Merge remote-tracking branch 'origin/terrain'

1 files changed, 109 insertions, 50 deletions

diff --git a/lib/maths.h b/lib/maths.h
index b95b706..c1bf61a 100644
--- a/lib/maths.h
+++ b/lib/maths.h
@@ -1,36 +1,38 @@
 #pragma once
 
+#include "config/types.h"
 #include <cmath>
 #include <glm/glm.hpp>
 #include <glm/gtc/constants.hpp>
 #include <numeric>
+#include <stdexcept>
 #include <utility>
 
 struct Arc : public std::pair<float, float> {
 	using std::pair<float, float>::pair;
 
-	Arc(const glm::vec3 & centre3, const glm::vec3 & e0p, const glm::vec3 & e1p);
+	template<typename T, glm::qualifier Q>
+	Arc(const glm::vec<3, T, Q> & centre3, const glm::vec<3, T, Q> & e0p, const glm::vec<3, T, Q> & e1p);
 
-	float
-	operator[](unsigned int i) const
+	auto
+	operator[](bool i) const
 	{
 		return i ? second : first;
 	}
 };
 
-constexpr const glm::vec3 origin {0, 0, 0};
-constexpr const glm::vec3 up {0, 0, 1};
-constexpr const glm::vec3 down {0, 0, -1};
-constexpr const glm::vec3 north {0, 1, 0};
-constexpr const glm::vec3 south {0, -1, 0};
-constexpr const glm::vec3 east {1, 0, 0};
-constexpr const glm::vec3 west {-1, 0, 0};
+constexpr const RelativePosition3D up {0, 0, 1};
+constexpr const RelativePosition3D down {0, 0, -1};
+constexpr const RelativePosition3D north {0, 1, 0};
+constexpr const RelativePosition3D south {0, -1, 0};
+constexpr const RelativePosition3D east {1, 0, 0};
+constexpr const RelativePosition3D west {-1, 0, 0};
 constexpr auto half_pi {glm::half_pi<float>()};
 constexpr auto quarter_pi {half_pi / 2};
 constexpr auto pi {glm::pi<float>()};
 constexpr auto two_pi {glm::two_pi<float>()};
 
-glm::mat4 flat_orientation(const glm::vec3 & diff);
+glm::mat4 flat_orientation(const Rotation3D & diff);
 
 // C++ wrapper for C's sincosf, but with references, not pointers
 inline auto
@@ -39,10 +41,10 @@ sincosf(float a, float & s, float & c)
 	return sincosf(a, &s, &c);
 }
 
-inline glm::vec2
+inline Rotation2D
 sincosf(float a)
 {
-	glm::vec2 sc;
+	Rotation2D sc;
 	sincosf(a, sc.x, sc.y);
 	return sc;
 }
@@ -51,11 +53,11 @@ glm::mat2 rotate_flat(float);
 glm::mat4 rotate_roll(float);
 glm::mat4 rotate_yaw(float);
 glm::mat4 rotate_pitch(float);
-glm::mat4 rotate_yp(glm::vec2);
-glm::mat4 rotate_ypr(glm::vec3);
+glm::mat4 rotate_yp(Rotation2D);
+glm::mat4 rotate_ypr(Rotation3D);
 
-float vector_yaw(const glm::vec3 & diff);
-float vector_pitch(const glm::vec3 & diff);
+float vector_yaw(const Direction3D & diff);
+float vector_pitch(const Direction3D & diff);
 
 float round_frac(const float & v, const float & frac);
 
@@ -66,6 +68,17 @@ sq(T v)
 	return v * v;
 }
 
+template<std::integral T, glm::qualifier Q>
+inline constexpr glm::vec<3, T, Q>
+crossInt(const glm::vec<3, T, Q> a, const glm::vec<3, T, Q> b)
+{
+	return {
+			(a.y * b.z) - (a.z * b.y),
+			(a.z * b.x) - (a.x * b.z),
+			(a.x * b.y) - (a.y * b.x),
+	};
+}
+
 template<typename R = float, typename Ta, typename Tb>
 inline constexpr auto
 ratio(Ta a, Tb b)
@@ -87,30 +100,6 @@ perspective_divide(glm::vec<4, T, Q> v)
 	return v / v.w;
 }
 
-constexpr inline glm::vec2
-operator!(const glm::vec3 & v)
-{
-	return {v.x, v.y};
-}
-
-constexpr inline glm::vec3
-operator^(const glm::vec2 & v, float z)
-{
-	return {v.x, v.y, z};
-}
-
-constexpr inline glm::vec4
-operator^(const glm::vec3 & v, float w)
-{
-	return {v.x, v.y, v.z, w};
-}
-
-constexpr inline glm::vec3
-operator!(const glm::vec2 & v)
-{
-	return v ^ 0.F;
-}
-
 template<glm::length_t L1, glm::length_t L2, typename T, glm::qualifier Q>
 inline constexpr glm::vec<L1 + L2, T, Q>
 operator||(const glm::vec<L1, T, Q> v1, const glm::vec<L2, T, Q> v2)
@@ -125,15 +114,17 @@ operator||(const glm::vec<L, T, Q> v1, const T v2)
 	return {v1, v2};
 }
 
-inline glm::vec3
-operator%(const glm::vec3 & p, const glm::mat4 & mutation)
+template<glm::length_t L, typename T, glm::qualifier Q>
+inline constexpr glm::vec<L, T, Q>
+operator%(const glm::vec<L, T, Q> & p, const glm::mat<L + 1, L + 1, T, Q> & mutation)
 {
-	const auto p2 = mutation * (p ^ 1);
+	const auto p2 = mutation * (p || T(1));
 	return p2 / p2.w;
 }
 
