math_util_unittest.cc

// Copyright 2012 The Chromium Authors. All rights reserved.
// Use of this source code is governed by a BSD-style license that can be
// found in the LICENSE file.

#include "cc/base/math_util.h"

#include <cmath>

#include "cc/test/geometry_test_utils.h"
#include "testing/gmock/include/gmock/gmock.h"
#include "testing/gtest/include/gtest/gtest.h"
#include "ui/gfx/geometry/rect.h"
#include "ui/gfx/geometry/rect_f.h"
#include "ui/gfx/transform.h"

namespace cc {
namespace {

TEST(MathUtilTest, ProjectionOfPerpendicularPlane) {
  // In this case, the m33() element of the transform becomes zero, which could
  // cause a divide-by-zero when projecting points/quads.

  gfx::Transform transform;
  transform.MakeIdentity();
  transform.matrix().set(2, 2, 0);

  gfx::RectF rect = gfx::RectF(0, 0, 1, 1);
  gfx::RectF projected_rect = MathUtil::ProjectClippedRect(transform, rect);

  EXPECT_EQ(0, projected_rect.x());
  EXPECT_EQ(0, projected_rect.y());
  EXPECT_TRUE(projected_rect.IsEmpty());
}

TEST(MathUtilTest, ProjectionOfAlmostPerpendicularPlane) {
  // In this case, the m33() element of the transform becomes almost zero, which
  // could cause a divide-by-zero when projecting points/quads.

  gfx::Transform transform;
  // The transform is from an actual test page:
  // [ +1.0000 +0.0000 -1.0000 +3144132.0000
  //   +0.0000 +1.0000 +0.0000 +0.0000
  //   +16331238407143424.0000 +0.0000 -0.0000 +51346917453137000267776.0000
  //   +0.0000 +0.0000 +0.0000 +1.0000 ]
  transform.MakeIdentity();
  transform.matrix().set(0, 2, static_cast<SkMScalar>(-1));
  transform.matrix().set(0, 3, static_cast<SkMScalar>(3144132.0));
  transform.matrix().set(2, 0, static_cast<SkMScalar>(16331238407143424.0));
  transform.matrix().set(2, 2, static_cast<SkMScalar>(-1e-33));
  transform.matrix().set(2, 3,
                         static_cast<SkMScalar>(51346917453137000267776.0));

  gfx::RectF rect = gfx::RectF(0, 0, 1, 1);
  gfx::RectF projected_rect = MathUtil::ProjectClippedRect(transform, rect);

  EXPECT_EQ(0, projected_rect.x());
  EXPECT_EQ(0, projected_rect.y());
  EXPECT_TRUE(projected_rect.IsEmpty()) << projected_rect.ToString();
}

TEST(MathUtilTest, EnclosingClippedRectUsesCorrectInitialBounds) {
  HomogeneousCoordinate h1(-100, -100, 0, 1);
  HomogeneousCoordinate h2(-10, -10, 0, 1);
  HomogeneousCoordinate h3(10, 10, 0, -1);
  HomogeneousCoordinate h4(100, 100, 0, -1);

  // The bounds of the enclosing clipped rect should be -100 to -10 for both x
  // and y. However, if there is a bug where the initial xmin/xmax/ymin/ymax are
  // initialized to numeric_limits<float>::min() (which is zero, not -flt_max)
  // then the enclosing clipped rect will be computed incorrectly.
  gfx::RectF result = MathUtil::ComputeEnclosingClippedRect(h1, h2, h3, h4);

  // Due to floating point math in ComputeClippedPointForEdge this result
  // is fairly imprecise.  0.15f was empirically determined.
  EXPECT_RECT_NEAR(
      gfx::RectF(gfx::PointF(-100, -100), gfx::SizeF(90, 90)), result, 0.15f);
}

TEST(MathUtilTest, EnclosingRectOfVerticesUsesCorrectInitialBounds) {
  gfx::PointF vertices[3];
  int num_vertices = 3;

  vertices[0] = gfx::PointF(-10, -100);
  vertices[1] = gfx::PointF(-100, -10);
  vertices[2] = gfx::PointF(-30, -30);

  // The bounds of the enclosing rect should be -100 to -10 for both x and y.
  // However, if there is a bug where the initial xmin/xmax/ymin/ymax are
  // initialized to numeric_limits<float>::min() (which is zero, not -flt_max)
  // then the enclosing clipped rect will be computed incorrectly.
  gfx::RectF result =
      MathUtil::ComputeEnclosingRectOfVertices(vertices, num_vertices);

