#lang typed/racket/base

(require typed/racket/class racket/match racket/list
         (only-in typed/pict pict)
         plot/utils
         "../common/type-doc.rkt"
         "../common/utils.rkt")

(provide (all-defined-out))

;; ===================================================================================================
  One contour line in 3D ( using marching squares )

(: isoline3d-render-proc (-> 2D-Sampler Real Positive-Integer
                             Plot-Color Nonnegative-Real Plot-Pen-Style
                             Nonnegative-Real
                             3D-Render-Proc))
(define ((isoline3d-render-proc f z samples color width style alpha) area)
  (match-define (vector x-ivl y-ivl z-ivl) (send area get-bounds-rect))
  (match-define (ivl z-min z-max) z-ivl)
  (define num (animated-samples samples))
  (define sample (f (vector x-ivl y-ivl) (vector num num)))
  
  (when (and z-min z-max (<= z-min z z-max))
    (send area put-alpha alpha)
    (send area put-pen color width style)
    (for-2d-sample
     (xa xb ya yb z1 z2 z3 z4) sample
     (for ([line  (in-list (heights->lines xa xb ya yb z z1 z2 z3 z4))])
       (match-define (list v1 v2) line)
       (send area put-line v1 v2))))
  (void))

(:: isoline3d
    (->* [(-> Real Real Real) Real]
         [(U #f Real) (U #f Real)
          (U #f Real) (U #f Real)
          #:z-min (U #f Real) #:z-max (U #f Real)
          #:samples Positive-Integer
          #:color Plot-Color
          #:width Nonnegative-Real
          #:style Plot-Pen-Style
          #:alpha Nonnegative-Real
          #:label (U String pict #f)]
         renderer3d))
(define (isoline3d f z
                   [x-min #f] [x-max #f]
                   [y-min #f] [y-max #f]
                   #:z-min [z-min #f] #:z-max [z-max #f]
                   #:samples [samples (plot3d-samples)]
                   #:color [color (line-color)]
                   #:width [width (line-width)]
                   #:style [style (line-style)]
                   #:alpha [alpha (line-alpha)]
                   #:label [label #f])
  (define fail/pos (make-raise-argument-error 'isoline3d f z x-min x-max y-min y-max))
  (define fail/kw (make-raise-keyword-error 'isoline3d))
  (cond
    [(not (rational? z))  (fail/pos "rational?" 1)]
    [(and x-min (not (rational? x-min)))  (fail/pos "#f or rational" 2)]
    [(and x-max (not (rational? x-max)))  (fail/pos "#f or rational" 3)]
    [(and y-min (not (rational? y-min)))  (fail/pos "#f or rational" 4)]
    [(and y-max (not (rational? y-max)))  (fail/pos "#f or rational" 5)]
    [(and z-min (not (rational? z-min)))  (fail/kw "#f or rational" '#:z-min z-min)]
    [(and z-max (not (rational? z-max)))  (fail/kw "#f or rational" '#:z-min z-max)]
    [(< samples 2)  (fail/kw "Integer >= 2" '#:samples samples)]
    [(or (> alpha 1) (not (rational? alpha)))  (fail/kw "real in [0,1]" '#:alpha alpha)]
    [else
     (let ([z-min  (if z-min z-min z)]
           [z-max  (if z-max z-max z)])
       (define x-ivl (ivl x-min x-max))
       (define y-ivl (ivl y-min y-max))
       (define z-ivl (ivl z-min z-max))
       (define g (2d-function->sampler f (vector x-ivl y-ivl)))
       (renderer3d (vector x-ivl y-ivl z-ivl)
                   #f default-ticks-fun
                   (and label (λ (_) (line-legend-entry label color width style)))
                   (isoline3d-render-proc g z samples color width style alpha)))]))

;; ===================================================================================================
  Contour lines in 3D ( using marching squares )

