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231 lines
8.6 KiB
231 lines
8.6 KiB
// Copyright 2014 The Chromium Authors. All rights reserved.
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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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#include "ui/gfx/geometry/cubic_bezier.h"
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#include <memory>
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#include "testing/gtest/include/gtest/gtest.h"
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namespace gfx {
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namespace {
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TEST(CubicBezierTest, Basic) {
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CubicBezier function(0.25, 0.0, 0.75, 1.0);
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double epsilon = 0.00015;
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EXPECT_NEAR(function.Solve(0), 0, epsilon);
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EXPECT_NEAR(function.Solve(0.05), 0.01136, epsilon);
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EXPECT_NEAR(function.Solve(0.1), 0.03978, epsilon);
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EXPECT_NEAR(function.Solve(0.15), 0.079780, epsilon);
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EXPECT_NEAR(function.Solve(0.2), 0.12803, epsilon);
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EXPECT_NEAR(function.Solve(0.25), 0.18235, epsilon);
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EXPECT_NEAR(function.Solve(0.3), 0.24115, epsilon);
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EXPECT_NEAR(function.Solve(0.35), 0.30323, epsilon);
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EXPECT_NEAR(function.Solve(0.4), 0.36761, epsilon);
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EXPECT_NEAR(function.Solve(0.45), 0.43345, epsilon);
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EXPECT_NEAR(function.Solve(0.5), 0.5, epsilon);
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EXPECT_NEAR(function.Solve(0.6), 0.63238, epsilon);
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EXPECT_NEAR(function.Solve(0.65), 0.69676, epsilon);
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EXPECT_NEAR(function.Solve(0.7), 0.75884, epsilon);
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EXPECT_NEAR(function.Solve(0.75), 0.81764, epsilon);
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EXPECT_NEAR(function.Solve(0.8), 0.87196, epsilon);
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EXPECT_NEAR(function.Solve(0.85), 0.92021, epsilon);
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EXPECT_NEAR(function.Solve(0.9), 0.96021, epsilon);
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EXPECT_NEAR(function.Solve(0.95), 0.98863, epsilon);
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EXPECT_NEAR(function.Solve(1), 1, epsilon);
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CubicBezier basic_use(0.5, 1.0, 0.5, 1.0);
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EXPECT_EQ(0.875, basic_use.Solve(0.5));
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CubicBezier overshoot(0.5, 2.0, 0.5, 2.0);
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EXPECT_EQ(1.625, overshoot.Solve(0.5));
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CubicBezier undershoot(0.5, -1.0, 0.5, -1.0);
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EXPECT_EQ(-0.625, undershoot.Solve(0.5));
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}
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// Tests that solving the bezier works with knots with y not in (0, 1).
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TEST(CubicBezierTest, UnclampedYValues) {
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CubicBezier function(0.5, -1.0, 0.5, 2.0);
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double epsilon = 0.00015;
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EXPECT_NEAR(function.Solve(0.0), 0.0, epsilon);
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EXPECT_NEAR(function.Solve(0.05), -0.08954, epsilon);
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EXPECT_NEAR(function.Solve(0.1), -0.15613, epsilon);
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EXPECT_NEAR(function.Solve(0.15), -0.19641, epsilon);
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EXPECT_NEAR(function.Solve(0.2), -0.20651, epsilon);
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EXPECT_NEAR(function.Solve(0.25), -0.18232, epsilon);
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EXPECT_NEAR(function.Solve(0.3), -0.11992, epsilon);
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EXPECT_NEAR(function.Solve(0.35), -0.01672, epsilon);
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EXPECT_NEAR(function.Solve(0.4), 0.12660, epsilon);
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EXPECT_NEAR(function.Solve(0.45), 0.30349, epsilon);
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EXPECT_NEAR(function.Solve(0.5), 0.50000, epsilon);
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EXPECT_NEAR(function.Solve(0.55), 0.69651, epsilon);
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EXPECT_NEAR(function.Solve(0.6), 0.87340, epsilon);
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EXPECT_NEAR(function.Solve(0.65), 1.01672, epsilon);
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EXPECT_NEAR(function.Solve(0.7), 1.11992, epsilon);
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EXPECT_NEAR(function.Solve(0.75), 1.18232, epsilon);
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EXPECT_NEAR(function.Solve(0.8), 1.20651, epsilon);
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EXPECT_NEAR(function.Solve(0.85), 1.19641, epsilon);
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EXPECT_NEAR(function.Solve(0.9), 1.15613, epsilon);
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EXPECT_NEAR(function.Solve(0.95), 1.08954, epsilon);
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EXPECT_NEAR(function.Solve(1.0), 1.0, epsilon);
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}
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TEST(CubicBezierTest, Range) {
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double epsilon = 0.00015;
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// Derivative is a constant.
