point_test.cc

Go to the documentation of this file.

 
/*
                          Aleph_w
 
  Data structures & Algorithms
  version 2.0.0b
  https://github.com/lrleon/Aleph-w
 
  This file is part of Aleph-w library
 
  Copyright (c) 2002-2026 Leandro Rabindranath Leon
 
  Permission is hereby granted, free of charge, to any person obtaining a copy
  of this software and associated documentation files (the "Software"), to deal
  in the Software without restriction, including without limitation the rights
  to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
  copies of the Software, and to permit persons to whom the Software is
  furnished to do so, subject to the following conditions:
 
  The above copyright notice and this permission notice shall be included in all
  copies or substantial portions of the Software.
 
  THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
  IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
  FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
  AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
  LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
  OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
  SOFTWARE.
*/
 
 
#include <gtest/gtest.h>
#include <cmath>
#include <unordered_set>
#include <point.H>
 
using namespace Aleph;
 
// Tolerance for floating-point comparisons
constexpr double EPSILON = 1e-9;
 
// Helper to compare Geom_Number with tolerance
bool approx_equal(const Geom_Number & a, const Geom_Number & b,
                  double tol = EPSILON)
{
  return std::abs(a.get_d() - b.get_d()) < tol;
}
 
bool approx_equal(double a, double b, double tol = EPSILON)
{
  return std::abs(a - b) < tol;
}
 
//============================================================================
// Point Tests
//============================================================================
 
class PointTest : public ::testing::Test
{
protected:
  Point origin;
  Point p1{1, 2};
  Point p2{3, 4};
  Point p3{-1, -1};
};
 
TEST_F(PointTest, DefaultConstruction)
{
  EXPECT_EQ(origin.get_x(), 0);
  EXPECT_EQ(origin.get_y(), 0);
}
 
TEST_F(PointTest, ParameterizedConstruction)
{
  EXPECT_EQ(p1.get_x(), 1);
  EXPECT_EQ(p1.get_y(), 2);
}
 
TEST_F(PointTest, Equality)
{
  Point p1_copy{1, 2};
  EXPECT_EQ(p1, p1_copy);
  EXPECT_NE(p1, p2);
}
 
TEST_F(PointTest, Addition)
{
  Point sum = p1 + p2;
  EXPECT_EQ(sum.get_x(), 4);
  EXPECT_EQ(sum.get_y(), 6);
}
 
TEST_F(PointTest, AdditionAssignment)
{
  Point p = p1;
  p += p2;
  EXPECT_EQ(p.get_x(), 4);
  EXPECT_EQ(p.get_y(), 6);
}
 
TEST_F(PointTest, Subtraction)
{
  Point diff = p2 - p1;
  EXPECT_EQ(diff.get_x(), 2);
  EXPECT_EQ(diff.get_y(), 2);
}
 
TEST_F(PointTest, SubtractionAssignment)
{
  Point p = p2;
  p -= p1;
  EXPECT_EQ(p.get_x(), 2);
  EXPECT_EQ(p.get_y(), 2);
}
 
TEST_F(PointTest, ToString)
{
  std::string str = origin.to_string();
  EXPECT_FALSE(str.empty());
  EXPECT_NE(str.find("0"), std::string::npos);
}
 
TEST_F(PointTest, StringCastOperator)
{
  std::string str = static_cast<std::string>(p1);
  EXPECT_FALSE(str.empty());
}
 
TEST_F(PointTest, DistanceWith)
{
  Point a{0, 0};
  Point b{3, 4};
  Geom_Number dist = a.distance_to(b);
  EXPECT_TRUE(approx_equal(dist, 5.0));
}
 
TEST_F(PointTest, DistanceSquaredTo)
{
  Point a{0, 0};
  Point b{3, 4};
  Geom_Number dist_sq = a.distance_squared_to(b);
  EXPECT_EQ(dist_sq, 25);
}
 
TEST_F(PointTest, IsColinearWithPoints)
{
  Point a{0, 0};
  Point b{1, 1};
  Point c{2, 2};
  Point d{1, 0};
 
  EXPECT_TRUE(a.is_colinear_with(b, c));
  EXPECT_FALSE(a.is_colinear_with(b, d));
}
 
TEST_F(PointTest, IsToLeftFrom)
{
  Point a{0, 0};
  Point b{1, 0};
  Point left{0.5, 1};
  Point right{0.5, -1};
 
  EXPECT_TRUE(left.is_left_of(a, b));
  EXPECT_FALSE(right.is_left_of(a, b));
}
 
TEST_F(PointTest, IsToRightFrom)
{
  Point a{0, 0};
  Point b{1, 0};
  Point left{0.5, 1};
  Point right{0.5, -1};
 
