cpp-game-engine/math/test/common_test.cxx

//
//  common_test.cxx
//  math-test
//
//  Created by Sam Jaffe on 5/5/19.
//  Copyright © 2019 Sam Jaffe. All rights reserved.
//

#include <cmath>
#include <gmock/gmock.h>

#include "game/math/angle.hpp"
#include "game/math/common.hpp"
#include "game/math/shape.hpp"

#include "test_printers.h"

using namespace math::dim2;
using namespace testing;

namespace math {
  bool intersects(dim2::triangle const &, dim2::triangle const &);
}

template <typename T, typename G>
decltype(auto) generate(T min, T max, T step, G && generator) {
  std::vector<decltype(generator(min))> out;
  for (T val = min; val < max; val += step) {
    out.emplace_back(generator(val));
  }
  return out;
}

template <typename T> decltype(auto) generate(T min, T max, T step) {
  auto identity = [](T const & val) { return val; };
  return generate(min, max, step, identity);
}

struct LineTest : TestWithParam<std::tuple<point, int>> {};

TEST_P(LineTest, ExistsOnOriginLine) {
  point const end = std::get<0>(GetParam());
  line const ln{{{0, 0}}, end};
  point const pt = end * std::get<1>(GetParam()) / 100.f;
  EXPECT_TRUE(math::contains(ln, pt));
}

TEST_P(LineTest, ColinearOutsideDoesNotContain) {
  point const end = std::get<0>(GetParam());
  line const ln{end, end * 2};
  point const pt = end * std::get<1>(GetParam()) / 100.f;
  EXPECT_FALSE(math::contains(ln, pt));
}

std::vector<point> const line_ends{{{1, 1}},   {{0, 1}},  {{1, 0}},
                                   {{-1, -1}}, {{0, -1}}, {{-1, 0}}};

INSTANTIATE_TEST_CASE_P(Contains, LineTest,
                        Combine(ValuesIn(line_ends),
                                ValuesIn(generate(0, 100, 10))));

struct UnitCircleTest : TestWithParam<point> {};

TEST_P(UnitCircleTest, ExistsInCircle) {
  circle unit{{{0, 0}}, 1};
  EXPECT_TRUE(math::contains(unit, GetParam()));
}

TEST_P(UnitCircleTest, OutsideSmallerCircle) {
  circle subunit{{{0, 0}}, 0.9999};
  EXPECT_FALSE(math::contains(subunit, GetParam()));
}

point unit_circle_angle(math::degree degs) {
  return point(make_vector(math::sin(degs), math::cos(degs)));
}

INSTANTIATE_TEST_CASE_P(Contains, UnitCircleTest,
                        ValuesIn(generate(0.0, 360.0, 5.0, unit_circle_angle)));

struct UnitSquareTest : TestWithParam<std::tuple<float, float>> {};

TEST_P(UnitSquareTest, PointInSquare) {
  square unit{{{0, 0}}, 1};
  point pt{{std::get<0>(GetParam()), std::get<1>(GetParam())}};
  EXPECT_TRUE(math::contains(unit, pt));
}

TEST_F(UnitSquareTest, PointOutsideSquare) {
  square unit{{{0, 0}}, 1};
  EXPECT_FALSE(math::contains(unit, {{0.f, 1.1f}}));
  EXPECT_FALSE(math::contains(unit, {{0.f, -0.1f}}));
  EXPECT_FALSE(math::contains(unit, {{-0.1f, 0.0f}}));
  EXPECT_FALSE(math::contains(unit, {{1.1f, 0.0f}}));
}

INSTANTIATE_TEST_CASE_P(Contains, UnitSquareTest,
                        Combine(ValuesIn(generate(0.f, 1.f, 0.25f)),
                                ValuesIn(generate(0.f, 1.f, 0.25f))));

struct LineQuadTest : TestWithParam<point> {};

TEST_P(LineQuadTest, OriginLineIntersectsUnitSquare) {
  square const unit{{{0, 0}}, 1};
  line const ln{{{0, 0}}, GetParam()};
  EXPECT_TRUE(math::intersects(ln, unit));
  EXPECT_TRUE(math::intersects(unit, ln));
}

TEST_P(LineQuadTest, CrossingLineIntersectsUnitSquare) {
  square const unit{{{0, 0}}, 1};
  line const ln{{{0.5, 0.5}}, GetParam()};
  EXPECT_TRUE(math::intersects(ln, unit));
  EXPECT_TRUE(math::intersects(unit, ln));
}

TEST_P(LineQuadTest, CrossingLineIntersectsSquare) {
  square const unit{{{0, 0}}, 0.9};
  line const ln{{{0.5, 0.5}}, GetParam()};
  EXPECT_TRUE(math::intersects(ln, unit));
  EXPECT_TRUE(math::intersects(unit, ln));
}