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std::unique_ptr<CubicBezier> function(
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new CubicBezier(0.25, (1.0 / 3.0), 0.75, (2.0 / 3.0)));
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EXPECT_EQ(0, function->range_min());
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EXPECT_EQ(1, function->range_max());
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// Derivative is linear.
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function.reset(new CubicBezier(0.25, -0.5, 0.75, (-1.0 / 6.0)));
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EXPECT_NEAR(function->range_min(), -0.225, epsilon);
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EXPECT_EQ(1, function->range_max());
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// Derivative has no real roots.
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function.reset(new CubicBezier(0.25, 0.25, 0.75, 0.5));
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EXPECT_EQ(0, function->range_min());
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EXPECT_EQ(1, function->range_max());
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// Derivative has exactly one real root.
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function.reset(new CubicBezier(0.0, 1.0, 1.0, 0.0));
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EXPECT_EQ(0, function->range_min());
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EXPECT_EQ(1, function->range_max());
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// Derivative has one root < 0 and one root > 1.
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function.reset(new CubicBezier(0.25, 0.1, 0.75, 0.9));
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EXPECT_EQ(0, function->range_min());
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EXPECT_EQ(1, function->range_max());
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// Derivative has two roots in [0,1].
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function.reset(new CubicBezier(0.25, 2.5, 0.75, 0.5));
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EXPECT_EQ(0, function->range_min());
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EXPECT_NEAR(function->range_max(), 1.28818, epsilon);
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function.reset(new CubicBezier(0.25, 0.5, 0.75, -1.5));
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EXPECT_NEAR(function->range_min(), -0.28818, epsilon);
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EXPECT_EQ(1, function->range_max());
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// Derivative has one root < 0 and one root in [0,1].
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function.reset(new CubicBezier(0.25, 0.1, 0.75, 1.5));
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EXPECT_EQ(0, function->range_min());
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EXPECT_NEAR(function->range_max(), 1.10755, epsilon);
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// Derivative has one root in [0,1] and one root > 1.
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function.reset(new CubicBezier(0.25, -0.5, 0.75, 0.9));
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EXPECT_NEAR(function->range_min(), -0.10755, epsilon);
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EXPECT_EQ(1, function->range_max());
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// Derivative has two roots < 0.
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function.reset(new CubicBezier(0.25, 0.3, 0.75, 0.633));
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EXPECT_EQ(0, function->range_min());
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EXPECT_EQ(1, function->range_max());
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// Derivative has two roots > 1.
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function.reset(new CubicBezier(0.25, 0.367, 0.75, 0.7));
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EXPECT_EQ(0.f, function->range_min());
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EXPECT_EQ(1.f, function->range_max());
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}
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TEST(CubicBezierTest, Slope) {
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CubicBezier function(0.25, 0.0, 0.75, 1.0);
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double epsilon = 0.00015;
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EXPECT_NEAR(function.Slope(-0.1), 0, epsilon);
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EXPECT_NEAR(function.Slope(0), 0, epsilon);
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EXPECT_NEAR(function.Slope(0.05), 0.42170, epsilon);
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EXPECT_NEAR(function.Slope(0.1), 0.69778, epsilon);
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EXPECT_NEAR(function.Slope(0.15), 0.89121, epsilon);
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EXPECT_NEAR(function.Slope(0.2), 1.03184, epsilon);
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EXPECT_NEAR(function.Slope(0.25), 1.13576, epsilon);
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EXPECT_NEAR(function.Slope(0.3), 1.21239, epsilon);
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EXPECT_NEAR(function.Slope(0.35), 1.26751, epsilon);
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EXPECT_NEAR(function.Slope(0.4), 1.30474, epsilon);
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EXPECT_NEAR(function.Slope(0.45), 1.32628, epsilon);
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EXPECT_NEAR(function.Slope(0.5), 1.33333, epsilon);
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EXPECT_NEAR(function.Slope(0.55), 1.32628, epsilon);
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EXPECT_NEAR(function.Slope(0.6), 1.30474, epsilon);
