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/**************************************************************************/
/* geometry_3d.h */
/**************************************************************************/
/* This file is part of: */
/* GODOT ENGINE */
/* https://godotengine.org */
/**************************************************************************/
/* Copyright (c) 2014-present Godot Engine contributors (see AUTHORS.md). */
/* Copyright (c) 2007-2014 Juan Linietsky, Ariel Manzur. */
/* */
/* Permission is hereby granted, free of charge, to any person obtaining */
/* a copy of this software and associated documentation files (the */
/* "Software"), to deal in the Software without restriction, including */
/* without limitation the rights to use, copy, modify, merge, publish, */
/* distribute, sublicense, and/or sell copies of the Software, and to */
/* permit persons to whom the Software is furnished to do so, subject to */
/* the following conditions: */
/* */
/* The above copyright notice and this permission notice shall be */
/* included in all copies or substantial portions of the Software. */
/* */
/* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, */
/* EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF */
/* MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. */
/* IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY */
/* CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, */
/* TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE */
/* SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. */
/**************************************************************************/
#ifndef GEOMETRY_3D_H
#define GEOMETRY_3D_H
#include "core/math/face3.h"
#include "core/object/object.h"
#include "core/templates/local_vector.h"
#include "core/templates/vector.h"
class Geometry3D {
public:
static void get_closest_points_between_segments(const Vector3 &p_p0, const Vector3 &p_p1, const Vector3 &p_q0, const Vector3 &p_q1, Vector3 &r_ps, Vector3 &r_qt);
static real_t get_closest_distance_between_segments(const Vector3 &p_p0, const Vector3 &p_p1, const Vector3 &p_q0, const Vector3 &p_q1);
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;
}
// 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;
LocalVector<int> indices;
};
LocalVector<Face> faces;
struct Edge {
int vertex_a, vertex_b;
int face_a, face_b;
};
LocalVector<Edge> edges;
LocalVector<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
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