(: make-contours3d-label-and-render (-> 2D-Sampler Contour-Levels Positive-Integer
                                        (Plot-Colors (Listof Real))
                                        (Pen-Widths (Listof Real))
                                        (Plot-Pen-Styles (Listof Real))
                                        (Alphas (Listof Real))
                                        (U String pict #f)
                                        (Values (U #f (-> Rect (Treeof legend-entry)))
                                                3D-Render-Proc)))
(define (make-contours3d-label-and-render f levels samples colors widths styles alphas label)
  ;; g is a 2D-sampler, which is a memoized proc. Recalculation here should be cheap.
  ;; if we memoize here based on rect, smooth interactions are disabled (because of the call to `plot-z-ticks`)
  (define (calculate-zs/labels [rect : Rect]) : (Values 2d-sample (Listof Real) (Listof String))
    (match-define (vector x-ivl y-ivl z-ivl) rect)
    (match-define (ivl x-min x-max) x-ivl)
    (match-define (ivl y-min y-max) y-ivl)
    (match-define (ivl z-min z-max) z-ivl)
    (cond
      [(and z-min z-max)
       (define num (animated-samples samples))
       (define sample (f (vector x-ivl y-ivl) (vector num num)))
       ;; can't use the actual z ticks because some or all could be collapsed
       (match-define (list (tick #{zs : (Listof Real)}
                                 #{_ : (Listof Boolean)}
                                 #{labels : (Listof String)})
                           ...)
         (contour-ticks (plot-z-ticks) z-min z-max levels #f))
       (values sample zs labels)]
      [else
       (values (2d-sample '() '() #() #f #f) empty empty)]))

  (define label-proc
    (and label
         (λ ([rect : Rect])
           (define-values (_ zs labels) (calculate-zs/labels rect))
           (cond
             [(empty? zs) empty]
             [else
              (let* ([colors  (generate-list colors zs)]
                     [widths  (generate-list widths zs)]
                     [styles  (generate-list styles zs)])
                (line-legend-entries label zs labels colors widths styles))]))))

  (: render-proc 3D-Render-Proc)
  (define (render-proc area)
    (define-values (sample zs _) (calculate-zs/labels (send area get-bounds-rect)))
    (match-define (vector x-ivl y-ivl z-ivl) (send area get-bounds-rect))
    (match-define (ivl x-min x-max) x-ivl)
    (match-define (ivl y-min y-max) y-ivl)
    (match-define (ivl z-min z-max) z-ivl)
    (unless (empty? zs)
      (let* ([colors  (generate-list colors zs)]
             [widths  (generate-list widths zs)]
             [styles  (generate-list styles zs)]
             [alphas  (generate-list alphas zs)])
        (for ([z  (in-list zs)]
              [color  (in-cycle* (in-list colors))]
              [width : Nonnegative-Real  (in-cycle* (in-list widths))]
              [style  (in-cycle* (in-list styles))]
              [alpha : Nonnegative-Real  (in-cycle* (in-list alphas))])
          (send area put-alpha alpha)
          (send area put-pen color width style)
          (for-2d-sample
           (xa xb ya yb z1 z2 z3 z4) sample
           (for ([line  (in-list (heights->lines xa xb ya yb z z1 z2 z3 z4))])
             (match-define (list v1 v2) line)
             (send area put-line v1 v2)))))))

  (values label-proc render-proc))

(:: contours3d
    (->* [(-> Real Real Real)]
         [(U #f Real) (U #f Real)
          (U #f Real) (U #f Real)
          #:z-min (U #f Real) #:z-max (U #f Real)
          #:samples Positive-Integer
          #:levels Contour-Levels
          #:colors (Plot-Colors (Listof Real))
          #:widths (Pen-Widths (Listof Real))
          #:styles (Plot-Pen-Styles (Listof Real))
          #:alphas (Alphas (Listof Real))
          #:label (U String pict #f)]
         renderer3d))
(define (contours3d f
                    [x-min #f] [x-max #f]
                    [y-min #f] [y-max #f]
                    #:z-min [z-min #f] #:z-max [z-max #f]
                    #:samples [samples (plot3d-samples)]
                    #:levels [levels (contour-levels)]
                    #:colors [colors (contour-colors)]
                    #:widths [widths (contour-widths)]
                    #:styles [styles (contour-styles)]
                    #:alphas [alphas (contour-alphas)]
                    #:label [label #f])
  (define fail/pos (make-raise-argument-error 'contours3d f x-min x-max y-min y-max))
  (define fail/kw (make-raise-keyword-error 'contours3d))
  (cond
    [(and x-min (not (rational? x-min)))  (fail/pos "#f or rational" 1)]
    [(and x-max (not (rational? x-max)))  (fail/pos "#f or rational" 2)]
    [(and y-min (not (rational? y-min)))  (fail/pos "#f or rational" 3)]
    [(and y-max (not (rational? y-max)))  (fail/pos "#f or rational" 4)]
    [(and z-min (not (rational? z-min)))  (fail/kw "#f or rational" '#:z-min z-min)]
    [(and z-max (not (rational? z-max)))  (fail/kw "#f or rational" '#:z-min z-max)]
    [(< samples 2)  (fail/kw "Integer >= 2" '#:samples samples)]
    [else
     (define x-ivl (ivl x-min x-max))
     (define y-ivl (ivl y-min y-max))
     (define z-ivl (ivl z-min z-max))
     (define g (2d-function->sampler f (vector x-ivl y-ivl)))
     (define-values (label-proc render-proc)
       (make-contours3d-label-and-render g levels samples colors widths styles alphas label))
     (renderer3d (vector x-ivl y-ivl z-ivl)
                 (surface3d-bounds-fun g samples)
                 default-ticks-fun
                 label-proc render-proc)]))

