LineSegment::getIntersection2DSValue incorrect results

[robomic]

Describe the bug
LineSegment::getIntersection2DSValue behaves incorrectly (does not return std::nullopt) when provided a point that lies within a vertical strip defined by the segment's endpoints.

Example
This example checks function behavior on numerous points that are disjoint with the segment. It showcases erroneous examples with a red cross.

scenario_simulator_v2/common/math/geometry/test/src/polygon/test_line_segment.cpp

Lines 496 to 515 in e74ea14

	TEST(LineSegment, getIntersection2DSValue_point_outside)
	{
	const auto line =
	math::geometry::LineSegment(makePoint(-2.0, -2.0, 0.0), makePoint(1.0, 4.0, 0.0));
	EXPECT_FALSE(line.getIntersection2DSValue(makePoint(-3.0, 1.0, 0.0), true).has_value());
	EXPECT_FALSE(line.getIntersection2DSValue(makePoint(-1.0, 1.0, 0.0), true).has_value());
	EXPECT_FALSE(line.getIntersection2DSValue(makePoint(0.0, 1.0, 0.0), true).has_value());
	EXPECT_FALSE(line.getIntersection2DSValue(makePoint(2.0, 1.0, 0.0), true).has_value());
	EXPECT_FALSE(line.getIntersection2DSValue(makePoint(-0.5, -5.0, 0.0), true).has_value());
	EXPECT_FALSE(line.getIntersection2DSValue(makePoint(-0.5, -1.0, 0.0), true).has_value());
	EXPECT_FALSE(line.getIntersection2DSValue(makePoint(-0.5, 3.0, 0.0), true).has_value());
	EXPECT_FALSE(line.getIntersection2DSValue(makePoint(-0.5, 7.0, 0.0), true).has_value());
	EXPECT_FALSE(line.getIntersection2DSValue(makePoint(7.0, 7.0, 0.0), true).has_value());
	EXPECT_FALSE(line.getIntersection2DSValue(makePoint(7.0, -7.0, 0.0), true).has_value());
	EXPECT_FALSE(line.getIntersection2DSValue(makePoint(-7.0, 7.0, 0.0), true).has_value());
	EXPECT_FALSE(line.getIntersection2DSValue(makePoint(-7.0, -7.0, 0.0), true).has_value());
	}

• Green dots mean no intersection; std::nullopt is returned.
• Red crosses mean an intersection; a value is returned.

To Reproduce
Steps to reproduce the behavior:

1. Switch to this branch, precisely, this commit.
2. Build and run tests.
3. See output.

Expected behavior
Function should return std::nullopt when provided with a point that is disjoint (with a tolerance).

Current source code

scenario_simulator_v2/common/math/geometry/src/polygon/line_segment.cpp

Lines 165 to 199 in e74ea14

	/**
	* @brief Find intersection point of 1 line segment and 1 point.
	* @param point point of you want to find intersection.
	* @return std::optional<double>
	*/
	auto LineSegment::getIntersection2DSValue(
	const geometry_msgs::msg::Point & point, const bool denormalize_s) const -> std::optional<double>
	{
	const auto get_s_normalized = [this](const auto & point) -> std::optional<double> {
	const auto get_s_from_x = [this](const auto & point) {
	const auto s = (point.x - start_point.x) / (end_point.x - start_point.x);
	return 0 <= s && s <= 1 ? s : std::optional<double>();
	};
	const auto get_s_from_y = [this](const auto & point) {
	const auto s = (point.y - start_point.y) / (end_point.y - start_point.y);
	return 0 <= s && s <= 1 ? s : std::optional<double>();
	};
	constexpr double epsilon = std::numeric_limits<double>::epsilon();
	if (std::abs(end_point.x - start_point.x) <= epsilon) {
	if (std::abs(end_point.y - start_point.y) <= epsilon) {
	/// @note If start_point and end_point is a same point, checking the point is same as end_point or not.
	return (std::abs(end_point.x - point.x) <= epsilon &&
	std::abs(end_point.y - point.y) <= epsilon)
	? std::optional<double>(0)
	: std::optional<double>();
	}
	/// @note If the line segment is parallel to y axis, calculate s value from y axis value.
	return std::abs(point.x - start_point.x) <= epsilon ? get_s_from_y(point)
	: std::optional<double>();
	}
	/// @note If the line segment is not parallel to x and y axis, calculate s value from x axis value.
	return get_s_from_x(point);
	};
	return denormalize_s ? denormalize(get_s_normalized(point)) : get_s_normalized(point);
	}