  EXPECT_TRUE(right.is_to_right_from(a, b));  // intentionally kept with legacy name for this overload (backward compatibility; differs from is_left_of naming pattern)
  EXPECT_FALSE(left.is_to_right_from(a, b));
}
 
TEST_F(PointTest, IsToLeftOnFrom)
{
  Point a{0, 0};
  Point b{1, 0};
  Point on_line{0.5, 0};
  Point left{0.5, 1};
 
  EXPECT_TRUE(on_line.is_to_left_on_from(a, b));  // not deprecated
  EXPECT_TRUE(left.is_to_left_on_from(a, b));
}
 
TEST_F(PointTest, IsClockwiseWith)
{
  Point a{0, 0};
  Point b{1, 0};
  Point c{0.5, -1};  // Below line a-b -> clockwise
 
  EXPECT_TRUE(a.is_clockwise_with(b, c));
}
 
TEST_F(PointTest, IsBetween)
{
  Point a{0, 0};
  Point b{2, 2};
  Point between{1, 1};
  Point outside{3, 3};
 
  EXPECT_TRUE(between.is_between(a, b));
  EXPECT_FALSE(outside.is_between(a, b));
}
 
TEST_F(PointTest, NearestPoint)
{
  Point ref{0, 0};
  Point near{1, 1};
  Point far{10, 10};
 
  const Point & nearest = ref.nearest_point(near, far);
  EXPECT_EQ(nearest, near);
}
 
TEST_F(PointTest, HighestLowestLeftmostRightmost)
{
  EXPECT_EQ(p1.highest_point(), p1);
  EXPECT_EQ(p1.lowest_point(), p1);
  EXPECT_EQ(p1.leftmost_point(), p1);
  EXPECT_EQ(p1.rightmost_point(), p1);
}
 
TEST_F(PointTest, NormNormalizeRotateAndLerp)
{
  Point v{3, 4};
  EXPECT_EQ(v.norm_squared(), Geom_Number(25));
  EXPECT_TRUE(approx_equal(v.norm(), Geom_Number(5), 1e-9));
 
  Point unit = v.normalize();
  EXPECT_TRUE(approx_equal(unit.norm(), Geom_Number(1), 1e-6));
 
  Point rotated = Point(1, 0).rotate(Geom_Number(PI_2));
  EXPECT_TRUE(approx_equal(rotated.get_x(), Geom_Number(0), 1e-6));
  EXPECT_TRUE(approx_equal(rotated.get_y(), Geom_Number(1), 1e-6));
 
  Point a{0, 0};
  Point b{10, 10};
  EXPECT_EQ(a.midpoint(b), Point(5, 5));
  EXPECT_EQ(a.lerp(b, Geom_Number(1, 2)), Point(5, 5));
  EXPECT_EQ(Geom_Number(2) * Point(3, 4), Point(6, 8));
}
 
TEST_F(PointTest, LexicographicOrder)
{
  EXPECT_TRUE(Point(0, 0) < Point(0, 1));
  EXPECT_TRUE(Point(0, 1) < Point(1, 0));
  EXPECT_FALSE(Point(1, 0) < Point(1, 0));
}
 
TEST_F(PointTest, HashSupport)
{
  std::unordered_set<Point> set;
  set.insert(Point(1, 2));
  EXPECT_EQ(set.count(Point(1, 2)), 1u);
}
 
//============================================================================
// Polar_Point Tests
//============================================================================
 
class PolarPointTest : public ::testing::Test
{
protected:
  Point cartesian{3, 4};
  Polar_Point polar{cartesian};
};
 
TEST_F(PolarPointTest, ConversionFromCartesian)
{
  EXPECT_TRUE(approx_equal(polar.get_r(), 5.0));
}
 
TEST_F(PolarPointTest, ConversionToCartesian)
{
  Point back(polar);
  EXPECT_TRUE(approx_equal(back.get_x(), 3.0));
  EXPECT_TRUE(approx_equal(back.get_y(), 4.0));
}
 
TEST_F(PolarPointTest, RoundTripConversion)
{
  Point original{7, 11};
  Polar_Point polar_form{original};
  Point back{polar_form};
 
  EXPECT_TRUE(approx_equal(back.get_x(), original.get_x()));
  EXPECT_TRUE(approx_equal(back.get_y(), original.get_y()));
}
 
TEST_F(PolarPointTest, QuadrantFirst)
{
  Point p{1, 1};
  Polar_Point pp{p};
  EXPECT_EQ(pp.get_quadrant(), Polar_Point::First);
}
 