;; ===================================================================================================
;; Contour intervals in 3D (using marching squares)

(: make-contour-intervals3d-label-and-renderer
   (-> 2D-Sampler Contour-Levels Positive-Integer
       (Plot-Colors (Listof ivl))
       (Plot-Brush-Styles (Listof ivl))
       (Plot-Colors (Listof ivl))
       (Pen-Widths (Listof ivl))
       (Plot-Pen-Styles (Listof ivl))
       (Plot-Colors (Listof Real))
       (Pen-Widths (Listof Real))
       (Plot-Pen-Styles (Listof Real))
       (Alphas (Listof ivl))
       (U String pict #f)
       (Values (U #f (-> Rect (Treeof legend-entry)))
               3D-Render-Proc)))
(define (make-contour-intervals3d-label-and-renderer
          f levels samples colors styles line-colors line-widths line-styles
          contour-colors contour-widths contour-styles alphas label)
  ;; g is a 2D-sampler, which is a memoized proc. Recalculation here should be cheap.
  ;; if we memoize here based on rect, smooth interactions are disabled (because of the call to `plot-z-ticks`)
  (define (calculate-zivls/labels [rect : Rect]) : (Values 2d-sample (Listof ivl) (Listof Real) (Listof String))
    (match-define (vector x-ivl y-ivl z-ivl) rect)
    (match-define (ivl x-min x-max) x-ivl)
    (match-define (ivl y-min y-max) y-ivl)
    (match-define (ivl z-min z-max) z-ivl)
    (cond
      [(and z-min z-max)
       (define num (animated-samples samples))
       (define sample (f (vector x-ivl y-ivl) (vector num num)))
       ;; can't use the actual z ticks because some or all could be collapsed
       (match-define (list (tick #{zs : (Listof Real)}
                                 #{_ : (Listof Boolean)}
                                 #{labels : (Listof String)})
                           ...)
         (contour-ticks (plot-z-ticks) z-min z-max levels #t))
     
       (define-values (z-ivls ivl-labels)
         (for/lists ([z-ivls : (Listof ivl)]
                     [ivl-labels : (Listof String)]
                     ) ([za  (in-list zs)]
                        [zb  (in-list (rest zs))]
                        [la  (in-list labels)]
                        [lb  (in-list (rest labels))])
           (values (ivl za zb) (format "[~a,~a]" la lb))))
          
       (values sample z-ivls zs ivl-labels)]
      [else
       (values (2d-sample '() '() #() #f #f) empty empty empty)]))

  (define label-proc
    (and label
         (λ ([rect : Rect])
           (define-values (_ z-ivls zs ivl-labels) (calculate-zivls/labels rect))
           (let* ([colors  (generate-list colors z-ivls)]
                  [styles  (generate-list styles z-ivls)]
                  [line-colors  (generate-list line-colors z-ivls)]
                  [line-widths  (generate-list line-widths z-ivls)]
                  [line-styles  (generate-list line-styles z-ivls)])
             (define n (- (length zs) 2))
             (define contour-colors*
               (append (list 0) (sequence-take (in-cycle* (generate-list contour-colors zs)) 0 n) (list 0)))
             (define contour-widths*
               (append (list 0) (sequence-take (in-cycle* (generate-list contour-widths zs)) 0 n) (list 0)))
             (define contour-styles*
               (append '(transparent) (sequence-take (in-cycle* (generate-list contour-styles zs)) 0 n)
                       '(transparent)))
       
             (cond [label  (interval-legend-entries
                            label z-ivls ivl-labels
                            colors styles line-colors line-widths line-styles
                            contour-colors* contour-widths* contour-styles*
                            (rest contour-colors*) (rest contour-widths*) (rest contour-styles*))]
                   [else  empty])))))
  
  (: render-proc 3D-Render-Proc)
  (define (render-proc area)
    (define-values (sample z-ivls zs _) (calculate-zivls/labels (send area get-bounds-rect)))
    (unless (empty? zs)
       
