godot/core/math/geometry_3d.h

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/*  geometry_3d.h                                                        */
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#ifndef GEOMETRY_3D_H
#define GEOMETRY_3D_H

#include "core/math/face3.h"
#include "core/object/object.h"
#include "core/templates/vector.h"

class Geometry3D {
public:
	static void get_closest_points_between_segments(const Vector3 &p1, const Vector3 &p2, const Vector3 &q1, const Vector3 &q2, Vector3 &c1, Vector3 &c2) {
// Do the function 'd' as defined by pb. I think it's a dot product of some sort.
#define d_of(m, n, o, p) ((m.x - n.x) * (o.x - p.x) + (m.y - n.y) * (o.y - p.y) + (m.z - n.z) * (o.z - p.z))

		// Calculate the parametric position on the 2 curves, mua and mub.
		real_t mua = (d_of(p1, q1, q2, q1) * d_of(q2, q1, p2, p1) - d_of(p1, q1, p2, p1) * d_of(q2, q1, q2, q1)) / (d_of(p2, p1, p2, p1) * d_of(q2, q1, q2, q1) - d_of(q2, q1, p2, p1) * d_of(q2, q1, p2, p1));
		real_t mub = (d_of(p1, q1, q2, q1) + mua * d_of(q2, q1, p2, p1)) / d_of(q2, q1, q2, q1);

		// Clip the value between [0..1] constraining the solution to lie on the original curves.
		if (mua < 0) {
			mua = 0;
		}
		if (mub < 0) {
			mub = 0;
		}
		if (mua > 1) {
			mua = 1;
		}
		if (mub > 1) {
			mub = 1;
		}
		c1 = p1.lerp(p2, mua);
		c2 = q1.lerp(q2, mub);
	}

	static real_t get_closest_distance_between_segments(const Vector3 &p_from_a, const Vector3 &p_to_a, const Vector3 &p_from_b, const Vector3 &p_to_b) {
		Vector3 u = p_to_a - p_from_a;
		Vector3 v = p_to_b - p_from_b;
		Vector3 w = p_from_a - p_to_a;
		real_t a = u.dot(u); // Always >= 0
		real_t b = u.dot(v);
		real_t c = v.dot(v); // Always >= 0
		real_t d = u.dot(w);
		real_t e = v.dot(w);
		real_t D = a * c - b * b; // Always >= 0
		real_t sc, sN, sD = D; // sc = sN / sD, default sD = D >= 0
		real_t tc, tN, tD = D; // tc = tN / tD, default tD = D >= 0

		// Compute the line parameters of the two closest points.
		if (D < (real_t)CMP_EPSILON) { // The lines are almost parallel.
			sN = 0.0f; // Force using point P0 on segment S1
			sD = 1.0f; // to prevent possible division by 0.0 later.
			tN = e;
			tD = c;
		} else { // Get the closest points on the infinite lines
			sN = (b * e - c * d);
			tN = (a * e - b * d);
			if (sN < 0.0f) { // sc < 0 => the s=0 edge is visible.
				sN = 0.0f;
				tN = e;
				tD = c;
			} else if (sN > sD) { // sc > 1 => the s=1 edge is visible.
				sN = sD;
				tN = e + b;
				tD = c;
			}
		}

		if (tN < 0.0f) { // tc < 0 => the t=0 edge is visible.
			tN = 0.0f;
			// Recompute sc for this edge.
			if (-d < 0.0f) {
				sN = 0.0f;
			} else if (-d > a) {
				sN = sD;
			} else {
				sN = -d;
				sD = a;
			}
		} else if (tN > tD) { // tc > 1 => the t=1 edge is visible.
			tN = tD;
			// Recompute sc for this edge.
			if ((-d + b) < 0.0f) {
				sN = 0;
			} else if ((-d + b) > a) {
				sN = sD;
			} else {
				sN = (-d + b);
				sD = a;
			}
		}
		// Finally do the division to get sc and tc.
		sc = (Math::is_zero_approx(sN) ? 0.0f : sN / sD);
		tc = (Math::is_zero_approx(tN) ? 0.0f : tN / tD);