TEST_F(LineQuadTest, JustPointIntersection) {
  square const unit{{{0, 0}}, 1};
  line const ln{{{1, 1}}, {{2, 1}}};
  EXPECT_TRUE(math::intersects(ln, unit));
  EXPECT_TRUE(math::intersects(unit, ln));
}

TEST_F(LineQuadTest, EntirelyEncasedIntersection) {
  square const unit{{{0, 0}}, 1};
  line const ln{{{0.5, 0.5}}, {{0.75, 0.75}}};
  EXPECT_TRUE(math::intersects(ln, unit));
  EXPECT_TRUE(math::intersects(unit, ln));
}

TEST_F(LineQuadTest, OutsideByAnInch) {
  square const unit{{{0, 0}}, 1};
  line const ln{{{1.001, 1}}, {{2, 1}}};
  math::intersects(ln, unit);
  EXPECT_FALSE(math::intersects(ln, unit));
  EXPECT_FALSE(math::intersects(unit, ln));
}

INSTANTIATE_TEST_CASE_P(Intersects, LineQuadTest, ValuesIn(line_ends));

TEST(CircleTest, CircleIntersectsSelf) {
  circle const c1{{{0, 0}}, 1};
  circle const c2{{{0, 0}}, 1};
  EXPECT_TRUE(math::intersects(c1, c2));
}

TEST(CircleTest, CircleIntersectsAtOnePoint) {
  circle const c1{{{0, 0}}, 1};
  circle const c2{{{0, 2}}, 1};
  EXPECT_TRUE(math::intersects(c1, c2));
}

TEST(CircleTest, CircleIntersectsWithChord) {
  circle const c1{{{0, 0}}, 0.5};
  circle const c2{{{0, 1}}, 0.5};
  EXPECT_TRUE(math::intersects(c1, c2));
}

TEST(CircleTest, CircleContainedWithin) {
  circle const c1{{{0, 0}}, 2};
  circle const c2{{{0, 1}}, 0.5};
  EXPECT_TRUE(math::intersects(c1, c2));
}

TEST(CircleTest, CircleOutsideDoesNotIntersect) {
  circle const c1{{{0, 0}}, 1};
  circle const c2{{{1.5, 1.5}}, 1};
  EXPECT_FALSE(math::intersects(c1, c2));
}

TEST(CircleTest, LineIntersectsFromWithin) {
  circle const c1{{{0, 0}}, 1};
  line const ln{{{0.5, 0.5}}, {{1, 1}}};
  EXPECT_TRUE(math::intersects(c1, ln));
}

TEST(CircleTest, LineIntersectsOnEdge) {
  circle const c1{{{0, 0}}, 1};
  line const ln{{{-1, 1}}, {{1, 1}}};
  EXPECT_TRUE(math::intersects(c1, ln));
}

TEST(CircleTest, LineIntersectsWhenContained) {
  circle const c1{{{0, 0}}, 1};
  line const ln{{{0.5, 0.5}}, {{-0.5, -0.5}}};
  EXPECT_TRUE(math::intersects(c1, ln));
}

TEST(CircleTest, ChordLineIntersects) {
  circle const c1{{{0, 0}}, 1};
  line const ln{{{1.5, -0.5}}, {{-0.5, 1.5}}};
  EXPECT_TRUE(math::intersects(c1, ln));
}

TEST(CircleTest, OutsideLineDoesntIntersect) {
  circle const c1{{{0, 0}}, 1};
  line const ln{{{1, 1}}, {{0, 1.5}}};
  EXPECT_FALSE(math::intersects(c1, ln));
}

TEST(CircleTest, OverlappingQuad) {
  circle const c1{{{0, 0}}, 1};
  square const sq{{{0.5, 0.5}}, 0.5};
  EXPECT_TRUE(math::intersects(c1, sq));
}

TEST(CircleTest, IntersectsAtEdge) {
  circle const c1{{{0, 0}}, 1};
  square const sq{{{-1, 1}}, 2};
  EXPECT_TRUE(math::intersects(c1, sq));
}

TEST(CircleTest, IntersectsAtCorner) {
  circle const c1{{{0, 0}}, 1};
  square const sq{{{0, 1}}, 1};
  EXPECT_TRUE(math::intersects(c1, sq));
}

TEST(CircleTest, ContainingQuad) {
  circle const c1{{{0, 0}}, 1};
  square const sq{{{0, 0}}, 0.5};
  EXPECT_TRUE(math::intersects(c1, sq));
}

TEST(CircleTest, ContainedInQuad) {
  circle const c1{{{0, 0}}, 0.5};
  square const sq{{{-1, -1}}, 2};
  EXPECT_TRUE(math::intersects(c1, sq));
}