     
       (let* ([colors  (generate-list colors z-ivls)]
              [styles  (generate-list styles z-ivls)]
              [alphas  (generate-list alphas z-ivls)]
              [line-colors  (generate-list line-colors z-ivls)]
              [line-widths  (generate-list line-widths z-ivls)]
              [line-styles  (generate-list line-styles z-ivls)])
         (for ([za  (in-list zs)]
               [zb  (in-list (rest zs))]
               [color  (in-cycle* (in-list colors))]
               [style  (in-cycle* (in-list styles))]
               [alpha : Nonnegative-Real  (in-cycle* (in-list alphas))]
               [line-color  (in-cycle* (in-list line-colors))]
               [line-width : Nonnegative-Real  (in-cycle* (in-list line-widths))]
               [line-style  (in-cycle* (in-list line-styles))])
           (send area put-alpha alpha)
           (send area put-pen line-color line-width line-style)
           (send area put-brush color style)
           (for-2d-sample
            (xa xb ya yb z1 z2 z3 z4) sample
            (for ([vs  (in-list (heights->polys xa xb ya yb za zb z1 z2 z3 z4))])
              (define ls
                (for/list : (Listof Boolean) ([v1  (in-list (cons (last vs) vs))]
                                              [v2  (in-list vs)])
                  (define z1 (vector-ref v1 2))
                  (define z2 (vector-ref v2 2))
                  (not (or (and (= z1 za) (= z2 za))
                           (and (= z1 zb) (= z2 zb))))))
              (send area put-polygon vs 'both ls))))

         (define-values (_ render-proc)
           (make-contours3d-label-and-render f levels samples contour-colors contour-widths contour-styles
                                             alphas #f))
         (render-proc area)
       
         )))

  (values label-proc render-proc))

(:: contour-intervals3d
    (->* [(-> Real Real Real)]
         [(U #f Real) (U #f Real)
          (U #f Real) (U #f Real)
          #:z-min (U #f Real) #:z-max (U #f Real)
          #:samples Positive-Integer
          #:levels Contour-Levels
          #:colors (Plot-Colors (Listof ivl))
          #:styles (Plot-Brush-Styles (Listof ivl))
          #:line-colors (Plot-Colors (Listof ivl))
          #:line-widths (Pen-Widths (Listof ivl))
          #:line-styles (Plot-Pen-Styles (Listof ivl))
          #:contour-colors (Plot-Colors (Listof Real))
          #:contour-widths (Pen-Widths (Listof Real))
          #:contour-styles (Plot-Pen-Styles (Listof Real))
          #:alphas (Alphas (Listof ivl))
          #:label (U String pict #f)]
         renderer3d))
(define (contour-intervals3d f
                             [x-min #f] [x-max #f]
                             [y-min #f] [y-max #f]
                             #:z-min [z-min #f] #:z-max [z-max #f]
                             #:samples [samples (plot3d-samples)]
                             #:levels [levels (contour-levels)]
                             #:colors [colors (contour-interval-colors)]
                             #:styles [styles (contour-interval-styles)]
                             #:line-colors [line-colors (contour-interval-line-colors)]
                             #:line-widths [line-widths (contour-interval-line-widths)]
                             #:line-styles [line-styles (contour-interval-line-styles)]
                             #:contour-colors [contour-colors (contour-colors)]
                             #:contour-widths [contour-widths (contour-widths)]
                             #:contour-styles [contour-styles (contour-styles)]
                             #:alphas [alphas (contour-interval-alphas)]
                             #:label [label #f])
  (define fail/pos (make-raise-argument-error 'contour-intervals3d f x-min x-max y-min y-max))
  (define fail/kw (make-raise-keyword-error 'contour-intervals3d))
  (cond
    [(and x-min (not (rational? x-min)))  (fail/pos "#f or rational" 1)]
    [(and x-max (not (rational? x-max)))  (fail/pos "#f or rational" 2)]
    [(and y-min (not (rational? y-min)))  (fail/pos "#f or rational" 3)]
    [(and y-max (not (rational? y-max)))  (fail/pos "#f or rational" 4)]
    [(and z-min (not (rational? z-min)))  (fail/kw "#f or rational" '#:z-min z-min)]
    [(and z-max (not (rational? z-max)))  (fail/kw "#f or rational" '#:z-min z-max)]
    [(< samples 2)  (fail/kw "Integer >= 2" '#:samples samples)]
    [else
     (define x-ivl (ivl x-min x-max))
     (define y-ivl (ivl y-min y-max))
     (define z-ivl (ivl z-min z-max))
     (define g (2d-function->sampler f (vector x-ivl y-ivl)))
     (define-values (label-proc render-proc)
       (make-contour-intervals3d-label-and-renderer g levels samples colors styles
                                                    line-colors line-widths line-styles
                                                    contour-colors contour-widths contour-styles
                                                    alphas label))
     (renderer3d (vector x-ivl y-ivl z-ivl)
                 (surface3d-bounds-fun g samples)
                 default-ticks-fun
                 label-proc render-proc)]))

