 lc rgb '#000000'~%set pm3d at s depthorder explicit hidden3d 1~%") ))
            (if (get-option '$surface_hide)
               (format nil "set hidden3d nooffset~%"))
            (if (get-option '$xyplane)
               (format nil "set xyplane at ~a~%" (get-option '$xyplane)))
            (if (get-option '$colorbox)
               (format nil "set colorbox~%")
               (format nil "unset colorbox~%"))
            (format nil "set cblabel '~a'~%" 
                        (if (stringp (get-option '$colorbox))
                          (get-option '$colorbox)
                          ""))
            (write-palette-code)
            (if (not (string= (get-option '$user_preamble) ""))
               (format nil "~a~%" (get-option '$user_preamble)))  ))
      ; scene allocation
      (setf *allocations* (cons (get-option '$allocation) *allocations*))
      ; scene description: (dimensions, gnuplot preamble in string format, list of objects)
      (list
         3       ; it's a 3d scene
         plotcmd ; gnuplot preamble
         objects ; list of objects to be plotted
         ) ))







(defmacro write-subarray (arr str)
  `(format ,str
           "~a~%"
           (apply 
             #'concatenate 'string 
             (map 
                'list 
                #'(lambda (z) (format nil "~a " z))
                ,arr))))



(defun draw_gnuplot (&rest args)
  (ini-global-options)
  (user-defaults)
  (setf *allocations* nil)
  (let ((counter 0)
        (scenes-list '((mlist simp)))  ; these two variables will be used
        gfn ; gnuplot_file_name
        dfn ; data_file_name
        scene-short-description        ; to build the text output
        scenes
        cmdstorage  ; file maxout.gnuplot
        datastorage ; file data.gnuplot
        datapath    ; path to data.gnuplot
        (ncols 1)
        nrows width height ; multiplot parameters
        isanimatedgif ismultipage is1stobj biglist grouplist largs)

    (setf largs (listify-arguments args))
    (dolist (x largs)
      (cond ((equal ($op x) "=")
              (case ($lhs x)
                ($terminal          (update-gr-option '$terminal ($rhs x)))
                ($columns           (update-gr-option '$columns ($rhs x)))
                ($dimensions        (update-gr-option '$dimensions ($rhs x)))
                ($file_name         (update-gr-option '$file_name ($rhs x)))
                ($gnuplot_file_name (update-gr-option '$gnuplot_file_name ($rhs x)))
                ($data_file_name    (update-gr-option '$data_file_name ($rhs x)))
                ($delay             (update-gr-option '$delay ($rhs x)))

                ; deprecated global options
                ($file_bgcolor      (update-gr-option '$file_bgcolor ($rhs x)))
                ($pic_width         (update-gr-option '$pic_width ($rhs x)))
                ($pic_height        (update-gr-option '$pic_height ($rhs x)))
                ($eps_width         (update-gr-option '$eps_width ($rhs x)))
                ($eps_height        (update-gr-option '$eps_height ($rhs x)))
                ($pdf_width         (update-gr-option '$pdf_width ($rhs x)))
                ($pdf_height        (update-gr-option '$pdf_height ($rhs x)))

                (otherwise (merror "draw: unknown global option ~M " ($lhs x)))))
            ((equal (caar x) '$gr3d)
              (setf scenes (append scenes (list (funcall #'make-scene-3d (rest x))))))
            ((equal (caar x) '$gr2d)
              (setf scenes (append scenes (list (funcall #'make-scene-2d (rest x))))))
            (t
              (merror "draw: item ~M is not recognized" x)))   )
    (setf isanimatedgif
          (equal (get-option '$terminal) '$animated_gif))
    (setf ismultipage
          (member (get-option '$terminal)
                  '($multipage_pdf $multipage_pdfcairo $multipage_eps $multipage_eps_color)))

    (setf
       gfn (plot-temp-file (get-option '$gnuplot_file_name))
       dfn (plot-temp-file (get-option '$data_file_name)))

