ui/gfx/geometry/cubic_bezier_unittest.cc

   1 // Copyright 2014 The Chromium Authors. All rights reserved.
   2 // Use of this source code is governed by a BSD-style license that can be
   3 // found in the LICENSE file.
   4
   5 #include "ui/gfx/geometry/cubic_bezier.h"
   6
   7 #include "base/memory/scoped_ptr.h"
   8 #include "testing/gtest/include/gtest/gtest.h"
   9
  10 namespace gfx {
  11 namespace {
  12
  13 TEST(CubicBezierTest, Basic) {
  14   CubicBezier function(0.25, 0.0, 0.75, 1.0);
  15
  16   double epsilon = 0.00015;
  17
  18   EXPECT_NEAR(function.Solve(0), 0, epsilon);
  19   EXPECT_NEAR(function.Solve(0.05), 0.01136, epsilon);
  20   EXPECT_NEAR(function.Solve(0.1), 0.03978, epsilon);
  21   EXPECT_NEAR(function.Solve(0.15), 0.079780, epsilon);
  22   EXPECT_NEAR(function.Solve(0.2), 0.12803, epsilon);
  23   EXPECT_NEAR(function.Solve(0.25), 0.18235, epsilon);
  24   EXPECT_NEAR(function.Solve(0.3), 0.24115, epsilon);
  25   EXPECT_NEAR(function.Solve(0.35), 0.30323, epsilon);
  26   EXPECT_NEAR(function.Solve(0.4), 0.36761, epsilon);
  27   EXPECT_NEAR(function.Solve(0.45), 0.43345, epsilon);
  28   EXPECT_NEAR(function.Solve(0.5), 0.5, epsilon);
  29   EXPECT_NEAR(function.Solve(0.6), 0.63238, epsilon);
  30   EXPECT_NEAR(function.Solve(0.65), 0.69676, epsilon);
  31   EXPECT_NEAR(function.Solve(0.7), 0.75884, epsilon);
  32   EXPECT_NEAR(function.Solve(0.75), 0.81764, epsilon);
  33   EXPECT_NEAR(function.Solve(0.8), 0.87196, epsilon);
  34   EXPECT_NEAR(function.Solve(0.85), 0.92021, epsilon);
  35   EXPECT_NEAR(function.Solve(0.9), 0.96021, epsilon);
  36   EXPECT_NEAR(function.Solve(0.95), 0.98863, epsilon);
  37   EXPECT_NEAR(function.Solve(1), 1, epsilon);
  38 }
  39
  40 // Tests that solving the bezier works with knots with y not in (0, 1).
  41 TEST(CubicBezierTest, UnclampedYValues) {
  42   CubicBezier function(0.5, -1.0, 0.5, 2.0);
  43
  44   double epsilon = 0.00015;
  45
  46   EXPECT_NEAR(function.Solve(0.0), 0.0, epsilon);
  47   EXPECT_NEAR(function.Solve(0.05), -0.08954, epsilon);
  48   EXPECT_NEAR(function.Solve(0.1), -0.15613, epsilon);
  49   EXPECT_NEAR(function.Solve(0.15), -0.19641, epsilon);
  50   EXPECT_NEAR(function.Solve(0.2), -0.20651, epsilon);
  51   EXPECT_NEAR(function.Solve(0.25), -0.18232, epsilon);
  52   EXPECT_NEAR(function.Solve(0.3), -0.11992, epsilon);
  53   EXPECT_NEAR(function.Solve(0.35), -0.01672, epsilon);
  54   EXPECT_NEAR(function.Solve(0.4), 0.12660, epsilon);
  55   EXPECT_NEAR(function.Solve(0.45), 0.30349, epsilon);
  56   EXPECT_NEAR(function.Solve(0.5), 0.50000, epsilon);
  57   EXPECT_NEAR(function.Solve(0.55), 0.69651, epsilon);
  58   EXPECT_NEAR(function.Solve(0.6), 0.87340, epsilon);
  59   EXPECT_NEAR(function.Solve(0.65), 1.01672, epsilon);
  60   EXPECT_NEAR(function.Solve(0.7), 1.11992, epsilon);
  61   EXPECT_NEAR(function.Solve(0.75), 1.18232, epsilon);
  62   EXPECT_NEAR(function.Solve(0.8), 1.20651, epsilon);
  63   EXPECT_NEAR(function.Solve(0.85), 1.19641, epsilon);
  64   EXPECT_NEAR(function.Solve(0.9), 1.15613, epsilon);
  65   EXPECT_NEAR(function.Solve(0.95), 1.08954, epsilon);
  66   EXPECT_NEAR(function.Solve(1.0), 1.0, epsilon);
  67 }
  68
  69 TEST(CubicBezierTest, Range) {
  70   double epsilon = 0.00015;
  71   double min, max;
  72
  73   // Derivative is a constant.
