refactor(editor): shared plan geometry and formatting helpers

editor/editorGeometry.hpp

@@ -0,0 +1,131 @@
+/*
+This Source Code Form is subject to the
+terms of the Mozilla Public License, v.
+2.0. If a copy of the MPL was not
+distributed with this file, You can
+obtain one at
+http://mozilla.org/MPL/2.0/.
+*/
+
+#pragma once
+
+#include <algorithm>
+#include <cmath>
+#include <glm/glm.hpp>
+
+#include "world/Segment.h"
+
+// plan (x, z) geometry and cubic Bezier curves of the paths, shared by the track tools
+namespace geometry
+{
+
+// points of the paths closer than this are taken for the same point
+double constexpr same_point{0.05};
+
+inline glm::dvec2 plan_of(glm::dvec3 const &Point)
+{
+	return {Point.x, Point.z};
+}
+
+inline double plan_distance(glm::dvec3 const &A, glm::dvec3 const &B)
+{
+	return std::hypot(A.x - B.x, A.z - B.z);
+}
+
+// z component of the 3d cross product; for a unit Direction it's the offset of the Point to its left
+inline double cross(glm::dvec2 const &Direction, glm::dvec2 const &Point)
+{
+	return Direction.x * Point.y - Direction.y * Point.x;
+}
+
+inline glm::dvec2 turned(glm::dvec2 const &Vector, double const Angle)
+{
+	auto const c{std::cos(Angle)};
+	auto const s{std::sin(Angle)};
+	return {Vector.x * c - Vector.y * s, Vector.x * s + Vector.y * c};
+}
+
+inline double signed_angle(glm::dvec2 const &From, glm::dvec2 const &To)
+{
+	return std::atan2(cross(From, To), glm::dot(From, To));
+}
+
+// slope of the direction, rise over the run in the plan
+inline double grade_of(glm::dvec3 const &Direction)
+{
+	return Direction.y / std::max(1e-9, std::hypot(Direction.x, Direction.z));
+}
+
+// path as a cubic Bezier curve; a path without control points is a straight with evenly spread parameter
+struct bezier
+{
+	glm::dvec3 p0, p1, p2, p3;
+
+	explicit bezier(segment_data const &Path)
+	{
+		p0 = Path.points[segment_data::point::start];
+		p3 = Path.points[segment_data::point::end];
+		auto const &control1{Path.points[segment_data::point::control1]};
+		auto const &control2{Path.points[segment_data::point::control2]};
+		if (control1 == glm::dvec3{} && control2 == glm::dvec3{})
+		{
+			p1 = glm::mix(p0, p3, 1.0 / 3.0);
+			p2 = glm::mix(p0, p3, 2.0 / 3.0);
+		}
+		else
+		{
+			p1 = p0 + control1;
+			p2 = p3 + control2;
+		}
+	}
+	glm::dvec3 point(double const T) const
+	{
+		auto const u{1.0 - T};
+		return u * u * u * p0 + 3.0 * u * u * T * p1 + 3.0 * u * T * T * p2 + T * T * T * p3;
+	}
+	glm::dvec3 first(double const T) const
+	{
+		auto const u{1.0 - T};
+		return 3.0 * u * u * (p1 - p0) + 6.0 * u * T * (p2 - p1) + 3.0 * T * T * (p3 - p2);
+	}
+	glm::dvec3 second(double const T) const
+	{
+		return 6.0 * (1.0 - T) * (p2 - 2.0 * p1 + p0) + 6.0 * T * (p3 - 2.0 * p2 + p1);
+	}
+	double plan_length(int const Steps = 32) const
+	{
+		double length{0.0};
+		auto previous{plan_of(p0)};
+		for (int i = 1; i <= Steps; ++i)
+		{
+			auto const next{plan_of(point(static_cast<double>(i) / Steps))};
+			length += glm::distance(previous, next);
+			previous = next;
+		}
+		return length;
+	}
+	// parameter at specified plan distance from the start
+	double parameter(double const Distance, int const Steps = 256) const
+	{
+		double length{0.0};
+		auto previous{plan_of(p0)};
+		for (int i = 1; i <= Steps; ++i)
+		{
+			auto const next{plan_of(point(static_cast<double>(i) / Steps))};
+			auto const step{glm::distance(previous, next)};
+			if (length + step >= Distance)
+				return (i - 1 + (step > 1e-12 ? (Distance - length) / step : 0.0)) / Steps;
+			length += step;
+			previous = next;
+		}
+		return 1.0;
+	}
+};
+
+// distance between the ends of the path, in the plan
+inline double chord_length(segment_data const &Path)
+{
+	return glm::length(plan_of(Path.points[segment_data::point::end] - Path.points[segment_data::point::start]));
+}
+
+} // namespace geometry