a7eba53efc
In an ultimately vain attempt to make plotting fast but still allow
plots with bounds that have very few flonums in them, Plot used to try
to detect when each axis's bounds had enough flonums in it and switch to
flonum-only math. There are two problems with this:
* It was trying to determine whether *future computations* would have
enough precision, which is very difficult to know for sure, so it
only *usually* worked. (Example fail: contour-intervals3d with 0 and
+max.0 endpoints. Half the isobands weren't drawn.)
* It caused extra conversions between flonums and exact rationals,
which are very slow.
Here's the new approach:
1. Always send exact rationals to user functions (e.g. the lambda
arguments to `function' and `contour-intervals3d').
2. Immediately convert user-given plot coordinates to exact
rationals (if rational; e.g. not +nan.0)
3. Always represent normalized coordinates (e.g. in [0,1]^2 for 2D
plots and [-1/2,1/2]^3 for 3D plots) using flonums.
4. Reduce the number of exact operations as much as possible.
IOW, plot coordinates, which can be incredibly huge or tiny and don't
always fit in flonums, are always exact internally. Normalized, view,
and device coordinates, which are used only internally, always have
bounds with plenty of flonums in them, so Plot uses flonums.
Doing #4 accounts for most of the changes; e.g. to the marching
squares and marching cubes implementations, and axial plane clipping.
Most plots' speeds seem to be unaffected by the changes. Surfaces and
contour intervals are sometimes faster. Isosurfaces are a tad slower
in some cases and faster in others. Points are about 50% slower,
partly undoing the speedup from a recent commit. Plots with axis
transforms can be much slower (4x), when long, straight lines are
subdivided many times. Plots with bounds outside flonum range seem
to be about 3x faster.
221 lines
11 KiB
Racket
221 lines
11 KiB
Racket
#lang racket/base
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;; Renderers for intervals between functions.
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(require racket/contract racket/class racket/match racket/math racket/list
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unstable/latent-contract/defthing
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unstable/contract
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plot/utils
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"../common/utils.rkt")
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(provide (all-defined-out))
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;; ===================================================================================================
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;; Lines, parametric, polar
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(define ((lines-interval-render-proc v1s v2s color style
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line1-color line1-width line1-style
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line2-color line2-width line2-style
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alpha label)
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area)
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(send area put-alpha alpha)
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(send area put-pen 0 0 'transparent)
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(send area put-brush color style)
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(send area put-polygon (append v1s (reverse v2s)))
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(send area put-pen line1-color line1-width line1-style)
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(send area put-lines v1s)
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(send area put-pen line2-color line2-width line2-style)
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(send area put-lines v2s)
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(cond [label (interval-legend-entry label color style 0 0 'transparent
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line1-color line1-width line1-style
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line2-color line2-width line2-style)]
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[else empty]))
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(defproc (lines-interval
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[v1s (sequence/c (sequence/c real?))]
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[v2s (sequence/c (sequence/c real?))]
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[#:x-min x-min (or/c rational? #f) #f] [#:x-max x-max (or/c rational? #f) #f]
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[#:y-min y-min (or/c rational? #f) #f] [#:y-max y-max (or/c rational? #f) #f]
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[#:color color plot-color/c (interval-color)]
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[#:style style plot-brush-style/c (interval-style)]
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[#:line1-color line1-color plot-color/c (interval-line1-color)]
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[#:line1-width line1-width (>=/c 0) (interval-line1-width)]
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[#:line1-style line1-style plot-pen-style/c (interval-line1-style)]
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[#:line2-color line2-color plot-color/c (interval-line2-color)]
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[#:line2-width line2-width (>=/c 0) (interval-line2-width)]
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[#:line2-style line2-style plot-pen-style/c (interval-line2-style)]
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[#:alpha alpha (real-in 0 1) (interval-alpha)]
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[#:label label (or/c string? #f) #f]
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) renderer2d?
