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/*************************************************************************/
/* geometry.h */
/*************************************************************************/
/* This file is part of: */
/* GODOT ENGINE */
/* https://godotengine.org */
/*************************************************************************/
/* Copyright (c) 2007-2020 Juan Linietsky, Ariel Manzur. */
/* Copyright (c) 2014-2020 Godot Engine contributors (cf. AUTHORS.md). */
/* */
/* 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_H
#define GEOMETRY_H
#include "core/math/delaunay_2d.h"
#include "core/math/face3.h"
#include "core/math/rect2.h"
#include "core/math/triangulate.h"
#include "core/math/vector3.h"
#include "core/object.h"
#include "core/print_string.h"
#include "core/vector.h"
class Geometry {
Geometry();
public:
static real_t get_closest_points_between_segments(const Vector2 &p1, const Vector2 &q1, const Vector2 &p2, const Vector2 &q2, Vector2 &c1, Vector2 &c2) {
Vector2 d1 = q1 - p1; // Direction vector of segment S1.
Vector2 d2 = q2 - p2; // Direction vector of segment S2.
Vector2 r = p1 - p2;
real_t a = d1.dot(d1); // Squared length of segment S1, always nonnegative.
real_t e = d2.dot(d2); // Squared length of segment S2, always nonnegative.
real_t f = d2.dot(r);
real_t s, t;
// Check if either or both segments degenerate into points.
if (a <= CMP_EPSILON && e <= CMP_EPSILON) {
// Both segments degenerate into points.
c1 = p1;
c2 = p2;
return Math::sqrt((c1 - c2).dot(c1 - c2));
}
if (a <= CMP_EPSILON) {
// First segment degenerates into a point.
s = 0.0;
t = f / e; // s = 0 => t = (b*s + f) / e = f / e
t = CLAMP(t, 0.0, 1.0);
} else {
real_t c = d1.dot(r);
if (e <= CMP_EPSILON) {
// Second segment degenerates into a point.
t = 0.0;
s = CLAMP(-c / a, 0.0, 1.0); // t = 0 => s = (b*t - c) / a = -c / a
} else {
// The general nondegenerate case starts here.
real_t b = d1.dot(d2);
real_t denom = a * e - b * b; // Always nonnegative.
// If segments not parallel, compute closest point on L1 to L2 and
// clamp to segment S1. Else pick arbitrary s (here 0).
if (denom != 0.0) {
s = CLAMP((b * f - c * e) / denom, 0.0, 1.0);
} else {
s = 0.0;
}
// Compute point on L2 closest to S1(s) using
// t = Dot((P1 + D1*s) - P2,D2) / Dot(D2,D2) = (b*s + f) / e
t = (b * s + f) / e;
//If t in [0,1] done. Else clamp t, recompute s for the new value
// of t using s = Dot((P2 + D2*t) - P1,D1) / Dot(D1,D1)= (t*b - c) / a
// and clamp s to [0, 1].
if (t < 0.0) {
t = 0.0;
s = CLAMP(-c / a, 0.0, 1.0);
} else if (t > 1.0) {
t = 1.0;
s = CLAMP((b - c) / a, 0.0, 1.0);
}
}
}
c1 = p1 + d1 * s;
c2 = p2 + d2 * t;
return Math::sqrt((c1 - c2).dot(c1 - c2));
}
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 is is 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 < CMP_EPSILON) { // The lines are almost parallel.
sN = 0.0; // Force using point P0 on segment S1
sD = 1.0; // 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 < 0.0) { // sc < 0 => the s=0 edge is visible.
sN = 0.0;
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 < 0.0) { // tc < 0 => the t=0 edge is visible.
tN = 0.0;
// Recompute sc for this edge.