		// Get the difference of the two closest points.
		Vector3 dP = w + (sc * u) - (tc * v); // = S1(sc) - S2(tc)

		return dP.length(); // Return the closest distance.
	}

	static inline bool ray_intersects_triangle(const Vector3 &p_from, const Vector3 &p_dir, const Vector3 &p_v0, const Vector3 &p_v1, const Vector3 &p_v2, Vector3 *r_res = nullptr) {
		Vector3 e1 = p_v1 - p_v0;
		Vector3 e2 = p_v2 - p_v0;
		Vector3 h = p_dir.cross(e2);
		real_t a = e1.dot(h);
		if (Math::is_zero_approx(a)) { // Parallel test.
			return false;
		}

		real_t f = 1.0f / a;

		Vector3 s = p_from - p_v0;
		real_t u = f * s.dot(h);

		if ((u < 0.0f) || (u > 1.0f)) {
			return false;
		}

		Vector3 q = s.cross(e1);

		real_t v = f * p_dir.dot(q);

		if ((v < 0.0f) || (u + v > 1.0f)) {
			return false;
		}

		// At this stage we can compute t to find out where
		// the intersection point is on the line.
		real_t t = f * e2.dot(q);

		if (t > 0.00001f) { // ray intersection
			if (r_res) {
				*r_res = p_from + p_dir * t;
			}
			return true;
		} else { // This means that there is a line intersection but not a ray intersection.
			return false;
		}
	}

	static inline bool segment_intersects_triangle(const Vector3 &p_from, const Vector3 &p_to, const Vector3 &p_v0, const Vector3 &p_v1, const Vector3 &p_v2, Vector3 *r_res = nullptr) {
		Vector3 rel = p_to - p_from;
		Vector3 e1 = p_v1 - p_v0;
		Vector3 e2 = p_v2 - p_v0;
		Vector3 h = rel.cross(e2);
		real_t a = e1.dot(h);
		if (Math::is_zero_approx(a)) { // Parallel test.
			return false;
		}

		real_t f = 1.0f / a;

		Vector3 s = p_from - p_v0;
		real_t u = f * s.dot(h);

		if ((u < 0.0f) || (u > 1.0f)) {
			return false;
		}

		Vector3 q = s.cross(e1);

		real_t v = f * rel.dot(q);

		if ((v < 0.0f) || (u + v > 1.0f)) {
			return false;
		}

		// At this stage we can compute t to find out where
		// the intersection point is on the line.
		real_t t = f * e2.dot(q);

		if (t > (real_t)CMP_EPSILON && t <= 1.0f) { // Ray intersection.
			if (r_res) {
				*r_res = p_from + rel * t;
			}
			return true;
		} else { // This means that there is a line intersection but not a ray intersection.
			return false;
		}
	}

	static inline bool segment_intersects_sphere(const Vector3 &p_from, const Vector3 &p_to, const Vector3 &p_sphere_pos, real_t p_sphere_radius, Vector3 *r_res = nullptr, Vector3 *r_norm = nullptr) {
		Vector3 sphere_pos = p_sphere_pos - p_from;
		Vector3 rel = (p_to - p_from);
		real_t rel_l = rel.length();
		if (rel_l < (real_t)CMP_EPSILON) {
			return false; // Both points are the same.
		}
		Vector3 normal = rel / rel_l;

		real_t sphere_d = normal.dot(sphere_pos);

		real_t ray_distance = sphere_pos.distance_to(normal * sphere_d);

		if (ray_distance >= p_sphere_radius) {
			return false;
		}

		real_t inters_d2 = p_sphere_radius * p_sphere_radius - ray_distance * ray_distance;
		real_t inters_d = sphere_d;

		if (inters_d2 >= (real_t)CMP_EPSILON) {
			inters_d -= Math::sqrt(inters_d2);
		}

		// Check in segment.
		if (inters_d < 0 || inters_d > rel_l) {
			return false;
		}