    ;; we now create two files: maxout.gnuplot and data.gnuplot
    (setf cmdstorage
          (open gfn
                :direction :output :if-exists :supersede))
    (if (eql cmdstorage nil)
      (merror "draw: Cannot create file '~a'. Probably maxima_tempdir doesn't point to a writable directory." gfn))
    (setf datastorage
          (open dfn
                :direction :output :if-exists :supersede))
    (if (eql datastorage nil)
      (merror "draw: Cannot create file '~a'. Probably maxima_tempdir doesn't point to a writable directory." dfn))
    
    (setf datapath (format nil "'~a'" dfn))
    ; when one multiplot window is active, change of terminal is not allowed
    (if (not *multiplot-is-active*)
      (case (get-option '$terminal)
        ($dumb (format cmdstorage "set terminal dumb size ~a, ~a"
                           (round (/ (first (get-option '$dimensions)) 10))
                           (round (/ (second (get-option '$dimensions)) 10))))
        ($dumb_file (format cmdstorage "set terminal dumb size ~a, ~a~%set out '~a.dumb'"
                           (round (/ (first (get-option '$dimensions)) 10))
                           (round (/ (second (get-option '$dimensions)) 10))
                           (get-option '$file_name)))
 	($canvas (format cmdstorage "set terminal canvas enhanced ~a size ~a, ~a~%set out '~a.html'"
 			 (write-font-type)
 			 (round (first (get-option '$dimensions)))
 			 (round (second (get-option '$dimensions)))
 			 (get-option '$file_name)))
        ($png (format cmdstorage "set terminal png enhanced truecolor ~a size ~a, ~a~%set out '~a.png'"
                           (write-font-type)
                           (round (first (get-option '$dimensions)))
                           (round (second (get-option '$dimensions)))
                           (get-option '$file_name) ) )
        ($pngcairo (format cmdstorage "set terminal pngcairo dashed enhanced truecolor ~a size ~a, ~a~%set out '~a.png'"
                           (write-font-type)
                           (round (first (get-option '$dimensions)))
                           (round (second (get-option '$dimensions)))
                           (get-option '$file_name) ) )
        (($eps $multipage_eps) (format cmdstorage "set terminal postscript dashed eps enhanced ~a size ~acm, ~acm~%set out '~a.eps'"
                           (write-font-type)
                           (/ (first (get-option '$dimensions)) 100.0)
                           (/ (second (get-option '$dimensions)) 100.0)
                           (get-option '$file_name)))
        (($eps_color $multipage_eps_color) (format cmdstorage "set terminal postscript dashed eps enhanced ~a color size ~acm, ~acm~%set out '~a.eps'"
                           (write-font-type)
                           (/ (first (get-option '$dimensions)) 100.0)
                           (/ (second (get-option '$dimensions)) 100.0)
                           (get-option '$file_name)))
        ($epslatex (format cmdstorage "set terminal epslatex ~a color size ~acm, ~acm~%set out '~a.tex'"
                           (write-font-type)
                           (/ (first (get-option '$dimensions)) 100.0)
                           (/ (second (get-option '$dimensions)) 100.0)
                           (get-option '$file_name)))
        ($epslatex_standalone (format cmdstorage "set terminal epslatex dashed standalone ~a color size ~acm, ~acm~%set out '~a.tex'"
                           (write-font-type)
                           (/ (first (get-option '$dimensions)) 100.0)
                           (/ (second (get-option '$dimensions)) 100.0)
                           (get-option '$file_name)))
        (($pdf $multipage_pdf) (format cmdstorage "set terminal pdf dashed enhanced ~a color size ~acm, ~acm~%set out '~a.pdf'"
                           (write-font-type)
                           (/ (first (get-option '$dimensions)) 100.0)
                           (/ (second (get-option '$dimensions)) 100.0)
                           (get-option '$file_name)))
        (($pdfcairo $multipage_pdfcairo) (format cmdstorage "set terminal pdfcairo dashed enhanced ~a color size ~acm, ~acm~%set out '~a.pdf'"
                           (write-font-type)
                           (/ (first (get-option '$dimensions)) 100.0)
                           (/ (second (get-option '$dimensions)) 100.0)
                           (get-option '$file_name)))
        ($jpg (format cmdstorage "set terminal jpeg enhanced ~a size ~a, ~a~%set out '~a.jpg'"
                           (write-font-type)
                           (round (first (get-option '$dimensions)))
                           (round (second (get-option '$dimensions)))
                           (get-option '$file_name)))
        ($gif (format cmdstorage "set terminal gif enhanced ~a size ~a, ~a~%set out '~a.gif'"
                           (write-font-type)
                           (round (first (get-option '$dimensions)))
                           (round (second (get-option '$dimensions)))
                           (get-option '$file_name)))
        ($svg (format cmdstorage "set terminal svg dashed enhanced ~a size ~a, ~a~%set out '~a.svg'"
                           (write-font-type)
                           (round (first (get-option '$dimensions)))
                           (round (second (get-option '$dimensions)))
                           (get-option '$file_name)))
        ($animated_gif (format cmdstorage "set terminal gif enhanced animate ~a size ~a, ~a delay ~a~%set out '~a.gif'"
                           (write-font-type)
                           (round (first (get-option '$dimensions)))
                           (round (second (get-option '$dimensions)))
                           (get-option '$delay)
                           (get-option '$file_name)))
        ($aquaterm (format cmdstorage "set terminal aqua enhanced ~a ~a size ~a ~a~%"
                           *draw-terminal-number*
                           (write-font-type)
                           (round (first (get-option '$dimensions)))
                           (round (second (get-option '$dimensions)))))
        ($wxt (format cmdstorage "set terminal wxt dashed enhanced ~a ~a size ~a, ~a~%"
                           *draw-terminal-number*
                           (write-font-type)
                           (round (first (get-option '$dimensions)))
                           (round (second (get-option '$dimensions)))))
        ($qt (format cmdstorage "set terminal qt dashed enhanced ~a ~a size ~a, ~a~%"
                           *draw-terminal-number*
                           (write-font-type)
                           (round (first (get-option '$dimensions)))
                           (round (second (get-option '$dimensions)))))
        ($x11 (format cmdstorage "set terminal x11 dashed enhanced ~a ~a size ~a, ~a~%"
                           *draw-terminal-number*
                           (write-font-type)
                           (round (first (get-option '$dimensions)))
                           (round (second (get-option '$dimensions)))))
        (otherwise ; default screen output
          (cond
            (*windows-OS*  ; running on windows operating system
              (format cmdstorage "set terminal windows enhanced ~a size ~a, ~a~%"
                          (write-font-type)
                          (round (first (get-option '$dimensions)))
                          (round (second (get-option '$dimensions)))))
            (t  ; other platforms
              (format cmdstorage "set terminal x11 dashed enhanced ~a ~a size ~a, ~a~%"
                           *draw-terminal-number*
                           (write-font-type)
                           (round (first (get-option '$dimensions)))
                           (round (second (get-option '$dimensions))))))) ))

