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skia2/tests/WangsFormulaTest.cpp
Tyler Denniston 4be95c541c Add test for quadratic Wang's formula 
Just verify that the max error on any of the intervals after splitting
is less than the specified tolerance. Looks like we're running into
some FP precision issues with large coord values, so I'm limiting the
max multiplier to 2^15 in this test.

Bug: skia:10419
Change-Id: I39e76dca5f77389833ba3c94930e6b67c2b1bc97
Reviewed-on: https://skia-review.googlesource.com/c/skia/+/340116
Reviewed-by: Chris Dalton <csmartdalton@google.com>
Commit-Queue: Tyler Denniston <tdenniston@google.com>
2020-12-02 20:50:27 +00:00

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/*
* Copyright 2020 Google Inc.
*
* Use of this source code is governed by a BSD-style license that can be
* found in the LICENSE file.
*/
#include "include/utils/SkRandom.h"
#include "src/core/SkGeometry.h"
#include "src/gpu/tessellate/GrWangsFormula.h"
#include "tests/Test.h"
constexpr static int kIntolerance = 4; // 1/4 pixel max error.
const SkPoint kSerp[4] = {
{285.625f, 499.687f}, {411.625f, 808.188f}, {1064.62f, 135.688f}, {1042.63f, 585.187f}};
const SkPoint kLoop[4] = {
{635.625f, 614.687f}, {171.625f, 236.188f}, {1064.62f, 135.688f}, {516.625f, 570.187f}};
const SkPoint kQuad[4] = {
{460.625f, 557.187f}, {707.121f, 209.688f}, {779.628f, 577.687f}};
static float wangs_formula_quadratic_reference_impl(float intolerance, const SkPoint p[3]) {
float k = (2 * 1) / 8.f * intolerance;
return sqrtf(k * (p[0] - p[1]*2 + p[2]).length());
}
static float wangs_formula_cubic_reference_impl(float intolerance, const SkPoint p[4]) {
float k = (3 * 2) / 8.f * intolerance;
return sqrtf(k * std::max((p[0] - p[1]*2 + p[2]).length(),
(p[1] - p[2]*2 + p[3]).length()));
}
static void for_random_matrices(SkRandom* rand, std::function<void(const SkMatrix&)> f) {
SkMatrix m;
m.setIdentity();
f(m);
for (int i = -10; i <= 30; ++i) {
for (int j = -10; j <= 30; ++j) {
m.setScaleX(std::ldexp(1 + rand->nextF(), i));
m.setSkewX(0);
m.setSkewY(0);
m.setScaleY(std::ldexp(1 + rand->nextF(), j));
f(m);
m.setScaleX(std::ldexp(1 + rand->nextF(), i));
m.setSkewX(std::ldexp(1 + rand->nextF(), (j + i) / 2));
m.setSkewY(std::ldexp(1 + rand->nextF(), (j + i) / 2));
m.setScaleY(std::ldexp(1 + rand->nextF(), j));
f(m);
}
}
}
static void for_random_beziers(int numPoints, SkRandom* rand,
std::function<void(const SkPoint[])> f,
int maxExponent = 30) {
SkASSERT(numPoints <= 4);
SkPoint pts[4];
for (int i = -10; i <= maxExponent; ++i) {
for (int j = 0; j < numPoints; ++j) {
pts[j].set(std::ldexp(1 + rand->nextF(), i), std::ldexp(1 + rand->nextF(), i));
}
f(pts);
}
}
// Ensure the optimized "*_log2" versions return the same value as ceil(std::log2(f)).
DEF_TEST(WangsFormula_log2, r) {
// Constructs a cubic such that the 'length' term in wang's formula == term.
//
// f = sqrt(k * length(max(abs(p0 - p1*2 + p2),
// abs(p1 - p2*2 + p3))));
auto setupCubicLengthTerm = [](int seed, SkPoint pts[], float term) {
memset(pts, 0, sizeof(SkPoint) * 4);
SkPoint term2d = (seed & 1) ?