		Vector3 result = p_from + normal * inters_d;

		if (r_res) {
			*r_res = result;
		}
		if (r_norm) {
			*r_norm = (result - p_sphere_pos).normalized();
		}

		return true;
	}

	static inline bool segment_intersects_cylinder(const Vector3 &p_from, const Vector3 &p_to, real_t p_height, real_t p_radius, Vector3 *r_res = nullptr, Vector3 *r_norm = nullptr, int p_cylinder_axis = 2) {
		Vector3 rel = (p_to - p_from);
		real_t rel_l = rel.length();
		if (rel_l < (real_t)CMP_EPSILON) {
			return false; // Both points are the same.
		}

		ERR_FAIL_COND_V(p_cylinder_axis < 0, false);
		ERR_FAIL_COND_V(p_cylinder_axis > 2, false);
		Vector3 cylinder_axis;
		cylinder_axis[p_cylinder_axis] = 1.0f;

		// First check if they are parallel.
		Vector3 normal = (rel / rel_l);
		Vector3 crs = normal.cross(cylinder_axis);
		real_t crs_l = crs.length();

		Vector3 axis_dir;

		if (crs_l < (real_t)CMP_EPSILON) {
			Vector3 side_axis;
			side_axis[(p_cylinder_axis + 1) % 3] = 1.0f; // Any side axis OK.
			axis_dir = side_axis;
		} else {
			axis_dir = crs / crs_l;
		}

		real_t dist = axis_dir.dot(p_from);

		if (dist >= p_radius) {
			return false; // Too far away.
		}

		// Convert to 2D.
		real_t w2 = p_radius * p_radius - dist * dist;
		if (w2 < (real_t)CMP_EPSILON) {
			return false; // Avoid numerical error.
		}
		Size2 size(Math::sqrt(w2), p_height * 0.5f);

		Vector3 side_dir = axis_dir.cross(cylinder_axis).normalized();

		Vector2 from2D(side_dir.dot(p_from), p_from[p_cylinder_axis]);
		Vector2 to2D(side_dir.dot(p_to), p_to[p_cylinder_axis]);

		real_t min = 0, max = 1;

		int axis = -1;

		for (int i = 0; i < 2; i++) {
			real_t seg_from = from2D[i];
			real_t seg_to = to2D[i];
			real_t box_begin = -size[i];
			real_t box_end = size[i];
			real_t cmin, cmax;

			if (seg_from < seg_to) {
				if (seg_from > box_end || seg_to < box_begin) {
					return false;
				}
				real_t length = seg_to - seg_from;
				cmin = (seg_from < box_begin) ? ((box_begin - seg_from) / length) : 0;
				cmax = (seg_to > box_end) ? ((box_end - seg_from) / length) : 1;

			} else {
				if (seg_to > box_end || seg_from < box_begin) {
					return false;
				}
				real_t length = seg_to - seg_from;
				cmin = (seg_from > box_end) ? (box_end - seg_from) / length : 0;
				cmax = (seg_to < box_begin) ? (box_begin - seg_from) / length : 1;
			}

			if (cmin > min) {
				min = cmin;
				axis = i;
			}
			if (cmax < max) {
				max = cmax;
			}
			if (max < min) {
				return false;
			}
		}

		// Convert to 3D again.
		Vector3 result = p_from + (rel * min);
		Vector3 res_normal = result;

		if (axis == 0) {
			res_normal[p_cylinder_axis] = 0;
		} else {
			int axis_side = (p_cylinder_axis + 1) % 3;
			res_normal[axis_side] = 0;
			axis_side = (axis_side + 1) % 3;
			res_normal[axis_side] = 0;
		}

		res_normal.normalize();

		if (r_res) {
			*r_res = result;
		}
		if (r_norm) {
			*r_norm = res_normal;
		}

		return true;
	}

	static bool segment_intersects_convex(const Vector3 &p_from, const Vector3 &p_to, const Plane *p_planes, int p_plane_count, Vector3 *p_res, Vector3 *p_norm) {
		real_t min = -1e20, max = 1e20;