-inline glm::vec3
-operator%=(glm::vec3 & p, const glm::mat4 & mutation)
+template<glm::length_t L, typename T, glm::qualifier Q>
+inline constexpr glm::vec<L, T, Q>
+operator%=(glm::vec<L, T, Q> & p, const glm::mat<L + 1, L + 1, T, Q> & mutation)
 {
 	return p = p % mutation;
 }
@@ -146,10 +137,63 @@ arc_length(const Arc & arc)
 
 float normalize(float ang);
 
-std::pair<glm::vec2, bool> find_arc_centre(glm::vec2 start, float entrys, glm::vec2 end, float entrye);
-std::pair<glm::vec2, bool> find_arc_centre(glm::vec2 start, glm::vec2 ad, glm::vec2 end, glm::vec2 bd);
-std::pair<float, float> find_arcs_radius(glm::vec2 start, float entrys, glm::vec2 end, float entrye);
-float find_arcs_radius(glm::vec2 start, glm::vec2 ad, glm::vec2 end, glm::vec2 bd);
+template<typename T, glm::qualifier Q>
+std::pair<glm::vec<2, T, Q>, bool>
+find_arc_centre(glm::vec<2, T, Q> start, Rotation2D startDir, glm::vec<2, T, Q> end, Rotation2D endDir)
+{
+	const auto det = endDir.x * startDir.y - endDir.y * startDir.x;
+	if (det != 0) { // near parallel line will yield noisy results
+		const auto d = end - start;
+		const auto u = (d.y * endDir.x - d.x * endDir.y) / det;
+		return {start + startDir * u, u < 0};
+	}
+	throw std::runtime_error("no intersection");
+}
+
+template<typename T, glm::qualifier Q>
+std::pair<glm::vec<2, T, Q>, bool>
+find_arc_centre(glm::vec<2, T, Q> start, Angle entrys, glm::vec<2, T, Q> end, Angle entrye)
+{
+	if (start == end) {
+		return {start, false};
+	}
+	return find_arc_centre(start, sincosf(entrys + half_pi), end, sincosf(entrye - half_pi));
+}
+
+template<typename T, glm::qualifier Q>
+Angle
+find_arcs_radius(glm::vec<2, T, Q> start, Rotation2D ad, glm::vec<2, T, Q> end, Rotation2D bd)
+{
+	using std::sqrt;
+
+	// Calculates path across both arcs along the normals... pythagorean theorem... for some known radius r
+	// (2r)^2 = ((m + (X*r)) - (o + (Z*r)))^2 + ((n + (Y*r)) - (p + (W*r)))^2
+	// According to symbolabs.com equation tool, that solves for r to give:
+	// r=(-2 m X+2 X o+2 m Z-2 o Z-2 n Y+2 Y p+2 n W-2 p W-sqrt((2 m X-2 X o-2 m Z+2 o Z+2 n Y-2 Y p-2 n W+2 p W)^(2)-4
+	// (X^(2)-2 X Z+Z^(2)+Y^(2)-2 Y W+W^(2)-4) (m^(2)-2 m o+o^(2)+n^(2)-2 n p+p^(2))))/(2 (X^(2)-2 X Z+Z^(2)+Y^(2)-2 Y
+	// W+W^(2)-4))
+
+	// These exist cos limitations of online formula rearrangement, and I'm OK with that.
+	const auto &m {start.x}, &n {start.y}, &o {end.x}, &p {end.y};
+	const auto &X {ad.x}, &Y {ad.y}, &Z {bd.x}, &W {bd.y};
+
+	return (2 * m * X - 2 * X * o - 2 * m * Z + 2 * o * Z + 2 * n * Y - 2 * Y * p - 2 * n * W + 2 * p * W
+				   - sqrt(sq(-2 * m * X + 2 * X * o + 2 * m * Z - 2 * o * Z - 2 * n * Y + 2 * Y * p + 2 * n * W
+								  - 2 * p * W)
+						   - (4 * (sq(X) - 2 * X * Z + sq(Z) + sq(Y) - 2 * Y * W + sq(W) - 4)
+								   * (sq(m) - 2 * m * o + sq(o) + sq(n) - 2 * n * p + sq(p)))))
+			/ (2 * (sq(X) - 2 * X * Z + sq(Z) + sq(Y) - 2 * Y * W + sq(W) - 4));
+}
+
+template<typename T, glm::qualifier Q>
+std::pair<Angle, Angle>
+find_arcs_radius(glm::vec<2, T, Q> start, Angle entrys, glm::vec<2, T, Q> end, Angle entrye)
+{
+	const auto getrad = [&](auto leftOrRight) {
+		return find_arcs_radius(start, sincosf(entrys + leftOrRight), end, sincosf(entrye + leftOrRight));
+	};
+	return {getrad(-half_pi), getrad(half_pi)};
+}
 
 template<typename T>
 auto
@@ -158,6 +202,21 @@ midpoint(const std::pair<T, T> & v)
 	return std::midpoint(v.first, v.second);
 }
 
+template<typename T, glm::qualifier Q>
+Arc::Arc(const glm::vec<3, T, Q> & centre3, const glm::vec<3, T, Q> & e0p, const glm::vec<3, T, Q> & e1p) :
+	Arc([&]() -> Arc {
+		const auto diffa = e0p - centre3;
+		const auto diffb = e1p - centre3;
+		const auto anga = vector_yaw(diffa);
+		const auto angb = [&diffb, &anga]() {
+			const auto angb = vector_yaw(diffb);
+			return (angb < anga) ? angb + two_pi : angb;
+		}();
+		return {anga, angb};
+	}())
+{
+}
+
 // Conversions
 template<typename T>
 inline constexpr auto