365ee2c70d
This makes it more efficient to plot piecewise functions by drawing each piece with one renderer, and possible to plot functions with discontinuities by using a renderer to draw each continuous piece.
302 lines
14 KiB
Racket
302 lines
14 KiB
Racket
#lang racket/base
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;; Functions that sample from functions, and functions that create memoized samplers.
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(require racket/match racket/flonum racket/math racket/contract racket/list racket/vector
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unstable/latent-contract/defthing
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"math.rkt"
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"axis-transform.rkt")
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(provide (all-defined-out))
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(defproc (build-linear-seq [start real?] [step real?]
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[num exact-nonnegative-integer?]
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[min-val real? start]
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[max-val real? (+ start (* (- num 1) step))]
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) (listof real?)
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(define n-start (max 0 (inexact->exact (floor (/ (- min-val start) step)))))
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(define n-end (min num (+ (inexact->exact (ceiling (/ (- max-val start) step))) 1)))
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(for*/list ([n (in-range n-start n-end)]
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[x (in-value (+ start (* n step)))]
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#:when (<= min-val x max-val))
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x))
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(defproc (linear-seq [start real?] [end real?] [num exact-nonnegative-integer?]
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[#:start? start? boolean? #t]
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[#:end? end? boolean? #t]) (listof real?)
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(cond
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[(zero? num) empty]
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; ambiguous request: arbitrarily return start
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[(and start? end? (= 1 num)) (list start)]
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[else
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(define size (- end start))
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(define step (/ size (cond [(and start? end?) (- num 1)]
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[(or start? end?) (- num 1/2)]
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[else num])))
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(define real-start
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(cond [start? start]
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[else (+ start (* 1/2 step))]))
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(build-linear-seq real-start step num)]))
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(defproc (linear-seq* [points (listof real?)] [num exact-nonnegative-integer?]
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[#:start? start? boolean? #t]
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[#:end? end? boolean? #t]) (listof real?)
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(let/ec return
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(when (empty? points) (raise-type-error 'linear-seq* "nonempty (listof real?)" points))
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(define pts (list->vector points))
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(define len (vector-length pts))
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(define indexes (linear-seq 0 (sub1 len) num #:start? start? #:end? end?))
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(define int-parts (map floor indexes))
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(define frac-parts (map - indexes int-parts))
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(map (λ (i f)
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(if (= i (sub1 len))
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(vector-ref pts i)
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(blend (vector-ref pts (add1 i)) (vector-ref pts i) f)))
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int-parts frac-parts)))
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(defproc (nonlinear-seq [start real?] [end real?] [num exact-nonnegative-integer?]
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[transform axis-transform/c]
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[#:start? start? boolean? #t]
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[#:end? end? boolean? #t]) (listof real?)
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(match-define (invertible-function _ finv) (apply-axis-transform transform start end))
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(map finv (linear-seq start end num #:start? start? #:end? end?)))
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;; ===================================================================================================
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(define (ensure-endpoints xs i-min i-max)
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(cond [(empty? xs) (cond [(i-min . = . i-max) (list i-min)]
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[else (list i-min i-max)])]
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[else
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(define xs-min (first xs))
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(define xs-max (last xs))
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(let* ([xs (if (xs-min . <= . i-min) xs (cons i-min xs))]
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[xs (if (xs-max . >= . i-max) xs (append xs (list i-max)))])
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xs)]))
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(defproc (sample-points [outer-ivl rational-ivl?] [inner-ivl ivl?]
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[num exact-nonnegative-integer?]
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[transform axis-transform/c id-transform]) (listof real?)
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(let* ([inner-ivl (ivl-meet inner-ivl outer-ivl)]
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[inner-ivl (ivl-inexact->exact inner-ivl)]
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[outer-ivl (ivl-inexact->exact outer-ivl)])
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(match-define (ivl o-min o-max) outer-ivl)
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(match-define (ivl i-min i-max) inner-ivl)
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(match-define (invertible-function f finv) (apply-axis-transform transform o-min o-max))
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(cond
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[(ivl-empty? inner-ivl) empty]
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[(= num 0) empty]
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[(or (= o-min o-max) (= num 1))
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(cond [(<= i-min o-min i-max) (build-list num (λ _ o-min))]
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[else empty])]
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[else
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(define step (/ (- o-max o-min) (- num 1)))
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(let* ([xs (map finv (build-linear-seq o-min step num (f i-min) (f i-max)))]
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[xs (remove-duplicates (map (λ (x) (clamp-real x inner-ivl)) xs))])
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(ensure-endpoints xs i-min i-max))])))
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;; ===================================================================================================
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(struct mapped-function (f fmap) #:transparent
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#:property prop:procedure
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(λ (g x) ((mapped-function-f g) x)))
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(define (map* f xs)
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(match f
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#;; gives obviously wrong chaperone error (tries to apply a hash?):
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[(mapped-function _ fmap) (fmap xs)]
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[(? mapped-function?) ((mapped-function-fmap f) xs)]
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[_ (map f xs)]))
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;; ===================================================================================================
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;; Making memoized samplers
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(struct sample (xs ys y-min y-max) #:transparent)
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(struct 2d-sample (xs ys zss z-min z-max) #:transparent)
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(struct 3d-sample (xs ys zs dsss d-min d-max) #:transparent)
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(defcontract sampler/c
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(-> rational-ivl? exact-nonnegative-integer? sample?))