    ; compute some parameters for multiplot
    (when (and (not isanimatedgif) (not ismultipage))
      (setf ncols (get-option '$columns))
      (setf nrows (ceiling (/ (length scenes) ncols)))
      (if (> (length scenes) 1)
        (format cmdstorage "~%set size 1.0, 1.0~%set origin 0.0, 0.0~%set multiplot~%")) )

    ; Make gnuplot versions newer than 5.0 understand that linetype means
    ; we try to set the dash type
    (format cmdstorage "~%if(GPVAL_VERSION >= 5.0){set for [i=1:8] linetype i dashtype i; set format '%h'}")

    ;; By default gnuplot assumes everything below 1e-8 to be a rounding error
    ;; and rounds it down to 0. This is handy for standalone gnuplot as it allows
    ;; to suppress pixels with imaginary part while allowing for small calculation
    ;; errors. As plot and draw handle the imaginary part without gnuplot's help
    ;; this isn't needed here and is turned off as it often surprises users.
    (format cmdstorage "~%set zero 0.0")

    ; write descriptions of 2d and 3d scenes
    (let ((i -1)
          (alloc (reverse *allocations*))
          (nilcounter 0)
          thisalloc origin1 origin2 size1 size2)

      ; recalculate nrows for automatic scene allocations
      (setf nrows (ceiling (/ (count nil alloc) ncols)))