		Vector3 rel = p_to - p_from;
		real_t rel_l = rel.length();

		if (rel_l < (real_t)CMP_EPSILON) {
			return false;
		}

		Vector3 dir = rel / rel_l;

		int min_index = -1;

		for (int i = 0; i < p_plane_count; i++) {
			const Plane &p = p_planes[i];

			real_t den = p.normal.dot(dir);

			if (Math::abs(den) <= (real_t)CMP_EPSILON) {
				continue; // Ignore parallel plane.
			}

			real_t dist = -p.distance_to(p_from) / den;

			if (den > 0) {
				// Backwards facing plane.
				if (dist < max) {
					max = dist;
				}
			} else {
				// Front facing plane.
				if (dist > min) {
					min = dist;
					min_index = i;
				}
			}
		}

		if (max <= min || min < 0 || min > rel_l || min_index == -1) { // Exit conditions.
			return false; // No intersection.
		}

		if (p_res) {
			*p_res = p_from + dir * min;
		}
		if (p_norm) {
			*p_norm = p_planes[min_index].normal;
		}

		return true;
	}

	static Vector3 get_closest_point_to_segment(const Vector3 &p_point, const Vector3 *p_segment) {
		Vector3 p = p_point - p_segment[0];
		Vector3 n = p_segment[1] - p_segment[0];
		real_t l2 = n.length_squared();
		if (l2 < 1e-20f) {
			return p_segment[0]; // Both points are the same, just give any.
		}

		real_t d = n.dot(p) / l2;

		if (d <= 0.0f) {
			return p_segment[0]; // Before first point.
		} else if (d >= 1.0f) {
			return p_segment[1]; // After first point.
		} else {
			return p_segment[0] + n * d; // Inside.
		}
	}

	static Vector3 get_closest_point_to_segment_uncapped(const Vector3 &p_point, const Vector3 *p_segment) {
		Vector3 p = p_point - p_segment[0];
		Vector3 n = p_segment[1] - p_segment[0];
		real_t l2 = n.length_squared();
		if (l2 < 1e-20f) {
			return p_segment[0]; // Both points are the same, just give any.
		}

		real_t d = n.dot(p) / l2;

		return p_segment[0] + n * d; // Inside.
	}

	static inline bool point_in_projected_triangle(const Vector3 &p_point, const Vector3 &p_v1, const Vector3 &p_v2, const Vector3 &p_v3) {
		Vector3 face_n = (p_v1 - p_v3).cross(p_v1 - p_v2);

		Vector3 n1 = (p_point - p_v3).cross(p_point - p_v2);

		if (face_n.dot(n1) < 0) {
			return false;
		}

		Vector3 n2 = (p_v1 - p_v3).cross(p_v1 - p_point);

		if (face_n.dot(n2) < 0) {
			return false;
		}

		Vector3 n3 = (p_v1 - p_point).cross(p_v1 - p_v2);

		if (face_n.dot(n3) < 0) {
			return false;
		}

		return true;
	}

	static inline bool triangle_sphere_intersection_test(const Vector3 *p_triangle, const Vector3 &p_normal, const Vector3 &p_sphere_pos, real_t p_sphere_radius, Vector3 &r_triangle_contact, Vector3 &r_sphere_contact) {
		real_t d = p_normal.dot(p_sphere_pos) - p_normal.dot(p_triangle[0]);

		if (d > p_sphere_radius || d < -p_sphere_radius) {
			// Not touching the plane of the face, return.
			return false;
		}

		Vector3 contact = p_sphere_pos - (p_normal * d);

		/** 2nd) TEST INSIDE TRIANGLE **/

		if (Geometry3D::point_in_projected_triangle(contact, p_triangle[0], p_triangle[1], p_triangle[2])) {
			r_triangle_contact = contact;
			r_sphere_contact = p_sphere_pos - p_normal * p_sphere_radius;
			//printf("solved inside triangle\n");
			return true;
		}

		/** 3rd TEST INSIDE EDGE CYLINDERS **/

		const Vector3 verts[4] = { p_triangle[0], p_triangle[1], p_triangle[2], p_triangle[0] }; // for() friendly

		for (int i = 0; i < 3; i++) {
			// Check edge cylinder.