 ===================================================================================================
 ===================================================================================================
 g is a 2D-sampler, which is a memoized proc. Recalculation here should be cheap.
 if we memoize here based on rect, smooth interactions are disabled (because of the call to `plot-z-ticks`)
 can't use the actual z ticks because some or all could be collapsed
 ===================================================================================================
 Contour intervals in 3D (using marching squares)
 g is a 2D-sampler, which is a memoized proc. Recalculation here should be cheap.
 if we memoize here based on rect, smooth interactions are disabled (because of the call to `plot-z-ticks`)
 can't use the actual z ticks because some or all could be collapsed
#lang typed/racket/base

(require typed/racket/class racket/match racket/list
         (only-in typed/pict pict)
         plot/utils
         "../common/type-doc.rkt"
         "../common/utils.rkt")

(provide (all-defined-out))

  One contour line in 3D ( using marching squares )

(: isoline3d-render-proc (-> 2D-Sampler Real Positive-Integer
                             Plot-Color Nonnegative-Real Plot-Pen-Style
                             Nonnegative-Real
                             3D-Render-Proc))
(define ((isoline3d-render-proc f z samples color width style alpha) area)
  (match-define (vector x-ivl y-ivl z-ivl) (send area get-bounds-rect))
  (match-define (ivl z-min z-max) z-ivl)
  (define num (animated-samples samples))
  (define sample (f (vector x-ivl y-ivl) (vector num num)))
  
  (when (and z-min z-max (<= z-min z z-max))
    (send area put-alpha alpha)
    (send area put-pen color width style)
    (for-2d-sample
     (xa xb ya yb z1 z2 z3 z4) sample
     (for ([line  (in-list (heights->lines xa xb ya yb z z1 z2 z3 z4))])
       (match-define (list v1 v2) line)
       (send area put-line v1 v2))))
  (void))

(:: isoline3d
    (->* [(-> Real Real Real) Real]
         [(U #f Real) (U #f Real)
          (U #f Real) (U #f Real)
          #:z-min (U #f Real) #:z-max (U #f Real)
          #:samples Positive-Integer
          #:color Plot-Color
          #:width Nonnegative-Real
          #:style Plot-Pen-Style
          #:alpha Nonnegative-Real
          #:label (U String pict #f)]
         renderer3d))
(define (isoline3d f z
                   [x-min #f] [x-max #f]
                   [y-min #f] [y-max #f]
                   #:z-min [z-min #f] #:z-max [z-max #f]
                   #:samples [samples (plot3d-samples)]
                   #:color [color (line-color)]
                   #:width [width (line-width)]
                   #:style [style (line-style)]
                   #:alpha [alpha (line-alpha)]
                   #:label [label #f])
  (define fail/pos (make-raise-argument-error 'isoline3d f z x-min x-max y-min y-max))
  (define fail/kw (make-raise-keyword-error 'isoline3d))
  (cond
    [(not (rational? z))  (fail/pos "rational?" 1)]
    [(and x-min (not (rational? x-min)))  (fail/pos "#f or rational" 2)]
    [(and x-max (not (rational? x-max)))  (fail/pos "#f or rational" 3)]
    [(and y-min (not (rational? y-min)))  (fail/pos "#f or rational" 4)]
    [(and y-max (not (rational? y-max)))  (fail/pos "#f or rational" 5)]
    [(and z-min (not (rational? z-min)))  (fail/kw "#f or rational" '#:z-min z-min)]
    [(and z-max (not (rational? z-max)))  (fail/kw "#f or rational" '#:z-min z-max)]
    [(< samples 2)  (fail/kw "Integer >= 2" '#:samples samples)]
    [(or (> alpha 1) (not (rational? alpha)))  (fail/kw "real in [0,1]" '#:alpha alpha)]
    [else
     (let ([z-min  (if z-min z-min z)]
           [z-max  (if z-max z-max z)])
       (define x-ivl (ivl x-min x-max))
       (define y-ivl (ivl y-min y-max))
       (define z-ivl (ivl z-min z-max))
       (define g (2d-function->sampler f (vector x-ivl y-ivl)))
       (renderer3d (vector x-ivl y-ivl z-ivl)
                   #f default-ticks-fun
                   (and label (λ (_) (line-legend-entry label color width style)))
                   (isoline3d-render-proc g z samples color width style alpha)))]))

  Contour lines in 3D ( using marching squares )