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(let ([v1s (sequence->listof-vector 'lines-interval v1s 2)]
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[v2s (sequence->listof-vector 'lines-interval v2s 2)])
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(define rvs (filter vrational? (append v1s v2s)))
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(cond
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[(empty? rvs) (renderer2d #f #f #f #f)]
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[else
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(match-define (list (vector rxs rys) ...) rvs)
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(let ([x-min (if x-min x-min (apply min* rxs))]
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[x-max (if x-max x-max (apply max* rxs))]
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[y-min (if y-min y-min (apply min* rys))]
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[y-max (if y-max y-max (apply max* rys))])
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(renderer2d (vector (ivl x-min x-max) (ivl y-min y-max)) #f default-ticks-fun
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(lines-interval-render-proc v1s v2s color style
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line1-color line1-width line1-style
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line2-color line2-width line2-style
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alpha label)))])))
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(defproc (parametric-interval
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[f1 (real? . -> . (sequence/c real?))]
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[f2 (real? . -> . (sequence/c real?))]
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[t-min rational?] [t-max rational?]
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[#:x-min x-min (or/c rational? #f) #f] [#:x-max x-max (or/c rational? #f) #f]
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[#:y-min y-min (or/c rational? #f) #f] [#:y-max y-max (or/c rational? #f) #f]
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[#:samples samples (and/c exact-integer? (>=/c 2)) (line-samples)]
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[#:color color plot-color/c (interval-color)]
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[#:style style plot-brush-style/c (interval-style)]
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[#:line1-color line1-color plot-color/c (interval-line1-color)]
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[#:line1-width line1-width (>=/c 0) (interval-line1-width)]
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[#:line1-style line1-style plot-pen-style/c (interval-line1-style)]
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[#:line2-color line2-color plot-color/c (interval-line2-color)]
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[#:line2-width line2-width (>=/c 0) (interval-line2-width)]
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[#:line2-style line2-style plot-pen-style/c (interval-line2-style)]
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[#:alpha alpha (real-in 0 1) (interval-alpha)]
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[#:label label (or/c string? #f) #f]
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) renderer2d?
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(let ([f1 (λ (t) (sequence-head-vector 'parametric-interval (f1 t) 2))]
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[f2 (λ (t) (sequence-head-vector 'parametric-interval (f2 t) 2))])
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(lines-interval
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(map f1 (linear-seq t-min t-max samples))
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(map f2 (linear-seq t-min t-max samples))
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#:x-min x-min #:x-max x-max #:y-min y-min #:y-max y-max
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#:color color #:style style
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#:line1-color line1-color #:line1-width line1-width #:line1-style line1-style
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#:line2-color line2-color #:line2-width line2-width #:line2-style line2-style
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#:alpha alpha #:label label)))
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(defproc (polar-interval
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[f1 (real? . -> . real?)] [f2 (real? . -> . real?)]
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[θ-min rational? 0] [θ-max rational? (* 2 pi)]
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[#:x-min x-min (or/c rational? #f) #f] [#:x-max x-max (or/c rational? #f) #f]
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[#:y-min y-min (or/c rational? #f) #f] [#:y-max y-max (or/c rational? #f) #f]
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[#:samples samples (and/c exact-integer? (>=/c 2)) (line-samples)]
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[#:color color plot-color/c (interval-color)]
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[#:style style plot-brush-style/c (interval-style)]
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[#:line1-color line1-color plot-color/c (interval-line1-color)]
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[#:line1-width line1-width (>=/c 0) (interval-line1-width)]
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[#:line1-style line1-style plot-pen-style/c (interval-line1-style)]
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[#:line2-color line2-color plot-color/c (interval-line2-color)]
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[#:line2-width line2-width (>=/c 0) (interval-line2-width)]
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[#:line2-style line2-style plot-pen-style/c (interval-line2-style)]
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[#:alpha alpha (real-in 0 1) (interval-alpha)]
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[#:label label (or/c string? #f) #f]
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) renderer2d?
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(define θs (linear-seq θ-min θ-max samples))
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(lines-interval
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(map polar->cartesian θs (map* f1 θs))
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(map polar->cartesian θs (map* f2 θs))
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#:x-min x-min #:x-max x-max #:y-min y-min #:y-max y-max
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#:color color #:style style
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#:line1-color line1-color #:line1-width line1-width #:line1-style line1-style
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#:line2-color line2-color #:line2-width line2-width #:line2-style line2-style
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#:alpha alpha #:label label))
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;; ===================================================================================================
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;; Function
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(define ((function-interval-render-proc f1 f2 samples color style
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line1-color line1-width line1-style
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line2-color line2-width line2-style
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alpha label)
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area)
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(match-define (vector x-ivl y-ivl) (send area get-bounds-rect))
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(match-define (sample x1s y1s _ _) (f1 x-ivl samples))
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(match-define (sample x2s y2s _ _) (f2 x-ivl samples))
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(define v1s (map vector x1s y1s))
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(define v2s (map vector x2s y2s))
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((lines-interval-render-proc v1s v2s color style
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line1-color line1-width line1-style
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line2-color line2-width line2-style
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alpha label)
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area))
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(defproc (function-interval
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[f1 (real? . -> . real?)] [f2 (real? . -> . real?)]