  74   scoped_ptr<CubicBezier> function(
  75       new CubicBezier(0.25, (1.0 / 3.0), 0.75, (2.0 / 3.0)));
  76   function->Range(&min, &max);
  77   EXPECT_EQ(0, min);
  78   EXPECT_EQ(1, max);
  79
  80   // Derivative is linear.
  81   function.reset(new CubicBezier(0.25, -0.5, 0.75, (-1.0 / 6.0)));
  82   function->Range(&min, &max);
  83   EXPECT_NEAR(min, -0.225, epsilon);
  84   EXPECT_EQ(1, max);
  85
  86   // Derivative has no real roots.
  87   function.reset(new CubicBezier(0.25, 0.25, 0.75, 0.5));
  88   function->Range(&min, &max);
  89   EXPECT_EQ(0, min);
  90   EXPECT_EQ(1, max);
  91
  92   // Derivative has exactly one real root.
  93   function.reset(new CubicBezier(0.0, 1.0, 1.0, 0.0));
  94   function->Range(&min, &max);
  95   EXPECT_EQ(0, min);
  96   EXPECT_EQ(1, max);
  97
  98   // Derivative has one root < 0 and one root > 1.
  99   function.reset(new CubicBezier(0.25, 0.1, 0.75, 0.9));
 100   function->Range(&min, &max);
 101   EXPECT_EQ(0, min);
 102   EXPECT_EQ(1, max);
 103
 104   // Derivative has two roots in [0,1].
 105   function.reset(new CubicBezier(0.25, 2.5, 0.75, 0.5));
 106   function->Range(&min, &max);
 107   EXPECT_EQ(0, min);
 108   EXPECT_NEAR(max, 1.28818, epsilon);
 109   function.reset(new CubicBezier(0.25, 0.5, 0.75, -1.5));
 110   function->Range(&min, &max);
 111   EXPECT_NEAR(min, -0.28818, epsilon);
 112   EXPECT_EQ(1, max);
 113
 114   // Derivative has one root < 0 and one root in [0,1].
 115   function.reset(new CubicBezier(0.25, 0.1, 0.75, 1.5));
 116   function->Range(&min, &max);
 117   EXPECT_EQ(0, min);
 118   EXPECT_NEAR(max, 1.10755, epsilon);
 119
 120   // Derivative has one root in [0,1] and one root > 1.
 121   function.reset(new CubicBezier(0.25, -0.5, 0.75, 0.9));
 122   function->Range(&min, &max);
 123   EXPECT_NEAR(min, -0.10755, epsilon);
 124   EXPECT_EQ(1, max);
 125
 126   // Derivative has two roots < 0.
 127   function.reset(new CubicBezier(0.25, 0.3, 0.75, 0.633));
 128   function->Range(&min, &max);
 129   EXPECT_EQ(0, min);
 130   EXPECT_EQ(1, max);
 131
 132   // Derivative has two roots > 1.
