d95794ec8a
As many open source projects have started doing it, we're removing the current year from the copyright notice, so that we don't need to bump it every year. It seems like only the first year of publication is technically relevant for copyright notices, and even that seems to be something that many companies stopped listing altogether (in a version controlled codebase, the commits are a much better source of date of publication than a hardcoded copyright statement). We also now list Godot Engine contributors first as we're collectively the current maintainers of the project, and we clarify that the "exclusive" copyright of the co-founders covers the timespan before opensourcing (their further contributions are included as part of Godot Engine contributors). Also fixed "cf." Frenchism - it's meant as "refer to / see".
833 lines
25 KiB
C++
833 lines
25 KiB
C++
/**************************************************************************/
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/* geometry_3d.h */
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/**************************************************************************/
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/* This file is part of: */
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/* GODOT ENGINE */
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/* https://godotengine.org */
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/**************************************************************************/
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/* Copyright (c) 2014-present Godot Engine contributors (see AUTHORS.md). */
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/* Copyright (c) 2007-2014 Juan Linietsky, Ariel Manzur. */
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/* */
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/* Permission is hereby granted, free of charge, to any person obtaining */
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/* a copy of this software and associated documentation files (the */
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/* "Software"), to deal in the Software without restriction, including */
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/* without limitation the rights to use, copy, modify, merge, publish, */
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/* distribute, sublicense, and/or sell copies of the Software, and to */
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/* permit persons to whom the Software is furnished to do so, subject to */
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/* the following conditions: */
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/* */
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/* The above copyright notice and this permission notice shall be */
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/* included in all copies or substantial portions of the Software. */
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/* */
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/* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, */
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/* EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF */
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/* MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. */
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/* IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY */
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/* CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, */
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/* TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE */
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/* SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. */
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/**************************************************************************/
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#ifndef GEOMETRY_3D_H
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#define GEOMETRY_3D_H
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#include "core/math/face3.h"
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#include "core/object/object.h"
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#include "core/templates/local_vector.h"
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#include "core/templates/vector.h"
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class Geometry3D {
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public:
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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);
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static real_t get_closest_distance_between_segments(const Vector3 &p_p0, const Vector3 &p_p1, const Vector3 &p_q0, const Vector3 &p_q1);
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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) {
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Vector3 e1 = p_v1 - p_v0;
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Vector3 e2 = p_v2 - p_v0;
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Vector3 h = p_dir.cross(e2);
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real_t a = e1.dot(h);
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if (Math::is_zero_approx(a)) { // Parallel test.
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return false;
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}
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real_t f = 1.0f / a;
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Vector3 s = p_from - p_v0;
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real_t u = f * s.dot(h);
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if ((u < 0.0f) || (u > 1.0f)) {
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return false;
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}
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Vector3 q = s.cross(e1);
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real_t v = f * p_dir.dot(q);
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if ((v < 0.0f) || (u + v > 1.0f)) {
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return false;
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}
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// At this stage we can compute t to find out where
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// the intersection point is on the line.
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real_t t = f * e2.dot(q);
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if (t > 0.00001f) { // ray intersection
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if (r_res) {
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*r_res = p_from + p_dir * t;
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}
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return true;
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} else { // This means that there is a line intersection but not a ray intersection.
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return false;
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}
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}
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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) {
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Vector3 rel = p_to - p_from;
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Vector3 e1 = p_v1 - p_v0;
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Vector3 e2 = p_v2 - p_v0;
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Vector3 h = rel.cross(e2);
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real_t a = e1.dot(h);
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if (Math::is_zero_approx(a)) { // Parallel test.
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return false;
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}
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real_t f = 1.0f / a;
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Vector3 s = p_from - p_v0;
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real_t u = f * s.dot(h);
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if ((u < 0.0f) || (u > 1.0f)) {
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return false;
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}
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Vector3 q = s.cross(e1);
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real_t v = f * rel.dot(q);
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if ((v < 0.0f) || (u + v > 1.0f)) {
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return false;
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}
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// At this stage we can compute t to find out where
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// the intersection point is on the line.
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real_t t = f * e2.dot(q);
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if (t > (real_t)CMP_EPSILON && t <= 1.0f) { // Ray intersection.
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if (r_res) {
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*r_res = p_from + rel * t;
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}
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return true;
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} else { // This means that there is a line intersection but not a ray intersection.
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return false;
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}
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}
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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) {
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Vector3 sphere_pos = p_sphere_pos - p_from;
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Vector3 rel = (p_to - p_from);
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real_t rel_l = rel.length();
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if (rel_l < (real_t)CMP_EPSILON) {
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return false; // Both points are the same.
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}
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Vector3 normal = rel / rel_l;
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real_t sphere_d = normal.dot(sphere_pos);
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real_t ray_distance = sphere_pos.distance_to(normal * sphere_d);
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if (ray_distance >= p_sphere_radius) {
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return false;
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}
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real_t inters_d2 = p_sphere_radius * p_sphere_radius - ray_distance * ray_distance;
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real_t inters_d = sphere_d;
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if (inters_d2 >= (real_t)CMP_EPSILON) {
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inters_d -= Math::sqrt(inters_d2);
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}
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// Check in segment.