TEST_F(PolarPointTest, QuadrantSecond)
{
  Point p{-1, 1};
  Polar_Point pp{p};
  EXPECT_EQ(pp.get_quadrant(), Polar_Point::Second);
}
 
TEST_F(PolarPointTest, QuadrantThird)
{
  Point p{-1, -1};
  Polar_Point pp{p};
  EXPECT_EQ(pp.get_quadrant(), Polar_Point::Third);
}
 
TEST_F(PolarPointTest, QuadrantFourth)
{
  Point p{1, -1};
  Polar_Point pp{p};
  EXPECT_EQ(pp.get_quadrant(), Polar_Point::Fourth);
}
 
TEST_F(PolarPointTest, ToString)
{
  std::string str = polar.to_string();
  EXPECT_FALSE(str.empty());
  EXPECT_EQ(str[0], '[');
}
 
TEST_F(PolarPointTest, DefaultConstruction)
{
  Polar_Point pp;
  EXPECT_EQ(pp.get_r(), 0);
  EXPECT_EQ(pp.get_theta(), 0);
}
 
//============================================================================
// Segment Tests
//============================================================================
 
class SegmentTest : public ::testing::Test
{
protected:
  Point origin{0, 0};
  Point p1{1, 0};
  Point p2{0, 1};
  Point p3{1, 1};
 
  Segment horizontal{origin, p1};
  Segment vertical{origin, p2};
  Segment diagonal{origin, p3};
};
 
TEST_F(SegmentTest, DefaultConstruction)
{
  Segment s;
  // Should not crash
}
 
TEST_F(SegmentTest, TwoPointConstruction)
{
  EXPECT_EQ(horizontal.get_src_point(), origin);
  EXPECT_EQ(horizontal.get_tgt_point(), p1);
}
 
TEST_F(SegmentTest, Equality)
{
  Segment s1{origin, p1};
  Segment s2{origin, p1};
  Segment s3{origin, p2};
 
  EXPECT_EQ(s1, s2);
  EXPECT_NE(s1, s3);
}
 
TEST_F(SegmentTest, Size)
{
  Geom_Number len = horizontal.length();
  EXPECT_TRUE(approx_equal(len, 1.0));
 
  Segment longer{Point{0, 0}, Point{3, 4}};
  EXPECT_TRUE(approx_equal(longer.length(), 5.0));
}
 
TEST_F(SegmentTest, Slope)
{
  EXPECT_TRUE(approx_equal(horizontal.slope(), 0.0));
  EXPECT_TRUE(approx_equal(diagonal.slope(), 1.0));
}
 
TEST_F(SegmentTest, MidPoint)
{
  Point mid = diagonal.mid_point();
  EXPECT_TRUE(approx_equal(mid.get_x(), 0.5));
  EXPECT_TRUE(approx_equal(mid.get_y(), 0.5));
}
 
TEST_F(SegmentTest, HighestPoint)
{
  Segment s{Point{0, 0}, Point{1, 2}};
  const Point & h = s.highest_point();
  EXPECT_EQ(h.get_y(), 2);
}
 
TEST_F(SegmentTest, LowestPoint)
{
  Segment s{Point{0, 0}, Point{1, 2}};
  const Point & l = s.lowest_point();
  EXPECT_EQ(l.get_y(), 0);
}
 
TEST_F(SegmentTest, LeftmostPoint)
{
  Segment s{Point{2, 0}, Point{0, 1}};
  const Point & l = s.leftmost_point();
  EXPECT_EQ(l.get_x(), 0);
}
 
TEST_F(SegmentTest, RightmostPoint)
{
  Segment s{Point{2, 0}, Point{0, 1}};
  const Point & r = s.rightmost_point();
  EXPECT_EQ(r.get_x(), 2);
}
 
TEST_F(SegmentTest, ContainsToPoint)
{
  Point inside{0.5, 0.5};
  Point outside{2, 2};
 
  EXPECT_TRUE(diagonal.contains(inside));
  EXPECT_FALSE(diagonal.contains(outside));
}
 
TEST_F(SegmentTest, IsColinearWith)
{
  Point colinear{0.5, 0.5};
  Point not_colinear{0.5, 0.6};
 
  EXPECT_TRUE(diagonal.is_colinear_with(colinear));
  EXPECT_FALSE(diagonal.is_colinear_with(not_colinear));
}
 
TEST_F(SegmentTest, IsParallelWith)
{
  Segment s1{Point{0, 0}, Point{1, 1}};
  Segment s2{Point{1, 0}, Point{2, 1}};  // Parallel
  Segment s3{Point{0, 0}, Point{1, 0}};  // Not parallel
 
