392fa03a1b
Fits a cubic to an arc on the unit circle using the following
constraints:
1) The endpoints and tangent directions at the endpoints must match
the arc.
2) The cubic must be symmetric (length(p1 - p0) == length(p3 - p2)).
3) The height of the cubic must match the height of the arc.
Using the above constraints, we arrive at the following formula for the
control length (c) (i.e., lengths of (p1 - p0) and (p3 - p2)):
d = x0*x1 + y0*y1
c = (sqrt(1 + d) * kM + kA) * rsqrt(1 - d)
(Where x0,y0,x1,y1 are the endpoints, kM = -4/3, and kA = 4/3 * sqrt(2).)
The sample also comes with a root finder that finds the max error value
of the curve, which ends up serving as a semi-formal proof that:
1) Max error always occurs at T=0.21132486540519, regardless of
endpoints.
2) Error is reduced by exactly 64x each time we halve the arc angle
Change-Id: I29ad60dda06743d79f71275c38ffdd97261159ac
Reviewed-on: https://skia-review.googlesource.com/c/skia/+/295303
Commit-Queue: Chris Dalton <csmartdalton@google.com>
Reviewed-by: Mike Reed <reed@google.com>
99 lines
3.5 KiB
Plaintext
99 lines
3.5 KiB
Plaintext
# Copyright 2016 Google Inc.
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#
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# Use of this source code is governed by a BSD-style license that can be
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# found in the LICENSE file.
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# Things are easiest for everyone if these source paths are absolute.
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_samplecode = get_path_info("../samplecode", "abspath")
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samples_sources = [
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"$_samplecode/PerlinPatch.cpp",
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"$_samplecode/Sample.cpp",
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"$_samplecode/Sample.h",
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"$_samplecode/Sample2PtRadial.cpp",
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"$_samplecode/Sample3D.cpp",
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"$_samplecode/SampleAAClip.cpp",
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"$_samplecode/SampleAAGeometry.cpp",
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"$_samplecode/SampleAARectModes.cpp",
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"$_samplecode/SampleAARects.cpp",
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"$_samplecode/SampleAndroidShadows.cpp",
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"$_samplecode/SampleAnimBlur.cpp",
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"$_samplecode/SampleAnimatedImage.cpp",
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"$_samplecode/SampleAnimatedText.cpp",
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"$_samplecode/SampleArc.cpp",
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"$_samplecode/SampleAtlas.cpp",
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"$_samplecode/SampleBackdropBounds.cpp",
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"$_samplecode/SampleBitmapRect.cpp",
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"$_samplecode/SampleCamera.cpp",
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"$_samplecode/SampleChart.cpp",
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"$_samplecode/SampleChineseFling.cpp",
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"$_samplecode/SampleCircle.cpp",
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"$_samplecode/SampleClip.cpp",
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"$_samplecode/SampleClipDrawMatch.cpp",
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"$_samplecode/SampleClock.cpp",
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"$_samplecode/SampleColorFilter.cpp",
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"$_samplecode/SampleComplexClip.cpp",
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"$_samplecode/SampleCowboy.cpp",
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"$_samplecode/SampleCusp.cpp",
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"$_samplecode/SampleDegenerateQuads.cpp",
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"$_samplecode/SampleDegenerateTwoPtRadials.cpp",
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"$_samplecode/SampleEffects.cpp",
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"$_samplecode/SampleEmboss.cpp",
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"$_samplecode/SampleFatBits.cpp",
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"$_samplecode/SampleFillType.cpp",
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"$_samplecode/SampleFilter2.cpp",
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"$_samplecode/SampleFilterQuality.cpp",
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"$_samplecode/SampleFitCubicToCircle.cpp",
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"$_samplecode/SampleFlutterAnimate.cpp",
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"$_samplecode/SampleGlyphTransform.cpp",
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"$_samplecode/SampleGradients.cpp",
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"$_samplecode/SampleHT.cpp",
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"$_samplecode/SampleHairCurves.cpp",
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"$_samplecode/SampleHairModes.cpp",
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"$_samplecode/SampleHairline.cpp",
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"$_samplecode/SampleIdentityScale.cpp",
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"$_samplecode/SampleImageFilterDAG.cpp",
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"$_samplecode/SampleLCD.cpp",
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"$_samplecode/SampleLayerMask.cpp",
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"$_samplecode/SampleLayers.cpp",
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"$_samplecode/SampleManyRects.cpp",
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"$_samplecode/SampleMegaStroke.cpp",
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"$_samplecode/SampleMixer.cpp",
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"$_samplecode/SamplePatch.cpp",
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"$_samplecode/SamplePath.cpp",
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"$_samplecode/SamplePathClip.cpp",
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"$_samplecode/SamplePathEffects.cpp",
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"$_samplecode/SamplePathOverstroke.cpp",
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"$_samplecode/SamplePathText.cpp",
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"$_samplecode/SamplePolyToPoly.cpp",
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"$_samplecode/SampleQuadStroker.cpp",
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"$_samplecode/SampleRectanizer.cpp",
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"$_samplecode/SampleRegion.cpp",
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"$_samplecode/SampleRepeatTile.cpp",
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"$_samplecode/SampleSG.cpp",
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"$_samplecode/SampleSVGFile.cpp",
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"$_samplecode/SampleShaders.cpp",
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"$_samplecode/SampleShadowColor.cpp",
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"$_samplecode/SampleShadowReference.cpp",
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"$_samplecode/SampleShadowUtils.cpp",
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"$_samplecode/SampleShip.cpp",
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"$_samplecode/SampleSlides.cpp",
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"$_samplecode/SampleStringArt.cpp",
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"$_samplecode/SampleStrokePath.cpp",
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"$_samplecode/SampleStrokeRect.cpp",
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"$_samplecode/SampleSubpixelTranslate.cpp",
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"$_samplecode/SampleTessellatedWedge.cpp",
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"$_samplecode/SampleTextBox.cpp",
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"$_samplecode/SampleTextEffects.cpp",
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"$_samplecode/SampleTextureUpload.cpp",
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"$_samplecode/SampleThinAA.cpp",
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"$_samplecode/SampleUnpremul.cpp",
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"$_samplecode/SampleVertices.cpp",
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"$_samplecode/SampleWritePixels.cpp",
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"$_samplecode/SampleXfer.cpp",
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"$_samplecode/SampleXfermodesBlur.cpp",
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"$_samplecode/vertexdump.cpp",
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]
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samples_sources_ccpr = [ "$_samplecode/SampleCCPRGeometry.cpp" ]
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