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if (inters_d < 0 || inters_d > rel_l) {
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return false;
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}
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Vector3 result = p_from + normal * inters_d;
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if (r_res) {
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*r_res = result;
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}
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if (r_norm) {
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*r_norm = (result - p_sphere_pos).normalized();
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}
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return true;
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}
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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) {
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Vector3 rel = (p_to - p_from);
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real_t rel_l = rel.length();
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if (rel_l < (real_t)CMP_EPSILON) {
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return false; // Both points are the same.
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}
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ERR_FAIL_COND_V(p_cylinder_axis < 0, false);
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ERR_FAIL_COND_V(p_cylinder_axis > 2, false);
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Vector3 cylinder_axis;
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cylinder_axis[p_cylinder_axis] = 1.0f;
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// First check if they are parallel.
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Vector3 normal = (rel / rel_l);
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Vector3 crs = normal.cross(cylinder_axis);
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real_t crs_l = crs.length();
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Vector3 axis_dir;
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if (crs_l < (real_t)CMP_EPSILON) {
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Vector3 side_axis;
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side_axis[(p_cylinder_axis + 1) % 3] = 1.0f; // Any side axis OK.
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axis_dir = side_axis;
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} else {
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axis_dir = crs / crs_l;
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}
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real_t dist = axis_dir.dot(p_from);
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if (dist >= p_radius) {
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return false; // Too far away.
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}
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// Convert to 2D.
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real_t w2 = p_radius * p_radius - dist * dist;
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if (w2 < (real_t)CMP_EPSILON) {
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return false; // Avoid numerical error.
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}
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Size2 size(Math::sqrt(w2), p_height * 0.5f);
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Vector3 side_dir = axis_dir.cross(cylinder_axis).normalized();
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Vector2 from2D(side_dir.dot(p_from), p_from[p_cylinder_axis]);
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Vector2 to2D(side_dir.dot(p_to), p_to[p_cylinder_axis]);
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real_t min = 0, max = 1;
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int axis = -1;
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for (int i = 0; i < 2; i++) {
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real_t seg_from = from2D[i];
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real_t seg_to = to2D[i];
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real_t box_begin = -size[i];
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real_t box_end = size[i];
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real_t cmin, cmax;
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if (seg_from < seg_to) {
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if (seg_from > box_end || seg_to < box_begin) {
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return false;
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}
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real_t length = seg_to - seg_from;
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cmin = (seg_from < box_begin) ? ((box_begin - seg_from) / length) : 0;
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cmax = (seg_to > box_end) ? ((box_end - seg_from) / length) : 1;
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} else {
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if (seg_to > box_end || seg_from < box_begin) {
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return false;
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}
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real_t length = seg_to - seg_from;
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cmin = (seg_from > box_end) ? (box_end - seg_from) / length : 0;
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cmax = (seg_to < box_begin) ? (box_begin - seg_from) / length : 1;
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}
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if (cmin > min) {
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min = cmin;
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axis = i;
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}
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if (cmax < max) {
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max = cmax;
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}
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if (max < min) {
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return false;
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}
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}
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// Convert to 3D again.
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Vector3 result = p_from + (rel * min);
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Vector3 res_normal = result;
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if (axis == 0) {
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res_normal[p_cylinder_axis] = 0;
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} else {
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int axis_side = (p_cylinder_axis + 1) % 3;
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res_normal[axis_side] = 0;
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axis_side = (axis_side + 1) % 3;
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res_normal[axis_side] = 0;
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}
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res_normal.normalize();
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if (r_res) {
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*r_res = result;
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}
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if (r_norm) {
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*r_norm = res_normal;
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}
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return true;
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}
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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) {
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real_t min = -1e20, max = 1e20;
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Vector3 rel = p_to - p_from;
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real_t rel_l = rel.length();
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if (rel_l < (real_t)CMP_EPSILON) {
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return false;
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}
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Vector3 dir = rel / rel_l;
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int min_index = -1;
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for (int i = 0; i < p_plane_count; i++) {
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const Plane &p = p_planes[i];
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real_t den = p.normal.dot(dir);
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if (Math::abs(den) <= (real_t)CMP_EPSILON) {
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continue; // Ignore parallel plane.
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}
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real_t dist = -p.distance_to(p_from) / den;
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if (den > 0) {
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// Backwards facing plane.
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if (dist < max) {
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max = dist;
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}
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} else {
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// Front facing plane.
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if (dist > min) {
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min = dist;
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min_index = i;
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}
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}
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}
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if (max <= min || min < 0 || min > rel_l || min_index == -1) { // Exit conditions.
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return false; // No intersection.