      (when (> nrows 0)
        (setf width (/ 1.0 ncols)
              height (/ 1.0 nrows)))
      (dolist (scn scenes)
        ; write size and origin if necessary
        (cond ((or isanimatedgif ismultipage)
                (format cmdstorage "~%set size 1.0, 1.0~%")
                (format cmdstorage "set obj 1 rectangle behind from screen 0.0,0.0 to screen 1.0,1.0~%") )
              (t ; it's not an animated gif
                (setf thisalloc (car alloc))
                (setf alloc (cdr alloc))
                (cond
                  (thisalloc ; user defined scene allocation
                     (setf origin1 (first thisalloc)
                           origin2 (second thisalloc)
                           size1   (third thisalloc)
                           size2   (fourth thisalloc)))
                  (t ; automatic scene allocation
                     (setf origin1 (* width (mod nilcounter ncols))
                           origin2 (* height (- nrows 1.0 (floor (/ nilcounter ncols))))
                           size1   width
                           size2   height)
                     (incf nilcounter)))
                (format cmdstorage "~%set size ~a, ~a~%" size1 size2)
                (format cmdstorage "set origin ~a, ~a~%" origin1 origin2)
                (unless (or *multiplot-is-active*
                            (member (get-option '$terminal) '($epslatex $epslatex_standalone)))
                  (format cmdstorage "set obj 1 rectangle behind from screen ~a,~a to screen ~a,~a~%" 
                                     origin1 origin2 (+ origin1 size1 ) (+ origin2 size2)))  ))
        (setf is1stobj t
              biglist '()
              grouplist '())
        (format cmdstorage "~a" (second scn))
        (cond ((= (first scn) 2)    ; it's a 2d scene
                 (setf scene-short-description '(($gr2d simp)))
                 (format cmdstorage "plot "))
              ((= (first scn) 3)    ; it's a 3d scene
                 (setf scene-short-description '(($gr3d simp)))
                 (format cmdstorage "splot ")))
        (dolist (obj (third scn))
           (setf scene-short-description
                 (cons (gr-object-name obj) scene-short-description))
           (if is1stobj
             (setf is1stobj nil)
             (format cmdstorage ", \\~%")  )
           (let ((pcom (gr-object-command obj)))
             (cond
               ((listp pcom)
                  (while (consp pcom)
                    (format cmdstorage "~a~a~a~a"
                                       datapath
                                       (format nil " index ~a" (incf i))
                                       (pop pcom)
                                       (if (null pcom)
                                           ""
                                           "," )) ) )
               (t (format cmdstorage "~a~a~a"
                                     datapath
                                     (format nil " index ~a" (incf i))
                                     pcom) )))
           (setf grouplist (append grouplist (gr-object-groups obj)))
           (setf biglist (append biglist (gr-object-points obj))) )

        ; let's write data in data.gnuplot
        (do ( (blis biglist (cdr blis))
              (glis grouplist (cdr glis) ))
            ((null blis) 'done)
          (let* ((vect (car blis))
                 (k (length vect))
                 (ncol (caar glis))
                 (l 0)
                 (m (cadar glis))
                 (non-numeric-region nil)
                 coordinates)
             (cond
                ((= m 0)     ; no blank lines
                   (do ((cont 0 (+ cont ncol)))
                       ((= cont k) 'done)
                     (setf coordinates (subseq vect cont (+ cont ncol)))
                     ; control of non numeric y values,
                     ; code related to draw_realpart
                     (cond
                       (non-numeric-region
                         (when (numberp (aref coordinates 1))
                           (setf non-numeric-region nil)
                           (write-subarray coordinates datastorage) ))
                       (t
                         (cond
                           ((numberp (aref coordinates 1))
                             (write-subarray coordinates datastorage))
                           (t
                             (setf non-numeric-region t)
                             (format datastorage "~%")))))) )

                (t           ; blank lines every m lines
                   (do ((cont 0 (+ cont ncol)))
                       ((= cont k) 'done)
                     (when (eql l m)
                           (format datastorage "~%")
                           (setf l 0) )
                     (write-subarray (subseq vect cont (+ cont ncol)) datastorage)
                     (incf l)))))
          (format datastorage "~%~%") )
        (incf counter)
        (setf scenes-list (cons (reverse scene-short-description) scenes-list)) ))  ; end let-dolist scenes
    (close datastorage)