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[x-min (or/c rational? #f) #f] [x-max (or/c rational? #f) #f]
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[#:y-min y-min (or/c rational? #f) #f] [#:y-max y-max (or/c rational? #f) #f]
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[#:samples samples (and/c exact-integer? (>=/c 2)) (line-samples)]
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[#:color color plot-color/c (interval-color)]
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[#:style style plot-brush-style/c (interval-style)]
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[#:line1-color line1-color plot-color/c (interval-line1-color)]
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[#:line1-width line1-width (>=/c 0) (interval-line1-width)]
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[#:line1-style line1-style plot-pen-style/c (interval-line1-style)]
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[#:line2-color line2-color plot-color/c (interval-line2-color)]
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[#:line2-width line2-width (>=/c 0) (interval-line2-width)]
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[#:line2-style line2-style plot-pen-style/c (interval-line2-style)]
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[#:alpha alpha (real-in 0 1) (interval-alpha)]
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[#:label label (or/c string? #f) #f]
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) renderer2d?
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(define x-ivl (ivl x-min x-max))
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(define y-ivl (ivl y-min y-max))
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(define g1 (function->sampler f1 x-ivl))
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(define g2 (function->sampler f2 x-ivl))
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(renderer2d (vector x-ivl y-ivl)
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(function-interval-bounds-fun g1 g2 samples)
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default-ticks-fun
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(function-interval-render-proc g1 g2 samples color style
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line1-color line1-width line1-style
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line2-color line2-width line2-style
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alpha label)))
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;; ===================================================================================================
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;; Inverse function
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(define ((inverse-interval-render-proc f1 f2 samples color style
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line1-color line1-width line1-style
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line2-color line2-width line2-style
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alpha label)
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area)
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(match-define (vector x-ivl y-ivl) (send area get-bounds-rect))
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(match-define (sample y1s x1s _ _) (f1 y-ivl samples))
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(match-define (sample y2s x2s _ _) (f2 y-ivl samples))
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(define v1s (map vector x1s y1s))
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(define v2s (map vector x2s y2s))
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((lines-interval-render-proc v1s v2s color style
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line1-color line1-width line1-style
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line2-color line2-width line2-style
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alpha label)
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area))
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(defproc (inverse-interval
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[f1 (real? . -> . real?)] [f2 (real? . -> . real?)]
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[y-min (or/c rational? #f) #f] [y-max (or/c rational? #f) #f]
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[#:x-min x-min (or/c rational? #f) #f] [#:x-max x-max (or/c rational? #f) #f]
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[#:samples samples (and/c exact-integer? (>=/c 2)) (line-samples)]
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[#:color color plot-color/c (interval-color)]
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[#:style style plot-brush-style/c (interval-style)]
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[#:line1-color line1-color plot-color/c (interval-line1-color)]
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[#:line1-width line1-width (>=/c 0) (interval-line1-width)]
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[#:line1-style line1-style plot-pen-style/c (interval-line1-style)]
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[#:line2-color line2-color plot-color/c (interval-line2-color)]
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[#:line2-width line2-width (>=/c 0) (interval-line2-width)]
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[#:line2-style line2-style plot-pen-style/c (interval-line2-style)]
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[#:alpha alpha (real-in 0 1) (interval-alpha)]
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[#:label label (or/c string? #f) #f]
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) renderer2d?
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(define x-ivl (ivl x-min x-max))
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(define y-ivl (ivl y-min y-max))
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(define g1 (inverse->sampler f1 y-ivl))
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(define g2 (inverse->sampler f2 y-ivl))
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(renderer2d (vector x-ivl y-ivl)
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(inverse-interval-bounds-fun g1 g2 samples)
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default-ticks-fun
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(inverse-interval-render-proc g1 g2 samples color style
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line1-color line1-width line1-style
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line2-color line2-width line2-style
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alpha label)))
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