SkPoint::Make(term, 0) : SkPoint::Make(.5f, std::sqrt(3)/2) * term;
seed >>= 1;
if (seed & 1) {
term2d.fX = -term2d.fX;
}
seed >>= 1;
if (seed & 1) {
std::swap(term2d.fX, term2d.fY);
}
seed >>= 1;
switch (seed % 4) {
case 0:
pts[0] = term2d;
pts[3] = term2d * .75f;
return;
case 1:
pts[1] = term2d * -.5f;
return;
case 2:
pts[1] = term2d * -.5f;
return;
case 3:
pts[3] = term2d;
pts[0] = term2d * .75f;
return;
}
};
// Constructs a quadratic such that the 'length' term in wang's formula == term.
//
// f = sqrt(k * length(p0 - p1*2 + p2));
auto setupQuadraticLengthTerm = [](int seed, SkPoint pts[], float term) {
memset(pts, 0, sizeof(SkPoint) * 3);
SkPoint term2d = (seed & 1) ?
SkPoint::Make(term, 0) : SkPoint::Make(.5f, std::sqrt(3)/2) * term;
seed >>= 1;
if (seed & 1) {
term2d.fX = -term2d.fX;
}
seed >>= 1;
if (seed & 1) {
std::swap(term2d.fX, term2d.fY);
}
seed >>= 1;
switch (seed % 3) {
case 0:
pts[0] = term2d;
return;
case 1:
pts[1] = term2d * -.5f;
return;
case 2:
pts[2] = term2d;
return;
}
};
// GrWangsFormula::cubic and ::quadratic both use rsqrt instead of sqrt for speed. Linearization
// is all approximate anyway, so as long as we are within ~1/2 tessellation segment of the
// reference value we are good enough.
constexpr static float kTessellationTolerance = 1/128.f;
for (int level = 0; level < 30; ++level) {
float epsilon = std::ldexp(SK_ScalarNearlyZero, level * 2);
SkPoint pts[4];
{
// Test cubic boundaries.
// f = sqrt(k * length(max(abs(p0 - p1*2 + p2),
// abs(p1 - p2*2 + p3))));
constexpr static float k = (3 * 2) / (8 * (1.f/kIntolerance));
float x = std::ldexp(1, level * 2) / k;
setupCubicLengthTerm(level << 1, pts, x - epsilon);
float referenceValue = wangs_formula_cubic_reference_impl(kIntolerance, pts);
REPORTER_ASSERT(r, std::ceil(std::log2(referenceValue)) == level);
float c = GrWangsFormula::cubic(kIntolerance, pts);
REPORTER_ASSERT(r, SkScalarNearlyEqual(c/referenceValue, 1, kTessellationTolerance));
REPORTER_ASSERT(r, GrWangsFormula::cubic_log2(kIntolerance, pts) == level);
setupCubicLengthTerm(level << 1, pts, x + epsilon);
referenceValue = wangs_formula_cubic_reference_impl(kIntolerance, pts);
REPORTER_ASSERT(r, std::ceil(std::log2(referenceValue)) == level + 1);
c = GrWangsFormula::cubic(kIntolerance, pts);
REPORTER_ASSERT(r, SkScalarNearlyEqual(c/referenceValue, 1, kTessellationTolerance));
REPORTER_ASSERT(r, GrWangsFormula::cubic_log2(kIntolerance, pts) == level + 1);
}
{
// Test quadratic boundaries.