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(defcontract 2d-sampler/c
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(-> (vector/c rational-ivl? rational-ivl?)
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(vector/c exact-nonnegative-integer? exact-nonnegative-integer?)
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2d-sample?))
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(defcontract 3d-sampler/c
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(-> (vector/c rational-ivl? rational-ivl? rational-ivl?)
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(vector/c exact-nonnegative-integer? exact-nonnegative-integer? exact-nonnegative-integer?)
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3d-sample?))
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(defproc (make-function->sampler [transform-thnk (-> axis-transform/c)]
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) (-> (real? . -> . real?) ivl? sampler/c)
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(λ (f inner-ivl)
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(define memo (make-hash))
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(λ (outer-ivl num)
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(define tx (transform-thnk))
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(hash-ref! memo (vector outer-ivl num tx)
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(λ ()
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(define xs (sample-points outer-ivl inner-ivl num tx))
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(define ys (map* f xs))
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(define rys (filter rational? ys))
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(define-values (y-min y-max)
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(cond [(empty? rys) (values #f #f)]
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[else (values (apply min* rys) (apply max* rys))]))
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(sample xs ys
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(maybe-inexact->exact y-min)
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(maybe-inexact->exact y-max)))))))
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(defproc (make-2d-function->sampler [transform-x-thnk (-> axis-transform/c)]
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[transform-y-thnk (-> axis-transform/c)]
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) (-> (real? real? . -> . real?)
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(vector/c ivl? ivl?)
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2d-sampler/c)
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(λ (f inner-rect)
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(define memo (make-hash))
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(λ (outer-rect nums)
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(define tx (transform-x-thnk))
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(define ty (transform-y-thnk))
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(hash-ref! memo (vector outer-rect nums tx ty)
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(λ ()
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(match-define (vector outer-x-ivl outer-y-ivl) outer-rect)
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(match-define (vector inner-x-ivl inner-y-ivl) inner-rect)
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(match-define (vector x-num y-num) nums)
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(define xs (sample-points outer-x-ivl inner-x-ivl x-num tx))
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(define ys (sample-points outer-y-ivl inner-y-ivl y-num ty))
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(define z-min #f)
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(define z-max #f)
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(define zss (for/vector #:length (length ys) ([y (in-list ys)])
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(for/vector #:length (length xs) ([x (in-list xs)])
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(let ([z (f x y)])
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(when (rational? z)
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(unless (and z-min (z . >= . z-min)) (set! z-min z))
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(unless (and z-max (z . <= . z-max)) (set! z-max z)))
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z))))
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(2d-sample xs ys zss
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(maybe-inexact->exact z-min)
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(maybe-inexact->exact z-max)))))))
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(defproc (make-3d-function->sampler [transform-x-thnk (-> axis-transform/c)]
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[transform-y-thnk (-> axis-transform/c)]
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[transform-z-thnk (-> axis-transform/c)]
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) (-> (real? real? real? . -> . real?)
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(vector/c ivl? ivl? ivl?)
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3d-sampler/c)
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(λ (f inner-rect)
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(define memo (make-hash))
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(λ (outer-rect nums)
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(define tx (transform-x-thnk))
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(define ty (transform-y-thnk))
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(define tz (transform-z-thnk))
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(hash-ref! memo (vector outer-rect nums tx ty tz)
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(λ ()
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(match-define (vector outer-x-ivl outer-y-ivl outer-z-ivl) outer-rect)
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(match-define (vector inner-x-ivl inner-y-ivl inner-z-ivl) inner-rect)
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(match-define (vector x-num y-num z-num) nums)
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(define xs (sample-points outer-x-ivl inner-x-ivl x-num tx))
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(define ys (sample-points outer-y-ivl inner-y-ivl y-num ty))
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(define zs (sample-points outer-z-ivl inner-z-ivl z-num tz))
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(define d-min #f)
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(define d-max #f)
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(define dsss (for/vector #:length (length zs) ([z (in-list zs)])
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(for/vector #:length (length ys) ([y (in-list ys)])
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(for/vector #:length (length xs) ([x (in-list xs)])
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(let ([d (f x y z)])
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(when (rational? d)
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(unless (and d-min (d . >= . d-min)) (set! d-min d))
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(unless (and d-max (d . <= . d-max)) (set! d-max d)))
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d)))))
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(3d-sample xs ys zs dsss
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(maybe-inexact->exact d-min)
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(maybe-inexact->exact d-max)))))))
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(define-syntax-rule (for-2d-sample (xa xb ya yb z1 z2 z3 z4) sample expr ...)