			Vector3 n1 = verts[i] - verts[i + 1];
			Vector3 n2 = p_sphere_pos - verts[i + 1];

			///@TODO Maybe discard by range here to make the algorithm quicker.

			// Check point within cylinder radius.
			Vector3 axis = n1.cross(n2).cross(n1);
			axis.normalize();

			real_t ad = axis.dot(n2);

			if (ABS(ad) > p_sphere_radius) {
				// No chance with this edge, too far away.
				continue;
			}

			// Check point within edge capsule cylinder.
			/** 4th TEST INSIDE EDGE POINTS **/

			real_t sphere_at = n1.dot(n2);

			if (sphere_at >= 0 && sphere_at < n1.dot(n1)) {
				r_triangle_contact = p_sphere_pos - axis * (axis.dot(n2));
				r_sphere_contact = p_sphere_pos - axis * p_sphere_radius;
				// Point inside here.
				return true;
			}

			real_t r2 = p_sphere_radius * p_sphere_radius;

			if (n2.length_squared() < r2) {
				Vector3 n = (p_sphere_pos - verts[i + 1]).normalized();

				r_triangle_contact = verts[i + 1];
				r_sphere_contact = p_sphere_pos - n * p_sphere_radius;
				return true;
			}

			if (n2.distance_squared_to(n1) < r2) {
				Vector3 n = (p_sphere_pos - verts[i]).normalized();

				r_triangle_contact = verts[i];
				r_sphere_contact = p_sphere_pos - n * p_sphere_radius;
				return true;
			}

			break; // It's pointless to continue at this point, so save some CPU cycles.
		}

		return false;
	}

	static inline Vector<Vector3> clip_polygon(const Vector<Vector3> &polygon, const Plane &p_plane) {
		enum LocationCache {
			LOC_INSIDE = 1,
			LOC_BOUNDARY = 0,
			LOC_OUTSIDE = -1
		};

		if (polygon.size() == 0) {
			return polygon;
		}

		int *location_cache = (int *)alloca(sizeof(int) * polygon.size());
		int inside_count = 0;
		int outside_count = 0;

		for (int a = 0; a < polygon.size(); a++) {
			real_t dist = p_plane.distance_to(polygon[a]);
			if (dist < (real_t)-CMP_POINT_IN_PLANE_EPSILON) {
				location_cache[a] = LOC_INSIDE;
				inside_count++;
			} else {
				if (dist > (real_t)CMP_POINT_IN_PLANE_EPSILON) {
					location_cache[a] = LOC_OUTSIDE;
					outside_count++;
				} else {
					location_cache[a] = LOC_BOUNDARY;
				}
			}
		}

		if (outside_count == 0) {
			return polygon; // No changes.
		} else if (inside_count == 0) {
			return Vector<Vector3>(); // Empty.
		}

		long previous = polygon.size() - 1;
		Vector<Vector3> clipped;

		for (int index = 0; index < polygon.size(); index++) {
			int loc = location_cache[index];
			if (loc == LOC_OUTSIDE) {
				if (location_cache[previous] == LOC_INSIDE) {
					const Vector3 &v1 = polygon[previous];
					const Vector3 &v2 = polygon[index];

					Vector3 segment = v1 - v2;
					real_t den = p_plane.normal.dot(segment);
					real_t dist = p_plane.distance_to(v1) / den;
					dist = -dist;
					clipped.push_back(v1 + segment * dist);
				}
			} else {
				const Vector3 &v1 = polygon[index];
				if ((loc == LOC_INSIDE) && (location_cache[previous] == LOC_OUTSIDE)) {
					const Vector3 &v2 = polygon[previous];
					Vector3 segment = v1 - v2;
					real_t den = p_plane.normal.dot(segment);
					real_t dist = p_plane.distance_to(v1) / den;
					dist = -dist;
					clipped.push_back(v1 + segment * dist);
				}

				clipped.push_back(v1);
			}

			previous = index;
		}

		return clipped;
	}

	static Vector<Vector<Face3>> separate_objects(Vector<Face3> p_array);