(: make-contours3d-label-and-render (-> 2D-Sampler Contour-Levels Positive-Integer
                                        (Plot-Colors (Listof Real))
                                        (Pen-Widths (Listof Real))
                                        (Plot-Pen-Styles (Listof Real))
                                        (Alphas (Listof Real))
                                        (U String pict #f)
                                        (Values (U #f (-> Rect (Treeof legend-entry)))
                                                3D-Render-Proc)))
(define (make-contours3d-label-and-render f levels samples colors widths styles alphas label)
  (define (calculate-zs/labels [rect : Rect]) : (Values 2d-sample (Listof Real) (Listof String))
    (match-define (vector x-ivl y-ivl z-ivl) rect)
    (match-define (ivl x-min x-max) x-ivl)
    (match-define (ivl y-min y-max) y-ivl)
    (match-define (ivl z-min z-max) z-ivl)
    (cond
      [(and z-min z-max)
       (define num (animated-samples samples))
       (define sample (f (vector x-ivl y-ivl) (vector num num)))
       (match-define (list (tick #{zs : (Listof Real)}
                                 #{_ : (Listof Boolean)}
                                 #{labels : (Listof String)})
                           ...)
         (contour-ticks (plot-z-ticks) z-min z-max levels #f))
       (values sample zs labels)]
      [else
       (values (2d-sample '() '() #() #f #f) empty empty)]))

  (define label-proc
    (and label
         (λ ([rect : Rect])
           (define-values (_ zs labels) (calculate-zs/labels rect))
           (cond
             [(empty? zs) empty]
             [else
              (let* ([colors  (generate-list colors zs)]
                     [widths  (generate-list widths zs)]
                     [styles  (generate-list styles zs)])
                (line-legend-entries label zs labels colors widths styles))]))))

  (: render-proc 3D-Render-Proc)
  (define (render-proc area)
    (define-values (sample zs _) (calculate-zs/labels (send area get-bounds-rect)))
    (match-define (vector x-ivl y-ivl z-ivl) (send area get-bounds-rect))
    (match-define (ivl x-min x-max) x-ivl)
    (match-define (ivl y-min y-max) y-ivl)
    (match-define (ivl z-min z-max) z-ivl)
    (unless (empty? zs)
      (let* ([colors  (generate-list colors zs)]
             [widths  (generate-list widths zs)]
             [styles  (generate-list styles zs)]
             [alphas  (generate-list alphas zs)])
        (for ([z  (in-list zs)]
              [color  (in-cycle* (in-list colors))]
              [width : Nonnegative-Real  (in-cycle* (in-list widths))]
              [style  (in-cycle* (in-list styles))]
              [alpha : Nonnegative-Real  (in-cycle* (in-list alphas))])
          (send area put-alpha alpha)
          (send area put-pen color width style)
          (for-2d-sample
           (xa xb ya yb z1 z2 z3 z4) sample
           (for ([line  (in-list (heights->lines xa xb ya yb z z1 z2 z3 z4))])
             (match-define (list v1 v2) line)
             (send area put-line v1 v2)))))))

  (values label-proc render-proc))

(:: contours3d
    (->* [(-> Real Real Real)]
         [(U #f Real) (U #f Real)
          (U #f Real) (U #f Real)
          #:z-min (U #f Real) #:z-max (U #f Real)
          #:samples Positive-Integer
          #:levels Contour-Levels
          #:colors (Plot-Colors (Listof Real))
          #:widths (Pen-Widths (Listof Real))
          #:styles (Plot-Pen-Styles (Listof Real))
          #:alphas (Alphas (Listof Real))
          #:label (U String pict #f)]
         renderer3d))
(define (contours3d f
                    [x-min #f] [x-max #f]
                    [y-min #f] [y-max #f]
                    #:z-min [z-min #f] #:z-max [z-max #f]
                    #:samples [samples (plot3d-samples)]
                    #:levels [levels (contour-levels)]
                    #:colors [colors (contour-colors)]
                    #:widths [widths (contour-widths)]
                    #:styles [styles (contour-styles)]
                    #:alphas [alphas (contour-alphas)]
                    #:label [label #f])
  (define fail/pos (make-raise-argument-error 'contours3d f x-min x-max y-min y-max))
  (define fail/kw (make-raise-keyword-error 'contours3d))
  (cond
    [(and x-min (not (rational? x-min)))  (fail/pos "#f or rational" 1)]
    [(and x-max (not (rational? x-max)))  (fail/pos "#f or rational" 2)]
    [(and y-min (not (rational? y-min)))  (fail/pos "#f or rational" 3)]
    [(and y-max (not (rational? y-max)))  (fail/pos "#f or rational" 4)]
    [(and z-min (not (rational? z-min)))  (fail/kw "#f or rational" '#:z-min z-min)]
    [(and z-max (not (rational? z-max)))  (fail/kw "#f or rational" '#:z-min z-max)]
    [(< samples 2)  (fail/kw "Integer >= 2" '#:samples samples)]
    [else
     (define x-ivl (ivl x-min x-max))
     (define y-ivl (ivl y-min y-max))
     (define z-ivl (ivl z-min z-max))
     (define g (2d-function->sampler f (vector x-ivl y-ivl)))
     (define-values (label-proc render-proc)
       (make-contours3d-label-and-render g levels samples colors widths styles alphas label))
     (renderer3d (vector x-ivl y-ivl z-ivl)
                 (surface3d-bounds-fun g samples)
                 default-ticks-fun
                 label-proc render-proc)]))