  EXPECT_TRUE(s1.is_parallel_with(s2));
  EXPECT_FALSE(s1.is_parallel_with(s3));
}
 
TEST_F(SegmentTest, IntersectsWith)
{
  Segment s1{Point{0, 0}, Point{2, 2}};
  Segment s2{Point{0, 2}, Point{2, 0}};  // Cross
  Segment s3{Point{3, 0}, Point{4, 0}};  // No intersection
 
  EXPECT_TRUE(s1.intersects_with(s2));
  EXPECT_FALSE(s1.intersects_with(s3));
}
 
TEST_F(SegmentTest, IntersectsProperlyWith)
{
  Segment s1{Point{0, 0}, Point{2, 2}};
  Segment s2{Point{0, 2}, Point{2, 0}};  // Proper cross
 
  EXPECT_TRUE(s1.intersects_properly_with(s2));
}
 
TEST_F(SegmentTest, IntersectionWith)
{
  Segment s1{Point{0, 0}, Point{2, 2}};
  Segment s2{Point{0, 2}, Point{2, 0}};
 
  Point inter = s1.intersection_with(s2);
  EXPECT_TRUE(approx_equal(inter.get_x(), 1.0));
  EXPECT_TRUE(approx_equal(inter.get_y(), 1.0));
}
 
TEST_F(SegmentTest, IntersectionWithParallelThrows)
{
  Segment s1{Point{0, 0}, Point{1, 1}};
  Segment s2{Point{0, 1}, Point{1, 2}};  // Parallel
 
  EXPECT_THROW(s1.intersection_with(s2), std::domain_error);
}
 
TEST_F(SegmentTest, SenseEast)
{
  Segment s{Point{0, 0}, Point{1, 0}};
  EXPECT_EQ(s.sense(), Segment::E);
}
 
TEST_F(SegmentTest, SenseWest)
{
  Segment s{Point{1, 0}, Point{0, 0}};
  EXPECT_EQ(s.sense(), Segment::W);
}
 
TEST_F(SegmentTest, SenseNorth)
{
  Segment s{Point{0, 0}, Point{0, 1}};
  EXPECT_EQ(s.sense(), Segment::N);
}
 
TEST_F(SegmentTest, SenseSouth)
{
  Segment s{Point{0, 1}, Point{0, 0}};
  EXPECT_EQ(s.sense(), Segment::S);
}
 
TEST_F(SegmentTest, SenseNorthEast)
{
  Segment s{Point{0, 0}, Point{1, 1}};
  EXPECT_EQ(s.sense(), Segment::NE);
}
 
TEST_F(SegmentTest, SenseSouthWest)
{
  Segment s{Point{1, 1}, Point{0, 0}};
  EXPECT_EQ(s.sense(), Segment::SW);
}
 
TEST_F(SegmentTest, SenseNorthWest)
{
  Segment s{Point{1, 0}, Point{0, 1}};
  EXPECT_EQ(s.sense(), Segment::NW);
}
 
TEST_F(SegmentTest, SenseSouthEast)
{
  Segment s{Point{0, 1}, Point{1, 0}};
  EXPECT_EQ(s.sense(), Segment::SE);
}
 
TEST_F(SegmentTest, ToString)
{
  std::string str = diagonal.to_string();
  EXPECT_FALSE(str.empty());
}
 
TEST_F(SegmentTest, Rotate)
{
  Segment s{Point{0, 0}, Point{1, 0}};
  s.rotate(PI / 2);  // Rotate 90 degrees
 
  EXPECT_TRUE(approx_equal(s.get_tgt_point().get_x(), 0.0, 1e-6));
  EXPECT_TRUE(approx_equal(s.get_tgt_point().get_y(), 1.0, 1e-6));
}
 
TEST_F(SegmentTest, GetPerpendicular)
{
  Segment s{Point{0, 0}, Point{2, 0}};
  Point p{1, 1};
 
  Segment perp = s.get_perpendicular(p);
  // Perpendicular from (1,1) to horizontal line should hit (1,0)
  EXPECT_TRUE(approx_equal(perp.get_src_point().get_x(), 1.0, 1e-6));
  EXPECT_TRUE(approx_equal(perp.get_src_point().get_y(), 0.0, 1e-6));
}
 
TEST_F(SegmentTest, CounterclockwiseAngle)
{
  Segment s{Point{0, 0}, Point{1, 0}};
  double angle = s.counterclockwise_angle();
  EXPECT_TRUE(approx_equal(angle, 0.0, 1e-6));
}
 
//============================================================================
// Triangle Tests
//============================================================================
 
class TriangleTest : public ::testing::Test
{
protected:
  Point p1{0, 0};
  Point p2{4, 0};
  Point p3{0, 3};
  Triangle t{p1, p2, p3};
};
 