	// Create a "wrap" that encloses the given geometry.
	static Vector<Face3> wrap_geometry(Vector<Face3> p_array, real_t *p_error = nullptr);

	struct MeshData {
		struct Face {
			Plane plane;
			Vector<int> indices;
		};

		Vector<Face> faces;

		struct Edge {
			int a, b;
		};

		Vector<Edge> edges;

		Vector<Vector3> vertices;

		void optimize_vertices();
	};

	static MeshData build_convex_mesh(const Vector<Plane> &p_planes);
	static Vector<Plane> build_sphere_planes(real_t p_radius, int p_lats, int p_lons, Vector3::Axis p_axis = Vector3::AXIS_Z);
	static Vector<Plane> build_box_planes(const Vector3 &p_extents);
	static Vector<Plane> build_cylinder_planes(real_t p_radius, real_t p_height, int p_sides, Vector3::Axis p_axis = Vector3::AXIS_Z);
	static Vector<Plane> build_capsule_planes(real_t p_radius, real_t p_height, int p_sides, int p_lats, Vector3::Axis p_axis = Vector3::AXIS_Z);

	static Vector<Vector3> compute_convex_mesh_points(const Plane *p_planes, int p_plane_count);

#define FINDMINMAX(x0, x1, x2, min, max) \
	min = max = x0;                      \
	if (x1 < min) {                      \
		min = x1;                        \
	}                                    \
	if (x1 > max) {                      \
		max = x1;                        \
	}                                    \
	if (x2 < min) {                      \
		min = x2;                        \
	}                                    \
	if (x2 > max) {                      \
		max = x2;                        \
	}

	_FORCE_INLINE_ static bool planeBoxOverlap(Vector3 normal, float d, Vector3 maxbox) {
		int q;
		Vector3 vmin, vmax;
		for (q = 0; q <= 2; q++) {
			if (normal[q] > 0.0f) {
				vmin[q] = -maxbox[q];
				vmax[q] = maxbox[q];
			} else {
				vmin[q] = maxbox[q];
				vmax[q] = -maxbox[q];
			}
		}
		if (normal.dot(vmin) + d > 0.0f) {
			return false;
		}
		if (normal.dot(vmax) + d >= 0.0f) {
			return true;
		}

		return false;
	}

/*======================== X-tests ========================*/
#define AXISTEST_X01(a, b, fa, fb)                 \
	p0 = a * v0.y - b * v0.z;                      \
	p2 = a * v2.y - b * v2.z;                      \
	if (p0 < p2) {                                 \
		min = p0;                                  \
		max = p2;                                  \
	} else {                                       \
		min = p2;                                  \
		max = p0;                                  \
	}                                              \
	rad = fa * boxhalfsize.y + fb * boxhalfsize.z; \
	if (min > rad || max < -rad) {                 \
		return false;                              \
	}

#define AXISTEST_X2(a, b, fa, fb)                  \
	p0 = a * v0.y - b * v0.z;                      \
	p1 = a * v1.y - b * v1.z;                      \
	if (p0 < p1) {                                 \
		min = p0;                                  \
		max = p1;                                  \
	} else {                                       \
		min = p1;                                  \
		max = p0;                                  \
	}                                              \
	rad = fa * boxhalfsize.y + fb * boxhalfsize.z; \
	if (min > rad || max < -rad) {                 \
		return false;                              \
	}

/*======================== Y-tests ========================*/
#define AXISTEST_Y02(a, b, fa, fb)                 \
	p0 = -a * v0.x + b * v0.z;                     \
	p2 = -a * v2.x + b * v2.z;                     \
	if (p0 < p2) {                                 \
		min = p0;                                  \
		max = p2;                                  \
	} else {                                       \
		min = p2;                                  \
		max = p0;                                  \
	}                                              \
	rad = fa * boxhalfsize.x + fb * boxhalfsize.z; \
	if (min > rad || max < -rad) {                 \
		return false;                              \
	}