TEST(CircleTest, NonIntersectingTangent) {
  circle const c1{{{0, 0}}, 1};
  square const sq{{{1, 1}}, 1};
  EXPECT_FALSE(math::intersects(c1, sq));
}

TEST(CircleTest, NonIntersecting) {
  circle const c1{{{0, 0}}, 1};
  square const sq{{{1.5, 0.5}}, 0.5};
  EXPECT_FALSE(math::intersects(c1, sq));
}

TEST(TriangleTest, TriangleIntersectsSelf) {
  triangle tri{{{0, 0}}, {{0, 1}}, {{1, 0}}};
  EXPECT_TRUE(math::intersects(tri, tri));
}

TEST(TriangleTest, DoesNotIntersectOffset) {
  triangle lhs{{{0, 0}}, {{0, 1}}, {{1, 0}}};
  auto tri = [](math::dim2::point const & pt) {
    return triangle{pt, pt, pt};
  };
  math::dim2::point const clock_ab{{1, 1}};
  math::dim2::point const clock_bc{{-1, -1}};
  math::dim2::point const clock_ca{{-1, 2}};

  // Each of these expectations fails one of the check-edges calls
  // in the intersection algorithm, which proves that each point of
  // the triangle is not within (or on) the bounds of the other triangle
  // Each of these tests indicates one edge of the triangle 'lhs', and
  // tests for whether it orients around any of the points of the other
  // 'triangle'.
  // Tests are done for each edge vs. the the opposite triangle,
  // starting with edges for the lhs, and then the edges on the rhs.
  EXPECT_FALSE(math::intersects(lhs, tri(clock_ab)));
  EXPECT_FALSE(math::intersects(lhs, tri(clock_bc)));
  EXPECT_FALSE(math::intersects(lhs, tri(clock_ca)));
  EXPECT_FALSE(math::intersects(tri(clock_ab), lhs));
  EXPECT_FALSE(math::intersects(tri(clock_bc), lhs));
  EXPECT_FALSE(math::intersects(tri(clock_ca), lhs));
}

TEST(QuadTest, IntersectsContain) {
  quad const lhs = square{{{-0.5f, -0.5f}}, 1};
  quad const rhs = square{{{-.25f, -.25f}}, 0.5};
  EXPECT_TRUE(math::intersects(lhs, rhs));
}

TEST(QuadTest, NoIntersectionAtEdge) {
  quad const lhs = square{{{-0.5f, -0.5f}}, 1};
  quad const rhs = square{{{ 0.0f,  0.5f}}, 1};
  EXPECT_FALSE(math::intersects(lhs, rhs));
}

TEST(QuadTest, NoIntersectionAtCorner) {
  quad const lhs = square{{{-0.5f, -0.5f}}, 1};
  quad const rhs = square{{{ 0.5f,  0.5f}}, 1};
  EXPECT_FALSE(math::intersects(lhs, rhs));
}

TEST(QuadTest, NoIntersection) {
  quad const lhs = square{{{-1.0f, -0.5f}}, 1};
  quad const rhs = square{{{ 0.5f,  0.5f}}, 1};
  EXPECT_FALSE(math::intersects(lhs, rhs));
}

TEST(RotateTest, RotatingSquareAroundOrigin) {
  math::degree degrees{90.0};
  // A square with a side-length of 2 and a center at the origin
  math::vec2 const origin = make_vector(0.f, 0.f);
  quad const object = square{{{-1, -1}}, 2};
  quad const rotated = math::rotate(origin, object, degrees);
  EXPECT_THAT(rotated.ll, Eq(make_vector(1.f, -1.f)));
  EXPECT_THAT(rotated.lr, Eq(make_vector(1.f, 1.f)));
  EXPECT_THAT(rotated.ur, Eq(make_vector(-1.f, 1.f)));
  EXPECT_THAT(rotated.ul, Eq(make_vector(-1.f, -1.f)));
  EXPECT_THAT(math::rotate(origin, rotated, -degrees), Eq(object));
}

TEST(RotateTest, RotatingSquareAroundOwnPoint) {
  math::degree degrees{90.0};
  // A square with a side-length of 2 and a center at the origin
  math::vec2 const axis = make_vector(-1.f, -1.f);
  quad const object = square{{{-1, -1}}, 2};
  quad const rotated = math::rotate(axis, object, degrees);
  EXPECT_THAT(rotated.ll, Eq(make_vector(-1.f, -1.f)));
  EXPECT_THAT(rotated.lr, Eq(make_vector(-1.f, 1.f)));
  EXPECT_THAT(rotated.ur, Eq(make_vector(-3.f, 1.f)));
  EXPECT_THAT(rotated.ul, Eq(make_vector(-3.f, -1.f)));
  EXPECT_THAT(math::rotate(axis, rotated, -degrees), Eq(object));
}