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}
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if (p_res) {
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*p_res = p_from + dir * min;
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}
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if (p_norm) {
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*p_norm = p_planes[min_index].normal;
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}
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return true;
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}
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static Vector3 get_closest_point_to_segment(const Vector3 &p_point, const Vector3 *p_segment) {
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Vector3 p = p_point - p_segment[0];
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Vector3 n = p_segment[1] - p_segment[0];
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real_t l2 = n.length_squared();
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if (l2 < 1e-20f) {
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return p_segment[0]; // Both points are the same, just give any.
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}
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real_t d = n.dot(p) / l2;
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if (d <= 0.0f) {
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return p_segment[0]; // Before first point.
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} else if (d >= 1.0f) {
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return p_segment[1]; // After first point.
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} else {
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return p_segment[0] + n * d; // Inside.
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}
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}
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static Vector3 get_closest_point_to_segment_uncapped(const Vector3 &p_point, const Vector3 *p_segment) {
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Vector3 p = p_point - p_segment[0];
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Vector3 n = p_segment[1] - p_segment[0];
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real_t l2 = n.length_squared();
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if (l2 < 1e-20f) {
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return p_segment[0]; // Both points are the same, just give any.
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}
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real_t d = n.dot(p) / l2;
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return p_segment[0] + n * d; // Inside.
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}
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static inline bool point_in_projected_triangle(const Vector3 &p_point, const Vector3 &p_v1, const Vector3 &p_v2, const Vector3 &p_v3) {
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Vector3 face_n = (p_v1 - p_v3).cross(p_v1 - p_v2);
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Vector3 n1 = (p_point - p_v3).cross(p_point - p_v2);
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if (face_n.dot(n1) < 0) {
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return false;
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}
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Vector3 n2 = (p_v1 - p_v3).cross(p_v1 - p_point);
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if (face_n.dot(n2) < 0) {
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return false;
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}
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Vector3 n3 = (p_v1 - p_point).cross(p_v1 - p_v2);
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if (face_n.dot(n3) < 0) {
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return false;
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}
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return true;
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}
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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) {
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real_t d = p_normal.dot(p_sphere_pos) - p_normal.dot(p_triangle[0]);
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if (d > p_sphere_radius || d < -p_sphere_radius) {
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// Not touching the plane of the face, return.
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return false;
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}
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Vector3 contact = p_sphere_pos - (p_normal * d);
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/** 2nd) TEST INSIDE TRIANGLE **/
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if (Geometry3D::point_in_projected_triangle(contact, p_triangle[0], p_triangle[1], p_triangle[2])) {
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r_triangle_contact = contact;
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r_sphere_contact = p_sphere_pos - p_normal * p_sphere_radius;
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//printf("solved inside triangle\n");
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return true;
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}
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/** 3rd TEST INSIDE EDGE CYLINDERS **/
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const Vector3 verts[4] = { p_triangle[0], p_triangle[1], p_triangle[2], p_triangle[0] }; // for() friendly
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for (int i = 0; i < 3; i++) {
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// Check edge cylinder.
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Vector3 n1 = verts[i] - verts[i + 1];
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Vector3 n2 = p_sphere_pos - verts[i + 1];
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///@TODO Maybe discard by range here to make the algorithm quicker.
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// Check point within cylinder radius.
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Vector3 axis = n1.cross(n2).cross(n1);
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axis.normalize();
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real_t ad = axis.dot(n2);
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if (ABS(ad) > p_sphere_radius) {
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// No chance with this edge, too far away.
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continue;
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}
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// Check point within edge capsule cylinder.
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/** 4th TEST INSIDE EDGE POINTS **/
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real_t sphere_at = n1.dot(n2);
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if (sphere_at >= 0 && sphere_at < n1.dot(n1)) {
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r_triangle_contact = p_sphere_pos - axis * (axis.dot(n2));
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r_sphere_contact = p_sphere_pos - axis * p_sphere_radius;
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// Point inside here.
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return true;
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}
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real_t r2 = p_sphere_radius * p_sphere_radius;
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if (n2.length_squared() < r2) {
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Vector3 n = (p_sphere_pos - verts[i + 1]).normalized();
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r_triangle_contact = verts[i + 1];
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r_sphere_contact = p_sphere_pos - n * p_sphere_radius;
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return true;
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}
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if (n2.distance_squared_to(n1) < r2) {
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Vector3 n = (p_sphere_pos - verts[i]).normalized();
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r_triangle_contact = verts[i];
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r_sphere_contact = p_sphere_pos - n * p_sphere_radius;
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return true;
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}
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break; // It's pointless to continue at this point, so save some CPU cycles.
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}
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return false;
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}
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static inline Vector<Vector3> clip_polygon(const Vector<Vector3> &polygon, const Plane &p_plane) {
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enum LocationCache {
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LOC_INSIDE = 1,
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LOC_BOUNDARY = 0,
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LOC_OUTSIDE = -1
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};
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if (polygon.size() == 0) {
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return polygon;
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}
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int *location_cache = (int *)alloca(sizeof(int) * polygon.size());
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int inside_count = 0;
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int outside_count = 0;
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for (int a = 0; a < polygon.size(); a++) {
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real_t dist = p_plane.distance_to(polygon[a]);
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|
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;
|
|
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
|