    (cond ((or isanimatedgif ismultipage)  ; this is an animated gif or multipage plot file
             (if isanimatedgif
               (format cmdstorage "~%unset output~%quit~%~%")
               (format cmdstorage "~%set term dumb~%~%") )
             (close cmdstorage)
	     #+(or (and sbcl win32) (and sbcl win64) (and ccl windows))
             ($system $gnuplot_command gfn)
	     #-(or (and sbcl win32) (and sbcl win64) (and ccl windows))
	     ($system (format nil "~a \"~a\"" 
			      $gnuplot_command
			      gfn) ))
          (t ; non animated gif
             ; command file maxout.gnuplot is now ready
             (format cmdstorage "~%")
             (cond ((> (length scenes) 1)
                      (format cmdstorage "unset multiplot~%"))
                   ; if we want to save the coordinates in a file,
                   ; print them when hitting the x key after clicking the mouse button
                   ((not (string= (get-option '$xy_file) ""))
                      (format cmdstorage
                              "set print \"~a\" append~%bind x \"print MOUSE_X,MOUSE_Y\"~%"
                              (get-option '$xy_file))) )

             ; in svg and pdfcairo terminals it is necessary to unset output to force
	     ; Gnuplot to write the last few bytes ("</svg>" in the svg case)
	     ; at the end of the file. On windows in all other terminals that write
	     ; to files if the output isn't unset the file isn't closed and therefore
	     ; cannot be moved or removed after a plot is finished.
	     ; 
	     ; If the plot isn't written to a file the variable "output" is empty and
	     ; unused and unsetting it a second time doesn't change anything
	     ; => It is always save to unset the output at the end of a scene.
             (format cmdstorage "unset output~%")
             (close cmdstorage)
             ; get the plot
             (cond
                ; connect to gnuplot via pipes
                ((and (not *windows-OS*)
                      (member (get-option '$terminal) '($screen $aquaterm $wxt $x11 $qt))
                      (equal $draw_renderer '$gnuplot_pipes))
                   (check-gnuplot-process)
                   (when (not *multiplot-is-active*) ; not in a one window multiplot
                     (send-gnuplot-command "unset output"))
                   (send-gnuplot-command "reset")
                   (send-gnuplot-command
                        (format nil "load '~a'" gfn)))
                ; call gnuplot via system command
                (t

		 #+(or (and sbcl win32) (and sbcl win64) (and ccl windows))
		 (if (member (get-option '$terminal) '($screen $aquaterm $wxt $x11 $qt))
		     ($system $gnuplot_command "-persist" gfn)
		     ($system $gnuplot_command gfn))
		 #-(or (and sbcl win32) (and sbcl win64) (and ccl windows))
		 ($system (if (member (get-option '$terminal) '($screen $aquaterm $wxt $x11 $qt))
			      (format nil "~a ~a"
				      $gnuplot_command
				      (format nil $gnuplot_view_args gfn))
			      (format nil "~a \"~a\"" 
				      $gnuplot_command
				      gfn))) ))))

    ; the output is a simplified description of the scene(s)
    (reverse scenes-list)) )


;; This function transforms an integer number into
;; a string, adding zeros at the left side until the
;; length of the string equals 10. This function is
;; useful to name a sequence of frames.
(defun $add_zeroes (num)
   (format nil "~10,'0d" ($sconcat num)) )


