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#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;
}
// Helper to lookup into a matrix given an xy vector coordinate
template<typename M>
inline auto &
operator^(M & m, glm::ivec2 xy)
{
return m[xy.x][xy.y];
}
// Create a matrix for the angle, given the targets into the matrix
template<typename M>
inline auto
rotation(typename M::value_type a, glm::ivec2 c1, glm::ivec2 s1, glm::ivec2 c2, glm::ivec2 ms2)
{
M m(1);
sincosf(a, m ^ s1, m ^ c1);
m ^ c2 = m ^ c1;
m ^ ms2 = -(m ^ s1);
return m;
}
// Create a flat (2D) transformation matrix
glm::mat2
rotate_flat(float a)
{
return rotation<glm::mat2>(a, {0, 0}, {0, 1}, {1, 1}, {1, 0});
}
// Create a roll transformation matrix
glm::mat4
rotate_roll(float a)
{
return rotation<glm::mat4>(a, {0, 0}, {0, 1}, {1, 1}, {1, 0});
}
// Create a yaw transformation matrix
glm::mat4
rotate_yaw(float a)
{
return rotation<glm::mat4>(a, {0, 0}, {2, 0}, {2, 2}, {0, 2});
}
// Create a pitch transformation matrix
glm::mat4
rotate_pitch(float a)
{
return rotation<glm::mat4>(a, {1, 1}, {1, 2}, {2, 2}, {2, 1});
}
// Create a bomcined yaw, pitch, roll transformation matrix
glm::mat4
rotate_ypr(glm::vec3 a)
{
return rotate_yaw(a.y) * rotate_pitch(a.x) * rotate_roll(a.z);
}
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};
}
return find_arc_centre(as, sincosf(entrys + half_pi), bs, sincosf(entrye - half_pi));
}
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) {
return find_arcs_radius(start, sincosf(entrys + leftOrRight), end, sincosf(entrye + leftOrRight));
};
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));
}
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