#define AXISTEST_Y1(a, b, fa, fb)                  \
	p0 = -a * v0.x + b * v0.z;                     \
	p1 = -a * v1.x + b * v1.z;                     \
	if (p0 < p1) {                                 \
		min = p0;                                  \
		max = p1;                                  \
	} else {                                       \
		min = p1;                                  \
		max = p0;                                  \
	}                                              \
	rad = fa * boxhalfsize.x + fb * boxhalfsize.z; \
	if (min > rad || max < -rad) {                 \
		return false;                              \
	}

	/*======================== Z-tests ========================*/

#define AXISTEST_Z12(a, b, fa, fb)                 \
	p1 = a * v1.x - b * v1.y;                      \
	p2 = a * v2.x - b * v2.y;                      \
	if (p2 < p1) {                                 \
		min = p2;                                  \
		max = p1;                                  \
	} else {                                       \
		min = p1;                                  \
		max = p2;                                  \
	}                                              \
	rad = fa * boxhalfsize.x + fb * boxhalfsize.y; \
	if (min > rad || max < -rad) {                 \
		return false;                              \
	}

#define AXISTEST_Z0(a, b, fa, fb)                  \
	p0 = a * v0.x - b * v0.y;                      \
	p1 = a * v1.x - b * v1.y;                      \
	if (p0 < p1) {                                 \
		min = p0;                                  \
		max = p1;                                  \
	} else {                                       \
		min = p1;                                  \
		max = p0;                                  \
	}                                              \
	rad = fa * boxhalfsize.x + fb * boxhalfsize.y; \
	if (min > rad || max < -rad) {                 \
		return false;                              \
	}

	_FORCE_INLINE_ static bool triangle_box_overlap(const Vector3 &boxcenter, const Vector3 boxhalfsize, const Vector3 *triverts) {
		/*    use separating axis theorem to test overlap between triangle and box */
		/*    need to test for overlap in these directions: */
		/*    1) the {x,y,z}-directions (actually, since we use the AABB of the triangle */
		/*       we do not even need to test these) */
		/*    2) normal of the triangle */
		/*    3) crossproduct(edge from tri, {x,y,z}-directin) */
		/*       this gives 3x3=9 more tests */
		Vector3 v0, v1, v2;
		float min, max, d, p0, p1, p2, rad, fex, fey, fez;
		Vector3 normal, e0, e1, e2;

		/* This is the fastest branch on Sun */
		/* move everything so that the boxcenter is in (0,0,0) */

		v0 = triverts[0] - boxcenter;
		v1 = triverts[1] - boxcenter;
		v2 = triverts[2] - boxcenter;

		/* compute triangle edges */
		e0 = v1 - v0; /* tri edge 0 */
		e1 = v2 - v1; /* tri edge 1 */
		e2 = v0 - v2; /* tri edge 2 */

		/* Bullet 3:  */
		/*  test the 9 tests first (this was faster) */
		fex = Math::abs(e0.x);
		fey = Math::abs(e0.y);
		fez = Math::abs(e0.z);
		AXISTEST_X01(e0.z, e0.y, fez, fey);
		AXISTEST_Y02(e0.z, e0.x, fez, fex);
		AXISTEST_Z12(e0.y, e0.x, fey, fex);

		fex = Math::abs(e1.x);
		fey = Math::abs(e1.y);
		fez = Math::abs(e1.z);
		AXISTEST_X01(e1.z, e1.y, fez, fey);
		AXISTEST_Y02(e1.z, e1.x, fez, fex);
		AXISTEST_Z0(e1.y, e1.x, fey, fex);

		fex = Math::abs(e2.x);
		fey = Math::abs(e2.y);
		fez = Math::abs(e2.z);
		AXISTEST_X2(e2.z, e2.y, fez, fey);
		AXISTEST_Y1(e2.z, e2.x, fez, fex);
		AXISTEST_Z12(e2.y, e2.x, fey, fex);