;; copies current plot in window into a file
(defun $draw_file (&rest opts)
 (let (str)
   (dolist (x opts)
      (if (equal ($op x) "=")
         (update-gr-option ($lhs x) ($rhs x))
         (merror "draw: item ~M is not recognized as an option assignment" x)))
   (case (get-option '$terminal)
      ($canvas (setf str (format nil "set terminal canvas enhanced ~a size ~a, ~a~%set out '~a.html'"
				 (write-font-type)
				 (round (first (get-option '$dimensions)))
				 (round (second (get-option '$dimensions)))
				 (get-option '$file_name))))
      ($png (setf str (format nil "set terminal png enhanced truecolor ~a size ~a, ~a~%set out '~a.png'"
                           (write-font-type)
                           (round (first (get-option '$dimensions)))
                           (round (second (get-option '$dimensions)))
                           (get-option '$file_name) ) ))
      ($pngcairo (setf str (format nil "set terminal pngcairo dashed enhanced truecolor ~a size ~a, ~a~%set out '~a.png'"
                           (write-font-type)
                           (round (first (get-option '$dimensions)))
                           (round (second (get-option '$dimensions)))
                           (get-option '$file_name) ) ))
      ($eps (setf str (format nil "set terminal postscript dashed eps enhanced ~a size ~acm, ~acm~%set out '~a.eps'"
                           (write-font-type) ; other alternatives are Arial, Courier
                           (/ (first (get-option '$dimensions)) 100.0)
                           (/ (second (get-option '$dimensions)) 100.0)
                           (get-option '$file_name))))
      ($epslatex (format str "set terminal epslatex ~a color dashed size ~acm, ~acm~%set out '~a.tex'"
                           (write-font-type)
                           (/ (first (get-option '$dimensions)) 100.0)
                           (/ (second (get-option '$dimensions)) 100.0)
                           (get-option '$file_name)))
      ($epslatex_standalone (format str "set terminal epslatex dashed standalone ~a color size ~acm, ~acm~%set out '~a.tex'"
                           (write-font-type)
                           (/ (first (get-option '$dimensions)) 100.0)
                           (/ (second (get-option '$dimensions)) 100.0)
                           (get-option '$file_name)))
      ($eps_color (setf str (format nil "set terminal postscript dashed eps enhanced ~a color size ~acm, ~acm~%set out '~a.eps'"
                           (write-font-type)
                           (/ (first (get-option '$dimensions)) 100.0)
                           (/ (second (get-option '$dimensions)) 100.0)
                           (get-option '$file_name))))
      ($pdf (setf str (format nil "set terminal pdf dashed enhanced ~a color size ~acm, ~acm~%set out '~a.pdf'"
                           (write-font-type)
                           (/ (first (get-option '$dimensions)) 100.0)
                           (/ (second (get-option '$dimensions)) 100.0)
                           (get-option '$file_name))))
      ($pdfcairo (setf str (format nil "set terminal pdfcairo dashed enhanced ~a color size ~acm, ~acm~%set out '~a.pdf'"
                           (write-font-type)
                           (/ (first (get-option '$dimensions)) 100.0)
                           (/ (second (get-option '$dimensions)) 100.0)
                           (get-option '$file_name))))
      ($jpg (setf str (format nil "set terminal jpeg ~a size ~a, ~a~%set out '~a.jpg'"
                           (write-font-type)
                           (round (first (get-option '$dimensions)))
                           (round (second (get-option '$dimensions)))
                           (get-option '$file_name))))
      ($gif (setf str (format nil "set terminal gif ~a size ~a, ~a~%set out '~a.gif'"
                           (write-font-type)
                           (round (first (get-option '$dimensions)))
                           (round (second (get-option '$dimensions)))
                           (get-option '$file_name))))
      ($svg (setf str (format nil "set terminal svg dashed enhanced ~a size ~a, ~a~%set out '~a.svg'"
			   (write-font-type)
                           (round (first (get-option '$dimensions)))
                           (round (second (get-option '$dimensions)))
                           (get-option '$file_name))))
      (otherwise (merror "draw: not a file format")))
   (send-gnuplot-command (format nil "~a~%replot~%unset output~%" str)) ))


;; When working with multiple windows, for example
;; terminal = [wxt, 5], only the newest window is active.
;; This function activates any other previous window at will.
(defun $activate_window (term num)
   (when (or (not (member term '($screen $wxt $aquaterm)))
             (not (integerp num))
             (< num 0) )
      (merror "draw: Incorrect terminal or window number"))
   (when *windows-OS*
      (merror "draw: Multiple windows are not allowed in Windows systems"))
   (let (str)
      (case term
         ($wxt      (setf str "wxt"))
         ($aquaterm (setf str "aquaterm"))
         ($qt       (setf str "qt"))
         (otherwise (setf str "x11")))
      (send-gnuplot-command (format nil "set terminal ~a ~a~%" str num))   ))