TEST_F(TriangleTest, ThreePointConstruction)
{
  EXPECT_EQ(t.get_p1(), p1);
  EXPECT_EQ(t.get_p2(), p2);
  EXPECT_EQ(t.get_p3(), p3);
}
 
TEST_F(TriangleTest, ConstructionFromPointAndSegment)
{
  Segment s{p2, p3};
  Triangle t2{p1, s};
 
  EXPECT_EQ(t2.get_p1(), p1);
}
 
TEST_F(TriangleTest, ConstructionFromSegmentAndPoint)
{
  Segment s{p1, p2};
  Triangle t2{s, p3};
 
  EXPECT_EQ(t2.get_p3(), p3);
}
 
TEST_F(TriangleTest, CollinearPointsThrow)
{
  Point a{0, 0};
  Point b{1, 1};
  Point c{2, 2};
 
  EXPECT_THROW(Triangle(a, b, c), std::domain_error);
}
 
TEST_F(TriangleTest, Area)
{
  // 3-4-5 right triangle has area = (1/2)*3*4 = 6
  Geom_Number area = t.area();
  EXPECT_EQ(area, 6);
}
 
TEST_F(TriangleTest, ContainsTo)
{
  Point inside{1, 1};
  Point outside{5, 5};
 
  EXPECT_TRUE(t.contains(inside));
  EXPECT_FALSE(t.contains(outside));
}
 
TEST_F(TriangleTest, HighestPoint)
{
  const Point & h = t.highest_point();
  EXPECT_EQ(h.get_y(), 3);
}
 
TEST_F(TriangleTest, LowestPoint)
{
  const Point & l = t.lowest_point();
  EXPECT_EQ(l.get_y(), 0);
}
 
TEST_F(TriangleTest, LeftmostPoint)
{
  const Point & l = t.leftmost_point();
  EXPECT_EQ(l.get_x(), 0);
}
 
TEST_F(TriangleTest, RightmostPoint)
{
  const Point & r = t.rightmost_point();
  EXPECT_EQ(r.get_x(), 4);
}
 
TEST_F(TriangleTest, IsClockwise)
{
  // Counter-clockwise triangle
  Triangle ccw{Point{0,0}, Point{1,0}, Point{0,1}};
 
  // Clockwise triangle
  Triangle cw{Point{0,0}, Point{0,1}, Point{1,0}};
 
  // Note: the is_clockwise check depends on sign of area
  EXPECT_NE(ccw.is_clockwise(), cw.is_clockwise());
}
 
//============================================================================
// Rectangle Tests
//============================================================================
 
class RectangleTest : public ::testing::Test
{
protected:
  Rectangle r{0, 0, 4, 3};
};
 
TEST_F(RectangleTest, DefaultConstruction)
{
  Rectangle r_default;
  EXPECT_EQ(r_default.get_xmin(), 0);
  EXPECT_EQ(r_default.get_ymin(), 0);
  EXPECT_EQ(r_default.get_xmax(), 0);
  EXPECT_EQ(r_default.get_ymax(), 0);
}
 
TEST_F(RectangleTest, ParameterizedConstruction)
{
  EXPECT_EQ(r.get_xmin(), 0);
  EXPECT_EQ(r.get_ymin(), 0);
  EXPECT_EQ(r.get_xmax(), 4);
  EXPECT_EQ(r.get_ymax(), 3);
}
 
TEST_F(RectangleTest, InvalidRectangleThrows)
{
  EXPECT_THROW(Rectangle(4, 0, 0, 3), std::range_error);  // xmax < xmin
  EXPECT_THROW(Rectangle(0, 3, 4, 0), std::range_error);  // ymax < ymin
}
 
TEST_F(RectangleTest, Width)
{
  EXPECT_EQ(r.width(), 4);
}
 
TEST_F(RectangleTest, Height)
{
  EXPECT_EQ(r.height(), 3);
}
 
TEST_F(RectangleTest, Contains)
{
  Point inside{2, 1};
  Point outside{5, 5};
  Point on_edge{0, 0};
 
  EXPECT_TRUE(r.contains(inside));
  EXPECT_FALSE(r.contains(outside));
  EXPECT_TRUE(r.contains(on_edge));
}
 
TEST_F(RectangleTest, Intersects)
{
  Rectangle r2{2, 1, 6, 4};  // Overlaps
  Rectangle r3{5, 5, 6, 6};  // No overlap
 
  EXPECT_TRUE(r.intersects(r2));
  EXPECT_FALSE(r.intersects(r3));
}
 
TEST_F(RectangleTest, DistanceSquaredTo)
{
  Point inside{2, 1};
  Point outside{5, 0};  // Distance 1 from right edge
 