		/* Bullet 1: */
		/*  first test overlap in the {x,y,z}-directions */
		/*  find min, max of the triangle each direction, and test for overlap in */
		/*  that direction -- this is equivalent to testing a minimal AABB around */
		/*  the triangle against the AABB */

		/* test in X-direction */
		FINDMINMAX(v0.x, v1.x, v2.x, min, max);
		if (min > boxhalfsize.x || max < -boxhalfsize.x) {
			return false;
		}

		/* test in Y-direction */
		FINDMINMAX(v0.y, v1.y, v2.y, min, max);
		if (min > boxhalfsize.y || max < -boxhalfsize.y) {
			return false;
		}

		/* test in Z-direction */
		FINDMINMAX(v0.z, v1.z, v2.z, min, max);
		if (min > boxhalfsize.z || max < -boxhalfsize.z) {
			return false;
		}

		/* Bullet 2: */
		/*  test if the box intersects the plane of the triangle */
		/*  compute plane equation of triangle: normal*x+d=0 */
		normal = e0.cross(e1);
		d = -normal.dot(v0); /* plane eq: normal.x+d=0 */
		return planeBoxOverlap(normal, d, boxhalfsize); /* if true, box and triangle overlaps */
	}

	static Vector<uint32_t> generate_edf(const Vector<bool> &p_voxels, const Vector3i &p_size, bool p_negative);
	static Vector<int8_t> generate_sdf8(const Vector<uint32_t> &p_positive, const Vector<uint32_t> &p_negative);

	static Vector3 triangle_get_barycentric_coords(const Vector3 &p_a, const Vector3 &p_b, const Vector3 &p_c, const Vector3 &p_pos) {
		Vector3 v0 = p_b - p_a;
		Vector3 v1 = p_c - p_a;
		Vector3 v2 = p_pos - p_a;

		float d00 = v0.dot(v0);
		float d01 = v0.dot(v1);
		float d11 = v1.dot(v1);
		float d20 = v2.dot(v0);
		float d21 = v2.dot(v1);
		float denom = (d00 * d11 - d01 * d01);
		if (denom == 0) {
			return Vector3(); //invalid triangle, return empty
		}
		float v = (d11 * d20 - d01 * d21) / denom;
		float w = (d00 * d21 - d01 * d20) / denom;
		float u = 1.0f - v - w;
		return Vector3(u, v, w);
	}

	static Color tetrahedron_get_barycentric_coords(const Vector3 &p_a, const Vector3 &p_b, const Vector3 &p_c, const Vector3 &p_d, const Vector3 &p_pos) {
		Vector3 vap = p_pos - p_a;
		Vector3 vbp = p_pos - p_b;

		Vector3 vab = p_b - p_a;
		Vector3 vac = p_c - p_a;
		Vector3 vad = p_d - p_a;

		Vector3 vbc = p_c - p_b;
		Vector3 vbd = p_d - p_b;
		// ScTP computes the scalar triple product
#define STP(m_a, m_b, m_c) ((m_a).dot((m_b).cross((m_c))))
		float va6 = STP(vbp, vbd, vbc);
		float vb6 = STP(vap, vac, vad);
		float vc6 = STP(vap, vad, vab);
		float vd6 = STP(vap, vab, vac);
		float v6 = 1 / STP(vab, vac, vad);
		return Color(va6 * v6, vb6 * v6, vc6 * v6, vd6 * v6);
#undef STP
	}

	_FORCE_INLINE_ static Vector3 octahedron_map_decode(const Vector2 &p_uv) {
		// https://twitter.com/Stubbesaurus/status/937994790553227264
		Vector2 f = p_uv * 2.0f - Vector2(1.0f, 1.0f);
		Vector3 n = Vector3(f.x, f.y, 1.0f - Math::abs(f.x) - Math::abs(f.y));
		float t = CLAMP(-n.z, 0.0f, 1.0f);
		n.x += n.x >= 0 ? -t : t;
		n.y += n.y >= 0 ? -t : t;
		return n.normalized();
	}
};

#endif // GEOMETRY_3D_H