  EXPECT_FLOAT_RECT_EQ(gfx::RectF(gfx::PointF(-100, -100), gfx::SizeF(90, 90)),
                       result);
}

TEST(MathUtilTest, SmallestAngleBetweenVectors) {
  gfx::Vector2dF x(1, 0);
  gfx::Vector2dF y(0, 1);
  gfx::Vector2dF test_vector(0.5, 0.5);

  // Orthogonal vectors are at an angle of 90 degress.
  EXPECT_EQ(90, MathUtil::SmallestAngleBetweenVectors(x, y));

  // A vector makes a zero angle with itself.
  EXPECT_EQ(0, MathUtil::SmallestAngleBetweenVectors(x, x));
  EXPECT_EQ(0, MathUtil::SmallestAngleBetweenVectors(y, y));
  EXPECT_EQ(0, MathUtil::SmallestAngleBetweenVectors(test_vector, test_vector));

  // Parallel but reversed vectors are at 180 degrees.
  EXPECT_FLOAT_EQ(180, MathUtil::SmallestAngleBetweenVectors(x, -x));
  EXPECT_FLOAT_EQ(180, MathUtil::SmallestAngleBetweenVectors(y, -y));
  EXPECT_FLOAT_EQ(
      180, MathUtil::SmallestAngleBetweenVectors(test_vector, -test_vector));

  // The test vector is at a known angle.
  EXPECT_FLOAT_EQ(
      45, std::floor(MathUtil::SmallestAngleBetweenVectors(test_vector, x)));
  EXPECT_FLOAT_EQ(
      45, std::floor(MathUtil::SmallestAngleBetweenVectors(test_vector, y)));
}

TEST(MathUtilTest, VectorProjection) {
  gfx::Vector2dF x(1, 0);
  gfx::Vector2dF y(0, 1);
  gfx::Vector2dF test_vector(0.3f, 0.7f);

  // Orthogonal vectors project to a zero vector.
  EXPECT_VECTOR_EQ(gfx::Vector2dF(0, 0), MathUtil::ProjectVector(x, y));
  EXPECT_VECTOR_EQ(gfx::Vector2dF(0, 0), MathUtil::ProjectVector(y, x));

  // Projecting a vector onto the orthonormal basis gives the corresponding
  // component of the vector.
  EXPECT_VECTOR_EQ(gfx::Vector2dF(test_vector.x(), 0),
                   MathUtil::ProjectVector(test_vector, x));
  EXPECT_VECTOR_EQ(gfx::Vector2dF(0, test_vector.y()),
                   MathUtil::ProjectVector(test_vector, y));

  // Finally check than an arbitrary vector projected to another one gives a
  // vector parallel to the second vector.
  gfx::Vector2dF target_vector(0.5, 0.2f);
  gfx::Vector2dF projected_vector =
      MathUtil::ProjectVector(test_vector, target_vector);
  EXPECT_EQ(projected_vector.x() / target_vector.x(),
            projected_vector.y() / target_vector.y());
}

TEST(MathUtilTest, MapEnclosedRectWith2dAxisAlignedTransform) {
  gfx::Rect input(1, 2, 3, 4);
  gfx::Rect output;
  gfx::Transform transform;

  // Identity.
  output =
      MathUtil::MapEnclosedRectWith2dAxisAlignedTransform(transform, input);
  EXPECT_EQ(input, output);

  // Integer translate.
  transform.Translate(2.0, 3.0);
  output =
      MathUtil::MapEnclosedRectWith2dAxisAlignedTransform(transform, input);
  EXPECT_EQ(gfx::Rect(3, 5, 3, 4), output);

  // Non-integer translate.
  transform.Translate(0.5, 0.5);
  output =
      MathUtil::MapEnclosedRectWith2dAxisAlignedTransform(transform, input);
  EXPECT_EQ(gfx::Rect(4, 6, 2, 3), output);

  // Scale.
  transform = gfx::Transform();
  transform.Scale(2.0, 3.0);
  output =
      MathUtil::MapEnclosedRectWith2dAxisAlignedTransform(transform, input);
  EXPECT_EQ(gfx::Rect(2, 6, 6, 12), output);

  // Rotate Z.
  transform = gfx::Transform();
  transform.Translate(1.0, 2.0);
  transform.RotateAboutZAxis(90.0);
  transform.Translate(-1.0, -2.0);
  output =
      MathUtil::MapEnclosedRectWith2dAxisAlignedTransform(transform, input);
  EXPECT_EQ(gfx::Rect(-3, 2, 4, 3), output);