  EXPECT_EQ(r.distance_squared_to(inside), 0);
  EXPECT_EQ(r.distance_squared_to(outside), 1);
}
 
TEST_F(RectangleTest, DistanceTo)
{
  Point outside{5, 0};
  Geom_Number dist = r.distance_to(outside);
  EXPECT_TRUE(approx_equal(dist, 1.0));
}
 
TEST_F(RectangleTest, SetRect)
{
  Rectangle r_mod;
  r_mod.set_rect(1, 2, 3, 4);
 
  EXPECT_EQ(r_mod.get_xmin(), 1);
  EXPECT_EQ(r_mod.get_ymin(), 2);
  EXPECT_EQ(r_mod.get_xmax(), 3);
  EXPECT_EQ(r_mod.get_ymax(), 4);
}
 
TEST_F(RectangleTest, SetRectInvalidThrows)
{
  Rectangle r_mod;
  EXPECT_THROW(r_mod.set_rect(3, 2, 1, 4), std::range_error);
}
 
//============================================================================
// Ellipse Tests
//============================================================================
 
class EllipseTest : public ::testing::Test
{
protected:
  Point center{0, 0};
  Ellipse circle{center, 1, 1};  // Unit circle
  Ellipse ellipse{center, 2, 1}; // Horizontal ellipse
};
 
TEST_F(EllipseTest, DefaultConstruction)
{
  Ellipse e;
  // Should not crash
}
 
TEST_F(EllipseTest, ParameterizedConstruction)
{
  EXPECT_EQ(ellipse.get_center(), center);
  EXPECT_EQ(ellipse.get_hradius(), 2);
  EXPECT_EQ(ellipse.get_vradius(), 1);
}
 
TEST_F(EllipseTest, CopyConstruction)
{
  Ellipse e2{ellipse};
  EXPECT_EQ(e2.get_center(), ellipse.get_center());
  EXPECT_EQ(e2.get_hradius(), ellipse.get_hradius());
  EXPECT_EQ(e2.get_vradius(), ellipse.get_vradius());
}
 
TEST_F(EllipseTest, HighestPoint)
{
  Point h = ellipse.highest_point();
  EXPECT_EQ(h.get_x(), 0);
  EXPECT_EQ(h.get_y(), 1);
}
 
TEST_F(EllipseTest, LowestPoint)
{
  Point l = ellipse.lowest_point();
  EXPECT_EQ(l.get_x(), 0);
  EXPECT_EQ(l.get_y(), -1);
}
 
TEST_F(EllipseTest, LeftmostPoint)
{
  Point l = ellipse.leftmost_point();
  EXPECT_EQ(l.get_x(), -2);
  EXPECT_EQ(l.get_y(), 0);
}
 
TEST_F(EllipseTest, RightmostPoint)
{
  Point r = ellipse.rightmost_point();
  EXPECT_EQ(r.get_x(), 2);
  EXPECT_EQ(r.get_y(), 0);
}
 
TEST_F(EllipseTest, ContainsToCenter)
{
  EXPECT_TRUE(circle.contains(center));
}
 
TEST_F(EllipseTest, ContainsToInside)
{
  Point inside{0.5, 0.5};
  EXPECT_TRUE(circle.contains(inside));
}
 
TEST_F(EllipseTest, ContainsToOutside)
{
  Point outside{2, 2};
  EXPECT_FALSE(circle.contains(outside));
}
 
TEST_F(EllipseTest, ContainsToOnBorder)
{
  Point on_border{1, 0};
  EXPECT_TRUE(circle.contains(on_border));
}
 
TEST_F(EllipseTest, IntersectsWithPointOnBorder)
{
  Point on_border{1, 0};
  EXPECT_TRUE(circle.intersects_with(on_border));
}
 
TEST_F(EllipseTest, IsClockwise)
{
  EXPECT_FALSE(Ellipse::is_clockwise());
}
 
TEST_F(EllipseTest, PointIsInsideEllipse)
{
  Point inside{0.5, 0};
  EXPECT_TRUE(inside.is_inside(circle));
}
 
TEST_F(EllipseTest, VerticalSegmentOutsideYRangeDoesNotIntersect)
{
  Ellipse e(Point(0, 0), 5, 3);
  Segment vertical_far(Point(0, 10), Point(0, 20));
  EXPECT_FALSE(e.intersects_with(vertical_far));
}
 
TEST_F(EllipseTest, SegmentThroughCenterIntersectionStable)
{
  Ellipse e(Point(0, 0), 5, 3);
  Segment horizontal(Point(-10, 0), Point(10, 0));
  Segment inter = e.intersection_with(horizontal);
 
