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-rw-r--r--lib/maths.cpp72
-rw-r--r--lib/maths.h84
2 files changed, 77 insertions, 79 deletions
diff --git a/lib/maths.cpp b/lib/maths.cpp
index 17082d4..68662fc 100644
--- a/lib/maths.cpp
+++ b/lib/maths.cpp
@@ -3,7 +3,6 @@
#include <glm/glm.hpp>
#include <glm/gtx/rotate_vector.hpp>
#include <glm/gtx/transform.hpp>
-#include <stdexcept>
glm::mat4
flat_orientation(const Direction3D & diff)
@@ -106,77 +105,6 @@ normalize(float ang)
return ang;
}
-Arc::Arc(const Position3D & centre3, const Position3D & e0p, const Position3D & 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<Position2D, bool>
-find_arc_centre(Position2D as, float entrys, Position2D 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<Position2D, bool>
-find_arc_centre(Position2D as, Position2D ad, Position2D bs, Position2D 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(Position2D start, float entrys, Position2D 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(Position2D start, Position2D ad, Position2D end, Position2D bd)
-{
- // Short name functions for big forula
- 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));
-}
-
float
operator"" _mph(const long double v)
{
diff --git a/lib/maths.h b/lib/maths.h
index f7ff148..ba8c0e6 100644
--- a/lib/maths.h
+++ b/lib/maths.h
@@ -5,15 +5,17 @@
#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 Position3D & centre3, const Position3D & e0p, const Position3D & 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;
}
@@ -136,10 +138,63 @@ arc_length(const Arc & arc)
float normalize(float ang);
-std::pair<Position2D, bool> find_arc_centre(Position2D start, float entrys, Position2D end, float entrye);
-std::pair<Position2D, bool> find_arc_centre(Position2D start, Position2D ad, Position2D end, Position2D bd);
-std::pair<float, float> find_arcs_radius(Position2D start, float entrys, Position2D end, float entrye);
-float find_arcs_radius(Position2D start, Position2D ad, Position2D end, Position2D 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
@@ -148,6 +203,21 @@ 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
generated by cgit v1.2.3 (git 2.25.1) at 2024-11-22 12:46:59 +0000