// f = std::sqrt(k * Length(p0 - p1*2 + p2));
constexpr static float k = 2 / (8 * (1.f/kIntolerance));
float x = std::ldexp(1, level * 2) / k;
setupQuadraticLengthTerm(level << 1, pts, x - epsilon);
float referenceValue = wangs_formula_quadratic_reference_impl(kIntolerance, pts);
REPORTER_ASSERT(r, std::ceil(std::log2(referenceValue)) == level);
float q = GrWangsFormula::quadratic(kIntolerance, pts);
REPORTER_ASSERT(r, SkScalarNearlyEqual(q/referenceValue, 1, kTessellationTolerance));
REPORTER_ASSERT(r, GrWangsFormula::quadratic_log2(kIntolerance, pts) == level);
setupQuadraticLengthTerm(level << 1, pts, x + epsilon);
referenceValue = wangs_formula_quadratic_reference_impl(kIntolerance, pts);
REPORTER_ASSERT(r, std::ceil(std::log2(referenceValue)) == level+1);
q = GrWangsFormula::quadratic(kIntolerance, pts);
REPORTER_ASSERT(r, SkScalarNearlyEqual(q/referenceValue, 1, kTessellationTolerance));
REPORTER_ASSERT(r, GrWangsFormula::quadratic_log2(kIntolerance, pts) == level + 1);
}
}
auto check_cubic_log2 = [&](const SkPoint* pts) {
float f = std::max(1.f, wangs_formula_cubic_reference_impl(kIntolerance, pts));
int f_log2 = GrWangsFormula::cubic_log2(kIntolerance, pts);
REPORTER_ASSERT(r, SkScalarCeilToInt(std::log2(f)) == f_log2);
float c = std::max(1.f, GrWangsFormula::cubic(kIntolerance, pts));
REPORTER_ASSERT(r, SkScalarNearlyEqual(c/f, 1, kTessellationTolerance));
};
auto check_quadratic_log2 = [&](const SkPoint* pts) {
float f = std::max(1.f, wangs_formula_quadratic_reference_impl(kIntolerance, pts));
int f_log2 = GrWangsFormula::quadratic_log2(kIntolerance, pts);
REPORTER_ASSERT(r, SkScalarCeilToInt(std::log2(f)) == f_log2);
float q = std::max(1.f, GrWangsFormula::quadratic(kIntolerance, pts));
REPORTER_ASSERT(r, SkScalarNearlyEqual(q/f, 1, kTessellationTolerance));
};
SkRandom rand;
for_random_matrices(&rand, [&](const SkMatrix& m) {
SkPoint pts[4];
m.mapPoints(pts, kSerp, 4);
check_cubic_log2(pts);
m.mapPoints(pts, kLoop, 4);
check_cubic_log2(pts);
m.mapPoints(pts, kQuad, 3);
check_quadratic_log2(pts);
});
for_random_beziers(4, &rand, [&](const SkPoint pts[]) {
check_cubic_log2(pts);
});
for_random_beziers(3, &rand, [&](const SkPoint pts[]) {
check_quadratic_log2(pts);
});
}
// Ensure using transformations gives the same result as pre-transforming all points.
DEF_TEST(WangsFormula_vectorXforms, r) {
auto check_cubic_log2_with_transform = [&](const SkPoint* pts, const SkMatrix& m){
SkPoint ptsXformed[4];
m.mapPoints(ptsXformed, pts, 4);
int expected = GrWangsFormula::cubic_log2(kIntolerance, ptsXformed);
int actual = GrWangsFormula::cubic_log2(kIntolerance, pts, GrVectorXform(m));
REPORTER_ASSERT(r, actual == expected);
};
auto check_quadratic_log2_with_transform = [&](const SkPoint* pts, const SkMatrix& m) {
SkPoint ptsXformed[3];
m.mapPoints(ptsXformed, pts, 3);
int expected = GrWangsFormula::quadratic_log2(kIntolerance, ptsXformed);
int actual = GrWangsFormula::quadratic_log2(kIntolerance, pts, GrVectorXform(m));
REPORTER_ASSERT(r, actual == expected);
};
SkRandom rand;
for_random_matrices(&rand, [&](const SkMatrix& m) {
check_cubic_log2_with_transform(kSerp, m);