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EXPECT_NEAR(function.Slope(0.65), 1.26751, epsilon);
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EXPECT_NEAR(function.Slope(0.7), 1.21239, epsilon);
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EXPECT_NEAR(function.Slope(0.75), 1.13576, epsilon);
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EXPECT_NEAR(function.Slope(0.8), 1.03184, epsilon);
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EXPECT_NEAR(function.Slope(0.85), 0.89121, epsilon);
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EXPECT_NEAR(function.Slope(0.9), 0.69778, epsilon);
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EXPECT_NEAR(function.Slope(0.95), 0.42170, epsilon);
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EXPECT_NEAR(function.Slope(1), 0, epsilon);
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EXPECT_NEAR(function.Slope(1.1), 0, epsilon);
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}
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TEST(CubicBezierTest, InputOutOfRange) {
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CubicBezier simple(0.5, 1.0, 0.5, 1.0);
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EXPECT_EQ(-2.0, simple.Solve(-1.0));
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EXPECT_EQ(1.0, simple.Solve(2.0));
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CubicBezier at_edge_of_range(0.5, 1.0, 0.5, 1.0);
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EXPECT_EQ(0.0, at_edge_of_range.Solve(0.0));
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EXPECT_EQ(1.0, at_edge_of_range.Solve(1.0));
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CubicBezier large_epsilon(0.5, 1.0, 0.5, 1.0);
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EXPECT_EQ(-2.0, large_epsilon.SolveWithEpsilon(-1.0, 1.0));
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EXPECT_EQ(1.0, large_epsilon.SolveWithEpsilon(2.0, 1.0));
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CubicBezier coincident_endpoints(0.0, 0.0, 1.0, 1.0);
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EXPECT_EQ(-1.0, coincident_endpoints.Solve(-1.0));
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EXPECT_EQ(2.0, coincident_endpoints.Solve(2.0));
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CubicBezier vertical_gradient(0.0, 1.0, 1.0, 0.0);
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EXPECT_EQ(0.0, vertical_gradient.Solve(-1.0));
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EXPECT_EQ(1.0, vertical_gradient.Solve(2.0));
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CubicBezier distinct_endpoints(0.1, 0.2, 0.8, 0.8);
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EXPECT_EQ(-2.0, distinct_endpoints.Solve(-1.0));
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EXPECT_EQ(2.0, distinct_endpoints.Solve(2.0));
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CubicBezier coincident_endpoint(0.0, 0.0, 0.8, 0.8);
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EXPECT_EQ(-1.0, coincident_endpoint.Solve(-1.0));
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EXPECT_EQ(2.0, coincident_endpoint.Solve(2.0));
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CubicBezier three_coincident_points(0.0, 0.0, 0.0, 0.0);
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EXPECT_EQ(0, three_coincident_points.Solve(-1.0));
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EXPECT_EQ(2.0, three_coincident_points.Solve(2.0));
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}
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TEST(CubicBezierTest, GetPoints) {
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double epsilon = 0.00015;
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CubicBezier cubic1(0.1, 0.2, 0.8, 0.9);
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EXPECT_NEAR(0.1, cubic1.GetX1(), epsilon);
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EXPECT_NEAR(0.2, cubic1.GetY1(), epsilon);
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EXPECT_NEAR(0.8, cubic1.GetX2(), epsilon);
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EXPECT_NEAR(0.9, cubic1.GetY2(), epsilon);
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CubicBezier cubic_zero(0, 0, 0, 0);
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EXPECT_NEAR(0, cubic_zero.GetX1(), epsilon);
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EXPECT_NEAR(0, cubic_zero.GetY1(), epsilon);
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EXPECT_NEAR(0, cubic_zero.GetX2(), epsilon);
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EXPECT_NEAR(0, cubic_zero.GetY2(), epsilon);
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CubicBezier cubic_one(1, 1, 1, 1);
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EXPECT_NEAR(1, cubic_one.GetX1(), epsilon);
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EXPECT_NEAR(1, cubic_one.GetY1(), epsilon);
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EXPECT_NEAR(1, cubic_one.GetX2(), epsilon);
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EXPECT_NEAR(1, cubic_one.GetY2(), epsilon);
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CubicBezier cubic_oor(-0.5, -1.5, 1.5, -1.6);
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EXPECT_NEAR(-0.5, cubic_oor.GetX1(), epsilon);
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EXPECT_NEAR(-1.5, cubic_oor.GetY1(), epsilon);
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EXPECT_NEAR(1.5, cubic_oor.GetX2(), epsilon);
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EXPECT_NEAR(-1.6, cubic_oor.GetY2(), epsilon);
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}
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} // namespace
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} // namespace gfx
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