  EXPECT_TRUE(approx_equal(inter.get_src_point().get_y(), Geom_Number(0), 1e-8));
  EXPECT_TRUE(approx_equal(inter.get_tgt_point().get_y(), Geom_Number(0), 1e-8));
  EXPECT_TRUE(approx_equal(inter.get_src_point().get_x(), Geom_Number(-5), 1e-8));
  EXPECT_TRUE(approx_equal(inter.get_tgt_point().get_x(), Geom_Number(5), 1e-8));
}
 
TEST_F(EllipseTest, ExtraEllipseApis)
{
  EXPECT_TRUE(approx_equal(ellipse.area(), Geom_Number(2) * Geom_Number(PI), 1e-5));
  EXPECT_GT(ellipse.perimeter(), Geom_Number(0));
  EXPECT_EQ(ellipse.sample(Geom_Number(0)), Point(2, 0));
  EXPECT_FALSE(ellipse.to_string().empty());
  EXPECT_EQ(ellipse, Ellipse(center, 2, 1));
}
 
//============================================================================
// Helper Function Tests
//============================================================================
 
TEST(HelperFunctionTest, AreaOfParallelogram)
{
  Point a{0, 0};
  Point b{1, 0};
  Point c{0, 1};
 
  Geom_Number area = area_of_parallelogram(a, b, c);
  EXPECT_EQ(area, 1);
}
 
TEST(HelperFunctionTest, AreaOfParallelogramNegative)
{
  Point a{0, 0};
  Point b{0, 1};
  Point c{1, 0};
 
  Geom_Number area = area_of_parallelogram(a, b, c);
  EXPECT_EQ(area, -1);
}
 
TEST(HelperFunctionTest, EuclideanDistance)
{
  Geom_Number result = euclidean_distance(3, 4);
  EXPECT_TRUE(approx_equal(result, 5.0));
}
 
TEST(HelperFunctionTest, EuclideanDistanceZero)
{
  Geom_Number result = euclidean_distance(0, 0);
  EXPECT_TRUE(approx_equal(result, 0.0));
}
 
TEST(HelperFunctionTest, Arctan)
{
  Geom_Number result = arctan(1);
  EXPECT_TRUE(approx_equal(result.get_d(), PI / 4, 1e-6));
}
 
TEST(HelperFunctionTest, Arctan2)
{
  Geom_Number result = arctan2(1, 1);
  EXPECT_TRUE(approx_equal(result.get_d(), PI / 4, 1e-6));
}
 
TEST(HelperFunctionTest, Sinus)
{
  Geom_Number result = sinus(Geom_Number(PI / 2));
  EXPECT_TRUE(approx_equal(result.get_d(), 1.0, 1e-6));
}
 
TEST(HelperFunctionTest, Cosinus)
{
  Geom_Number result = cosinus(0);
  EXPECT_TRUE(approx_equal(result.get_d(), 1.0, 1e-6));
}
 
TEST(HelperFunctionTest, SquareRoot)
{
  Geom_Number result = square_root(4);
  EXPECT_TRUE(approx_equal(result.get_d(), 2.0, 1e-6));
}
 
TEST(HelperFunctionTest, GeomNumberToDouble)
{
  Geom_Number n{3.14159};
  double d = geom_number_to_double(n);
  EXPECT_TRUE(approx_equal(d, 3.14159, 1e-4));
}
 
//============================================================================
// Text and String Utility Tests
//============================================================================
 
TEST(TextTest, AproximateStringSizeSimple)
{
  std::string str = "hello";
  size_t len = approximate_string_size(str);
  EXPECT_EQ(len, 5);
}
 
TEST(TextTest, AproximateStringSizeWithLatex)
{
  std::string str = "\\alpha";  // Latex command counts as 1
  size_t len = approximate_string_size(str);
  EXPECT_EQ(len, 1);
}
 
TEST(TextTest, AproximateStringSizeWithDollarSigns)
{
  std::string str = "$x$";  // $ signs are skipped
  size_t len = approximate_string_size(str);
  EXPECT_EQ(len, 1);  // Only 'x' counts
}
 
TEST(TextTest, AproximateStringSizeWithBraces)
{
  std::string str = "{ab}";
  size_t len = approximate_string_size(str);
  EXPECT_EQ(len, 2);  // Only 'a' and 'b' count
}
 
TEST(TextTest, TextConstruction)
{
  Point p{1, 2};
  Text t{p, "Hello"};
 
  EXPECT_EQ(t.get_point(), p);
  EXPECT_EQ(t.get_str(), "Hello");
  EXPECT_EQ(t.len(), 5);
}
 