(: make-contour-intervals3d-label-and-renderer
   (-> 2D-Sampler Contour-Levels Positive-Integer
       (Plot-Colors (Listof ivl))
       (Plot-Brush-Styles (Listof ivl))
       (Plot-Colors (Listof ivl))
       (Pen-Widths (Listof ivl))
       (Plot-Pen-Styles (Listof ivl))
       (Plot-Colors (Listof Real))
       (Pen-Widths (Listof Real))
       (Plot-Pen-Styles (Listof Real))
       (Alphas (Listof ivl))
       (U String pict #f)
       (Values (U #f (-> Rect (Treeof legend-entry)))
               3D-Render-Proc)))
(define (make-contour-intervals3d-label-and-renderer
          f levels samples colors styles line-colors line-widths line-styles
          contour-colors contour-widths contour-styles alphas label)
  (define (calculate-zivls/labels [rect : Rect]) : (Values 2d-sample (Listof ivl) (Listof Real) (Listof String))
    (match-define (vector x-ivl y-ivl z-ivl) rect)
    (match-define (ivl x-min x-max) x-ivl)
    (match-define (ivl y-min y-max) y-ivl)
    (match-define (ivl z-min z-max) z-ivl)
    (cond
      [(and z-min z-max)
       (define num (animated-samples samples))
       (define sample (f (vector x-ivl y-ivl) (vector num num)))
       (match-define (list (tick #{zs : (Listof Real)}
                                 #{_ : (Listof Boolean)}
                                 #{labels : (Listof String)})
                           ...)
         (contour-ticks (plot-z-ticks) z-min z-max levels #t))
     
       (define-values (z-ivls ivl-labels)
         (for/lists ([z-ivls : (Listof ivl)]
                     [ivl-labels : (Listof String)]
                     ) ([za  (in-list zs)]
                        [zb  (in-list (rest zs))]
                        [la  (in-list labels)]
                        [lb  (in-list (rest labels))])
           (values (ivl za zb) (format "[~a,~a]" la lb))))
          
       (values sample z-ivls zs ivl-labels)]
      [else
       (values (2d-sample '() '() #() #f #f) empty empty empty)]))

  (define label-proc
    (and label
         (λ ([rect : Rect])
           (define-values (_ z-ivls zs ivl-labels) (calculate-zivls/labels rect))
           (let* ([colors  (generate-list colors z-ivls)]
                  [styles  (generate-list styles z-ivls)]
                  [line-colors  (generate-list line-colors z-ivls)]
                  [line-widths  (generate-list line-widths z-ivls)]
                  [line-styles  (generate-list line-styles z-ivls)])
             (define n (- (length zs) 2))
             (define contour-colors*
               (append (list 0) (sequence-take (in-cycle* (generate-list contour-colors zs)) 0 n) (list 0)))
             (define contour-widths*
               (append (list 0) (sequence-take (in-cycle* (generate-list contour-widths zs)) 0 n) (list 0)))
             (define contour-styles*
               (append '(transparent) (sequence-take (in-cycle* (generate-list contour-styles zs)) 0 n)
                       '(transparent)))
       
             (cond [label  (interval-legend-entries
                            label z-ivls ivl-labels
                            colors styles line-colors line-widths line-styles
                            contour-colors* contour-widths* contour-styles*
                            (rest contour-colors*) (rest contour-widths*) (rest contour-styles*))]
                   [else  empty])))))
  
  (: render-proc 3D-Render-Proc)
  (define (render-proc area)
    (define-values (sample z-ivls zs _) (calculate-zivls/labels (send area get-bounds-rect)))
    (unless (empty? zs)
       