check_cubic_log2_with_transform(kLoop, m);
check_quadratic_log2_with_transform(kQuad, m);
for_random_beziers(4, &rand, [&](const SkPoint pts[]) {
check_cubic_log2_with_transform(pts, m);
});
for_random_beziers(3, &rand, [&](const SkPoint pts[]) {
check_quadratic_log2_with_transform(pts, m);
});
});
}
DEF_TEST(WangsFormula_worst_case_cubic, r) {
{
SkPoint worstP[] = {{0,0}, {100,100}, {0,0}, {0,0}};
REPORTER_ASSERT(r, GrWangsFormula::worst_case_cubic(kIntolerance, 100, 100) ==
wangs_formula_cubic_reference_impl(kIntolerance, worstP));
REPORTER_ASSERT(r, GrWangsFormula::worst_case_cubic_log2(kIntolerance, 100, 100) ==
GrWangsFormula::cubic_log2(kIntolerance, worstP));
}
{
SkPoint worstP[] = {{100,100}, {100,100}, {200,200}, {100,100}};
REPORTER_ASSERT(r, GrWangsFormula::worst_case_cubic(kIntolerance, 100, 100) ==
wangs_formula_cubic_reference_impl(kIntolerance, worstP));
REPORTER_ASSERT(r, GrWangsFormula::worst_case_cubic_log2(kIntolerance, 100, 100) ==
GrWangsFormula::cubic_log2(kIntolerance, worstP));
}
auto check_worst_case_cubic = [&](const SkPoint* pts) {
SkRect bbox;
bbox.setBoundsNoCheck(pts, 4);
float worst = GrWangsFormula::worst_case_cubic(kIntolerance, bbox.width(), bbox.height());
int worst_log2 = GrWangsFormula::worst_case_cubic_log2(kIntolerance, bbox.width(),
bbox.height());
float actual = wangs_formula_cubic_reference_impl(kIntolerance, pts);
REPORTER_ASSERT(r, worst >= actual);
REPORTER_ASSERT(r, std::ceil(std::log2(std::max(1.f, worst))) == worst_log2);
};
SkRandom rand;
for (int i = 0; i < 100; ++i) {
for_random_beziers(4, &rand, [&](const SkPoint pts[]) {
check_worst_case_cubic(pts);
});
}
}
// Ensure Wang's formula for quads produces max error within tolerance.
DEF_TEST(WangsFormula_quad_within_tol, r) {
// Wang's formula and the quad math starts to lose precision with very large
// coordinate values, so limit the magnitude a bit to prevent test failures
// due to loss of precision.
constexpr int maxExponent = 15;
SkRandom rand;
for_random_beziers(3, &rand, [&r](const SkPoint pts[]) {
const int nsegs = static_cast<int>(
std::ceil(wangs_formula_quadratic_reference_impl(kIntolerance, pts)));
const float tdelta = 1.f / nsegs;
for (int j = 0; j < nsegs; ++j) {
const float tmin = j * tdelta, tmax = (j + 1) * tdelta;
// Get section of quad in [tmin,tmax]
const SkPoint* sectionPts;
SkPoint tmp0[5];
SkPoint tmp1[5];
if (tmin == 0) {
if (tmax == 1) {
sectionPts = pts;
} else {
SkChopQuadAt(pts, tmp0, tmax);
sectionPts = tmp0;
}
} else {
SkChopQuadAt(pts, tmp0, tmin);
if (tmax == 1) {
sectionPts = tmp0 + 2;
} else {
SkChopQuadAt(tmp0 + 2, tmp1, (tmax - tmin) / (1 - tmin));
sectionPts = tmp1;
}
}
// For quads, max distance from baseline is always at t=0.5.
SkPoint p;
p = SkEvalQuadAt(sectionPts, 0.5f);
// Get distance of p to baseline
const SkPoint n = {sectionPts[2].fY - sectionPts[0].fY,
sectionPts[0].fX - sectionPts[2].fX};
const float d = std::abs((p - sectionPts[0]).dot(n)) / n.length();
// Check distance is within specified tolerance
REPORTER_ASSERT(r, d <= (1.f / kIntolerance) + SK_ScalarNearlyZero);
}
}, maxExponent);
}
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