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(let ()
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(match-define (2d-sample xs ys zss fz-min fz-max) sample)
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(define ya (first ys))
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(define zs0 (vector-ref zss 0))
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(for/fold ([ya ya] [zs0 zs0]) ([yb (in-list (rest ys))]
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[zs1 (in-vector zss 1)])
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(define xa (first xs))
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(define z1 (vector-ref zs0 0))
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(define z4 (vector-ref zs1 0))
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(for/fold ([xa xa] [z1 z1] [z4 z4]) ([xb (in-list (rest xs))]
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[z2 (in-vector zs0 1)]
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[z3 (in-vector zs1 1)])
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expr ...
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(values xb z2 z3))
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(values yb zs1))))
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(define-syntax-rule (for-3d-sample (xa xb ya yb za zb d1 d2 d3 d4 d5 d6 d7 d8) sample expr ...)
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(let ()
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(match-define (3d-sample xs ys zs dsss fd-min fd-max) sample)
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(define za (first zs))
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(define dss0 (vector-ref dsss 0))
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(for/fold ([za za] [dss0 dss0]) ([zb (in-list (rest zs))]
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[dss1 (in-vector dsss 1)])
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(define ya (first ys))
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(define ds00 (vector-ref dss0 0))
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(define ds10 (vector-ref dss1 0))
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(for/fold ([ya ya] [ds00 ds00] [ds10 ds10]) ([yb (in-list (rest ys))]
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[ds01 (in-vector dss0 1)]
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[ds11 (in-vector dss1 1)])
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(define xa (first xs))
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(define d1 (vector-ref ds00 0))
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(define d4 (vector-ref ds01 0))
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(define d5 (vector-ref ds10 0))
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(define d8 (vector-ref ds11 0))
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(for/fold ([xa xa] [d1 d1] [d4 d4] [d5 d5] [d8 d8]) ([xb (in-list (rest xs))]
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[d2 (in-vector ds00 1)]
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[d3 (in-vector ds01 1)]
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[d6 (in-vector ds10 1)]
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[d7 (in-vector ds11 1)])
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expr ...
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(values xb d2 d3 d6 d7))
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(values yb ds01 ds11))
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(values zb dss1))))
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(defproc (sample-exact->inexact [s sample?]) sample?
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(match-define (sample xs ys y-min y-max) s)
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(sample (map exact->inexact xs) (map exact->inexact ys)
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y-min y-max))
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(defproc (2d-sample-exact->inexact [s 2d-sample?]) 2d-sample?
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(match-define (2d-sample xs ys zss z-min z-max) s)
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(2d-sample (map exact->inexact xs) (map exact->inexact ys)
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(for/vector #:length (vector-length zss) ([zs (in-vector zss)])
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(for/vector #:length (vector-length zs) ([z (in-vector zs)])
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(exact->inexact z)))
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z-min z-max))
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(defproc (3d-sample-exact->inexact [s 3d-sample?]) 3d-sample?
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(match-define (3d-sample xs ys zs dsss d-min d-max) s)
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(3d-sample (map exact->inexact xs) (map exact->inexact ys) (map exact->inexact zs)
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(for/vector #:length (vector-length dsss) ([dss (in-vector dsss)])
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(for/vector #:length (vector-length dss) ([ds (in-vector dss)])
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(for/vector #:length (vector-length ds) ([d (in-vector ds)])
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(exact->inexact d))))
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d-min d-max))
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(defproc (flonum-ok-for-2d? [x-min rational?] [x-max rational?]
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[y-min rational?] [y-max rational?]) boolean?
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(and (flonum-ok-for-range? x-min x-max 10000)
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(flonum-ok-for-range? y-min y-max 10000)))
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(defproc (flonum-ok-for-3d? [x-min rational?] [x-max rational?]
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[y-min rational?] [y-max rational?]
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[z-min rational?] [z-max rational?]) boolean?
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(and (flonum-ok-for-range? x-min x-max 10000)
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(flonum-ok-for-range? y-min y-max 10000)
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(flonum-ok-for-range? z-min z-max 10000)))
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(defproc (flonum-ok-for-4d? [x-min rational?] [x-max rational?]
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[y-min rational?] [y-max rational?]
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[z-min rational?] [z-max rational?]
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[d-min rational?] [d-max rational?]) boolean?
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(and (flonum-ok-for-range? x-min x-max 10000)
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(flonum-ok-for-range? y-min y-max 10000)
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(flonum-ok-for-range? z-min z-max 10000)
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(flonum-ok-for-range? d-min d-max 10000)))
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