     
       (let* ([colors  (generate-list colors z-ivls)]
              [styles  (generate-list styles z-ivls)]
              [alphas  (generate-list alphas z-ivls)]
              [line-colors  (generate-list line-colors z-ivls)]
              [line-widths  (generate-list line-widths z-ivls)]
              [line-styles  (generate-list line-styles z-ivls)])
         (for ([za  (in-list zs)]
               [zb  (in-list (rest zs))]
               [color  (in-cycle* (in-list colors))]
               [style  (in-cycle* (in-list styles))]
               [alpha : Nonnegative-Real  (in-cycle* (in-list alphas))]
               [line-color  (in-cycle* (in-list line-colors))]
               [line-width : Nonnegative-Real  (in-cycle* (in-list line-widths))]
               [line-style  (in-cycle* (in-list line-styles))])
           (send area put-alpha alpha)
           (send area put-pen line-color line-width line-style)
           (send area put-brush color style)
           (for-2d-sample
            (xa xb ya yb z1 z2 z3 z4) sample
            (for ([vs  (in-list (heights->polys xa xb ya yb za zb z1 z2 z3 z4))])
              (define ls
                (for/list : (Listof Boolean) ([v1  (in-list (cons (last vs) vs))]
                                              [v2  (in-list vs)])
                  (define z1 (vector-ref v1 2))
                  (define z2 (vector-ref v2 2))
                  (not (or (and (= z1 za) (= z2 za))
                           (and (= z1 zb) (= z2 zb))))))
              (send area put-polygon vs 'both ls))))

         (define-values (_ render-proc)
           (make-contours3d-label-and-render f levels samples contour-colors contour-widths contour-styles
                                             alphas #f))
         (render-proc area)
       
         )))

  (values label-proc render-proc))

(:: contour-intervals3d
    (->* [(-> Real Real Real)]
         [(U #f Real) (U #f Real)
          (U #f Real) (U #f Real)
          #:z-min (U #f Real) #:z-max (U #f Real)
          #:samples Positive-Integer
          #:levels Contour-Levels
          #:colors (Plot-Colors (Listof ivl))
          #:styles (Plot-Brush-Styles (Listof ivl))
          #:line-colors (Plot-Colors (Listof ivl))
          #:line-widths (Pen-Widths (Listof ivl))
          #:line-styles (Plot-Pen-Styles (Listof ivl))
          #:contour-colors (Plot-Colors (Listof Real))
          #:contour-widths (Pen-Widths (Listof Real))
          #:contour-styles (Plot-Pen-Styles (Listof Real))
          #:alphas (Alphas (Listof ivl))
          #:label (U String pict #f)]
         renderer3d))
(define (contour-intervals3d f
                             [x-min #f] [x-max #f]
                             [y-min #f] [y-max #f]
                             #:z-min [z-min #f] #:z-max [z-max #f]
                             #:samples [samples (plot3d-samples)]
                             #:levels [levels (contour-levels)]
                             #:colors [colors (contour-interval-colors)]
                             #:styles [styles (contour-interval-styles)]
                             #:line-colors [line-colors (contour-interval-line-colors)]
                             #:line-widths [line-widths (contour-interval-line-widths)]
                             #:line-styles [line-styles (contour-interval-line-styles)]
                             #:contour-colors [contour-colors (contour-colors)]
                             #:contour-widths [contour-widths (contour-widths)]
                             #:contour-styles [contour-styles (contour-styles)]
                             #:alphas [alphas (contour-interval-alphas)]
                             #:label [label #f])
  (define fail/pos (make-raise-argument-error 'contour-intervals3d f x-min x-max y-min y-max))
  (define fail/kw (make-raise-keyword-error 'contour-intervals3d))
  (cond
    [(and x-min (not (rational? x-min)))  (fail/pos "#f or rational" 1)]
    [(and x-max (not (rational? x-max)))  (fail/pos "#f or rational" 2)]
    [(and y-min (not (rational? y-min)))  (fail/pos "#f or rational" 3)]
    [(and y-max (not (rational? y-max)))  (fail/pos "#f or rational" 4)]
    [(and z-min (not (rational? z-min)))  (fail/kw "#f or rational" '#:z-min z-min)]
    [(and z-max (not (rational? z-max)))  (fail/kw "#f or rational" '#:z-min z-max)]
    [(< samples 2)  (fail/kw "Integer >= 2" '#:samples samples)]
    [else
     (define x-ivl (ivl x-min x-max))
     (define y-ivl (ivl y-min y-max))
     (define z-ivl (ivl z-min z-max))
     (define g (2d-function->sampler f (vector x-ivl y-ivl)))
     (define-values (label-proc render-proc)
       (make-contour-intervals3d-label-and-renderer g levels samples colors styles
                                                    line-colors line-widths line-styles
                                                    contour-colors contour-widths contour-styles
                                                    alphas label))
     (renderer3d (vector x-ivl y-ivl z-ivl)
                 (surface3d-bounds-fun g samples)
                 default-ticks-fun
                 label-proc render-proc)]))