  // Rotate X.
  transform = gfx::Transform();
  transform.RotateAboutXAxis(90.0);
  output =
      MathUtil::MapEnclosedRectWith2dAxisAlignedTransform(transform, input);
  EXPECT_TRUE(output.IsEmpty());

  transform = gfx::Transform();
  transform.RotateAboutXAxis(180.0);
  output =
      MathUtil::MapEnclosedRectWith2dAxisAlignedTransform(transform, input);
  EXPECT_EQ(gfx::Rect(1, -6, 3, 4), output);

  // Rotate Y.
  transform = gfx::Transform();
  transform.RotateAboutYAxis(90.0);
  output =
      MathUtil::MapEnclosedRectWith2dAxisAlignedTransform(transform, input);
  EXPECT_TRUE(output.IsEmpty());

  transform = gfx::Transform();
  transform.RotateAboutYAxis(180.0);
  output =
      MathUtil::MapEnclosedRectWith2dAxisAlignedTransform(transform, input);
  EXPECT_EQ(gfx::Rect(-4, 2, 3, 4), output);

  // Translate Z.
  transform = gfx::Transform();
  transform.ApplyPerspectiveDepth(10.0);
  transform.Translate3d(0.0, 0.0, 5.0);
  output =
      MathUtil::MapEnclosedRectWith2dAxisAlignedTransform(transform, input);
  EXPECT_EQ(gfx::Rect(2, 4, 6, 8), output);
}

TEST(MathUtilTest, RoundUp) {
  for (int multiplier = 1; multiplier <= 10; ++multiplier) {
    // Try attempts in descending order, so that we can
    // determine the correct value before it's needed.
    int correct;
    for (int attempt = 5 * multiplier; attempt >= -5 * multiplier; --attempt) {
      if ((attempt % multiplier) == 0)
        correct = attempt;
      EXPECT_EQ(correct, MathUtil::UncheckedRoundUp(attempt, multiplier))
          << "attempt=" << attempt << " multiplier=" << multiplier;
    }
  }

  for (unsigned multiplier = 1; multiplier <= 10; ++multiplier) {
    // Try attempts in descending order, so that we can
    // determine the correct value before it's needed.
    unsigned correct;
    for (unsigned attempt = 5 * multiplier; attempt > 0; --attempt) {
      if ((attempt % multiplier) == 0)
        correct = attempt;
      EXPECT_EQ(correct, MathUtil::UncheckedRoundUp(attempt, multiplier))
          << "attempt=" << attempt << " multiplier=" << multiplier;
    }
    EXPECT_EQ(0u, MathUtil::UncheckedRoundUp(0u, multiplier))
        << "attempt=0 multiplier=" << multiplier;
  }
}

TEST(MathUtilTest, RoundUpOverflow) {
  // Rounding up 123 by 50 is 150, which overflows int8_t, but fits in uint8_t.
  EXPECT_FALSE(MathUtil::VerifyRoundup<int8_t>(123, 50));
  EXPECT_TRUE(MathUtil::VerifyRoundup<uint8_t>(123, 50));
}

TEST(MathUtilTest, RoundDown) {
  for (int multiplier = 1; multiplier <= 10; ++multiplier) {
    // Try attempts in ascending order, so that we can
    // determine the correct value before it's needed.
    int correct;
    for (int attempt = -5 * multiplier; attempt <= 5 * multiplier; ++attempt) {
      if ((attempt % multiplier) == 0)
        correct = attempt;
      EXPECT_EQ(correct, MathUtil::UncheckedRoundDown(attempt, multiplier))
          << "attempt=" << attempt << " multiplier=" << multiplier;
    }
  }

  for (unsigned multiplier = 1; multiplier <= 10; ++multiplier) {
    // Try attempts in ascending order, so that we can
    // determine the correct value before it's needed.
    unsigned correct;
    for (unsigned attempt = 0; attempt <= 5 * multiplier; ++attempt) {
      if ((attempt % multiplier) == 0)
        correct = attempt;
      EXPECT_EQ(correct, MathUtil::UncheckedRoundDown(attempt, multiplier))
          << "attempt=" << attempt << " multiplier=" << multiplier;
    }
  }
}

TEST(MathUtilTest, RoundDownUnderflow) {
  // Rounding down -123 by 50 is -150, which underflows int8_t, but fits in
  // int16_t.
  EXPECT_FALSE(MathUtil::VerifyRoundDown<int8_t>(-123, 50));
  EXPECT_TRUE(MathUtil::VerifyRoundDown<int16_t>(-123, 50));
}

}  // namespace
}  // namespace cc