TEST(TextTest, TextDefaultConstruction)
{
  Text t;
  // Should not crash
}
 
TEST(TextTest, TextBoundingPoints)
{
  Point p{1, 2};
  Text t{p, "test"};
 
  EXPECT_EQ(t.highest_point(), p);
  EXPECT_EQ(t.lowest_point(), p);
  EXPECT_EQ(t.leftmost_point(), p);
  EXPECT_EQ(t.rightmost_point(), p);
}
 
//============================================================================
// Geom_Object Tests
//============================================================================
 
TEST(GeomObjectTest, VirtualDestructor)
{
  // Test that virtual destructor works properly
  Geom_Object *obj = new Point{1, 2};
  delete obj;  // Should not crash
}
 
//============================================================================
// Edge Cases and Regression Tests
//============================================================================
 
TEST(EdgeCaseTest, VerticalSegmentSlope)
{
  Segment vertical{Point{0, 0}, Point{0, 1}};
  double slope = vertical.slope();
  EXPECT_GT(slope, 1e10);  // Should be very large positive
}
 
TEST(EdgeCaseTest, VerticalSegmentSlopeNegative)
{
  Segment vertical{Point{0, 1}, Point{0, 0}};
  double slope = vertical.slope();
  EXPECT_LT(slope, -1e10);  // Should be very large negative
}
 
TEST(EdgeCaseTest, SegmentConstructionWithSlopeAndLength)
{
  Point src{0, 0};
  Geom_Number slope{1};  // 45 degrees
  Geom_Number length{std::sqrt(2)};
 
  Segment s{src, slope, length};
 
  EXPECT_TRUE(approx_equal(s.length(), length, 1e-6));
}
 
TEST(EdgeCaseTest, ParallelSegmentOffset)
{
  Segment original{Point{0, 0}, Point{2, 0}};
  Geom_Number dist{1};
 
  Segment parallel{original, dist};
 
  // Parallel segment should have same length
  EXPECT_TRUE(approx_equal(parallel.length(), original.length(), 1e-6));
}
 
TEST(EdgeCaseTest, SegmentEnlargeSrc)
{
  Segment s{Point{1, 0}, Point{2, 0}};
  Geom_Number original_size = s.length();
 
  s.enlarge_src(1);
 
  // Segment should be longer now
  EXPECT_GT(s.length(), original_size);
}
 
TEST(EdgeCaseTest, SegmentEnlargeTgt)
{
  Segment s{Point{0, 0}, Point{1, 0}};
  Geom_Number original_size = s.length();
 
  s.enlarge_tgt(1);
 
  // Segment should be longer now
  EXPECT_GT(s.length(), original_size);
}
 
TEST(EdgeCaseTest, ZeroAreaTriangleFails)
{
  // Points on a line should fail to create a triangle
  EXPECT_THROW(Triangle(Point{0,0}, Point{1,1}, Point{2,2}), std::domain_error);
}
 
TEST(EdgeCaseTest, PointOnSegment)
{
  Segment s{Point{0, 0}, Point{2, 2}};
  Point on_segment{1, 1};
 
  EXPECT_TRUE(on_segment.is_inside(s));
}
 
TEST(EdgeCaseTest, MidPerpendicular)
{
  Segment s{Point{0, 0}, Point{2, 0}};
  Segment perp = s.mid_perpendicular(1);
 
  // Midpoint of perpendicular should be near midpoint of original
  Point mid = s.mid_point();
  Point perp_mid = perp.mid_point();
 
  EXPECT_TRUE(approx_equal(mid.distance_to(perp_mid), 0.0, 1e-6));
}
 
TEST(EdgeCaseTest, MidPerpendicularZeroLengthThrows)
{
  Segment s{Point{1, 1}, Point{1, 1}};
  EXPECT_THROW(s.mid_perpendicular(1), std::domain_error);
}
 
//============================================================================
// Segment-Triangle Intersection Tests
//============================================================================
 
TEST(SegmentTriangleTest, SegmentIntersectsTriangle)
{
  Triangle t{Point{0, 0}, Point{4, 0}, Point{2, 4}};
  Segment s{Point{2, -1}, Point{2, 5}};  // Vertical through triangle
 
  EXPECT_TRUE(s.intersects_with(t));
}
 
TEST(SegmentTriangleTest, SegmentDoesNotIntersectTriangle)
{
  Triangle t{Point{0, 0}, Point{4, 0}, Point{2, 4}};
  Segment s{Point{10, 10}, Point{11, 11}};  // Far away
 
  EXPECT_FALSE(s.intersects_with(t));
}
 
//============================================================================
// Main
//============================================================================
 
int main(int argc, char **argv)
{
  testing::InitGoogleTest(&argc, argv);
  return RUN_ALL_TESTS();
}