1 files changed, 128 insertions, 0 deletions
diff --git a/lib/maths.cpp b/lib/maths.cpp
new file mode 100644
index 0000000..543c887
--- /dev/null
+++ b/lib/maths.cpp
@@ -0,0 +1,128 @@
+#include "maths.h"
+#include <cmath>
+#include <glm/glm.hpp>
+#include <glm/gtx/rotate_vector.hpp>
+#include <glm/gtx/transform.hpp>
+#include <stdexcept>
+
+glm::mat4
+flat_orientation(const glm::vec3 & diff)
+{
+	static const auto oneeighty {glm::rotate(pi, up)};
+	const auto flatdiff {glm::normalize(glm::vec3 {diff.x, 0, diff.z})};
+	auto e {glm::orientation(flatdiff, north)};
+	// Handle if diff is exactly opposite to north
+	return (std::isnan(e[0][0])) ? oneeighty : e;
+}
+
+float
+vector_yaw(const glm::vec3 & diff)
+{
+	return std::atan2(diff.x, diff.z);
+}
+
+float
+vector_pitch(const glm::vec3 & diff)
+{
+	return std::atan(diff.y);
+}
+
+float
+round_frac(const float & v, const float & frac)
+{
+	return std::round(v / frac) * frac;
+}
+
+float
+normalize(float ang)
+{
+	while (ang > pi) {
+		ang -= two_pi;
+	}
+	while (ang <= -pi) {
+		ang += two_pi;
+	}
+	return ang;
+}
+
+Arc::Arc(const glm::vec3 & centre3, const glm::vec3 & e0p, const glm::vec3 & 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};
+	}())
+{
+}
+
+std::pair<glm::vec2, bool>
+find_arc_centre(glm::vec2 as, float entrys, glm::vec2 bs, float entrye)
+{
+	if (as == bs) {
+		return {as, false};
+	}
+	const auto perps = entrys + half_pi;
+	const auto perpe = entrye - half_pi;
+	const glm::vec2 ad {std::sin(perps), std::cos(perps)};
+	const glm::vec2 bd {std::sin(perpe), std::cos(perpe)};
+	return find_arc_centre(as, ad, bs, bd);
+}
+
+std::pair<glm::vec2, bool>
+find_arc_centre(glm::vec2 as, glm::vec2 ad, glm::vec2 bs, glm::vec2 bd)
+{
+	const auto det = bd.x * ad.y - bd.y * ad.x;
+	if (det != 0) { // near parallel line will yield noisy results
+		const auto d = bs - as;
+		const auto u = (d.y * bd.x - d.x * bd.y) / det;
+		return {as + ad * u, u < 0};
+	}
+	throw std::runtime_error("no intersection");
+}
+
+std::pair<float, float>
+find_arcs_radius(glm::vec2 start, float entrys, glm::vec2 end, float entrye)
+{
+	const auto getrad = [&](float leftOrRight) {
+		const auto perps = entrys + leftOrRight;
+		const auto perpe = entrye + leftOrRight;
+		const glm::vec2 ad {std::sin(perps), std::cos(perps)};
+		const glm::vec2 bd {std::sin(perpe), std::cos(perpe)};
+		return find_arcs_radius(start, ad, end, bd);
+	};
+	return {getrad(-half_pi), getrad(half_pi)};
+}
+
+float
+find_arcs_radius(glm::vec2 start, glm::vec2 ad, glm::vec2 end, glm::vec2 bd)
+{
+	// Short name functions for big forula
+	auto sq = [](auto v) {
+		return v * v;
+	};
+	auto sqrt = [](float v) {
+		return std::sqrt(v);
+	};
+
+	// 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));
+}