 133   function.reset(new CubicBezier(0.25, 0.367, 0.75, 0.7));
 134   function->Range(&min, &max);
 135   EXPECT_EQ(0.f, min);
 136   EXPECT_EQ(1.f, max);
 137 }
 138
 139 TEST(CubicBezierTest, Slope) {
 140   CubicBezier function(0.25, 0.0, 0.75, 1.0);
 141
 142   double epsilon = 0.00015;
 143
 144   EXPECT_NEAR(function.Slope(0), 0, epsilon);
 145   EXPECT_NEAR(function.Slope(0.05), 0.42170, epsilon);
 146   EXPECT_NEAR(function.Slope(0.1), 0.69778, epsilon);
 147   EXPECT_NEAR(function.Slope(0.15), 0.89121, epsilon);
 148   EXPECT_NEAR(function.Slope(0.2), 1.03184, epsilon);
 149   EXPECT_NEAR(function.Slope(0.25), 1.13576, epsilon);
 150   EXPECT_NEAR(function.Slope(0.3), 1.21239, epsilon);
 151   EXPECT_NEAR(function.Slope(0.35), 1.26751, epsilon);
 152   EXPECT_NEAR(function.Slope(0.4), 1.30474, epsilon);
 153   EXPECT_NEAR(function.Slope(0.45), 1.32628, epsilon);
 154   EXPECT_NEAR(function.Slope(0.5), 1.33333, epsilon);
 155   EXPECT_NEAR(function.Slope(0.55), 1.32628, epsilon);
 156   EXPECT_NEAR(function.Slope(0.6), 1.30474, epsilon);
 157   EXPECT_NEAR(function.Slope(0.65), 1.26751, epsilon);
 158   EXPECT_NEAR(function.Slope(0.7), 1.21239, epsilon);
 159   EXPECT_NEAR(function.Slope(0.75), 1.13576, epsilon);
 160   EXPECT_NEAR(function.Slope(0.8), 1.03184, epsilon);
 161   EXPECT_NEAR(function.Slope(0.85), 0.89121, epsilon);
 162   EXPECT_NEAR(function.Slope(0.9), 0.69778, epsilon);
 163   EXPECT_NEAR(function.Slope(0.95), 0.42170, epsilon);
 164   EXPECT_NEAR(function.Slope(1), 0, epsilon);
 165 }
 166
 167 TEST(CubicBezierTest, InputOutOfRange) {
 168   CubicBezier simple(0.5, 1.0, 0.5, 1.0);
 169   EXPECT_EQ(-2.0, simple.Solve(-1.0));
 170   EXPECT_EQ(1.0, simple.Solve(2.0));
 171
 172   CubicBezier coincidentEndpoints(0.0, 0.0, 1.0, 1.0);
 173   EXPECT_EQ(-1.0, coincidentEndpoints.Solve(-1.0));
 174   EXPECT_EQ(2.0, coincidentEndpoints.Solve(2.0));
 175
 176   CubicBezier verticalGradient(0.0, 1.0, 1.0, 0.0);
 177   EXPECT_EQ(0.0, verticalGradient.Solve(-1.0));
 178   EXPECT_EQ(1.0, verticalGradient.Solve(2.0));
 179
 180   CubicBezier distinctEndpoints(0.1, 0.2, 0.8, 0.8);
 181   EXPECT_EQ(-2.0, distinctEndpoints.Solve(-1.0));
 182   EXPECT_EQ(2.0, distinctEndpoints.Solve(2.0));
 183
 184   CubicBezier coincidentEndpoint(0.0, 0.0, 0.8, 0.8);
 185   EXPECT_EQ(-1.0, coincidentEndpoint.Solve(-1.0));
 186   EXPECT_EQ(2.0, coincidentEndpoint.Solve(2.0));
 187
 188   CubicBezier threeCoincidentPoints(0.0, 0.0, 0.0, 0.0);
 189   EXPECT_EQ(0, threeCoincidentPoints.Solve(-1.0));
 190   EXPECT_EQ(2.0, threeCoincidentPoints.Solve(2.0));
 191
 192 }
 193
 194 }  // namespace
 195 }  // namespace gfx