if (-d < 0.0) {
sN = 0.0;
} 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) < 0.0) {
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) ? 0.0 : sN / sD);
tc = (Math::is_zero_approx(tN) ? 0.0 : 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 = 1.0 / a;
Vector3 s = p_from - p_v0;
real_t u = f * s.dot(h);
if (u < 0.0 || u > 1.0) {
return false;
}
Vector3 q = s.cross(e1);
real_t v = f * p_dir.dot(q);
if (v < 0.0 || u + v > 1.0) {
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 > 0.00001) { // 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 = 1.0 / a;
Vector3 s = p_from - p_v0;
real_t u = f * s.dot(h);
if (u < 0.0 || u > 1.0) {
return false;
}
Vector3 q = s.cross(e1);
real_t v = f * rel.dot(q);
if (v < 0.0 || u + v > 1.0) {
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 > CMP_EPSILON && t <= 1.0) { // 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 < 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 >= 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) {
Vector3 rel = (p_to - p_from);
real_t rel_l = rel.length();
if (rel_l < CMP_EPSILON) {
return false; // Both points are the same.
}
// First check if they are parallel.
Vector3 normal = (rel / rel_l);
Vector3 crs = normal.cross(Vector3(0, 0, 1));
real_t crs_l = crs.length();
Vector3 z_dir;
if (crs_l < CMP_EPSILON) {
z_dir = Vector3(1, 0, 0); // Any x/y vector OK.
} else {
z_dir = crs / crs_l;
}
real_t dist = z_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 < CMP_EPSILON) {
return false; // Avoid numerical error.
}
Size2 size(Math::sqrt(w2), p_height * 0.5);
Vector3 x_dir = z_dir.cross(Vector3(0, 0, 1)).normalized();
Vector2 from2D(x_dir.dot(p_from), p_from.z);
Vector2 to2D(x_dir.dot(p_to), p_to.z);
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.z = 0;
} else {
res_normal.x = 0;
res_normal.y = 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 < 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) <= 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-20) {
return p_segment[0]; // Both points are the same, just give any.
}
real_t d = n.dot(p) / l2;
if (d <= 0.0) {
return p_segment[0]; // Before first point.
} else if (d >= 1.0) {
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-20) {
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 Vector2 get_closest_point_to_segment_2d(const Vector2 &p_point, const Vector2 *p_segment) {
Vector2 p = p_point - p_segment[0];
Vector2 n = p_segment[1] - p_segment[0];
real_t l2 = n.length_squared();
if (l2 < 1e-20) {
return p_segment[0]; // Both points are the same, just give any.
}
real_t d = n.dot(p) / l2;
if (d <= 0.0) {
return p_segment[0]; // Before first point.
} else if (d >= 1.0) {
return p_segment[1]; // After first point.
} else {
return p_segment[0] + n * d; // Inside.
}
}
static bool is_point_in_triangle(const Vector2 &s, const Vector2 &a, const Vector2 &b, const Vector2 &c) {
Vector2 an = a - s;
Vector2 bn = b - s;
Vector2 cn = c - s;
bool orientation = an.cross(bn) > 0;
if ((bn.cross(cn) > 0) != orientation) {
return false;
}
return (cn.cross(an) > 0) == orientation;
}
static Vector2 get_closest_point_to_segment_uncapped_2d(const Vector2 &p_point, const Vector2 *p_segment) {
Vector2 p = p_point - p_segment[0];
Vector2 n = p_segment[1] - p_segment[0];
real_t l2 = n.length_squared();
if (l2 < 1e-20) {
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 bool line_intersects_line_2d(const Vector2 &p_from_a, const Vector2 &p_dir_a, const Vector2 &p_from_b, const Vector2 &p_dir_b, Vector2 &r_result) {
// See http://paulbourke.net/geometry/pointlineplane/
const real_t denom = p_dir_b.y * p_dir_a.x - p_dir_b.x * p_dir_a.y;
if (Math::is_zero_approx(denom)) { // Parallel?
return false;
}
const Vector2 v = p_from_a - p_from_b;
const real_t t = (p_dir_b.x * v.y - p_dir_b.y * v.x) / denom;
r_result = p_from_a + t * p_dir_a;
return true;
}
static bool segment_intersects_segment_2d(const Vector2 &p_from_a, const Vector2 &p_to_a, const Vector2 &p_from_b, const Vector2 &p_to_b, Vector2 *r_result) {
Vector2 B = p_to_a - p_from_a;
Vector2 C = p_from_b - p_from_a;
Vector2 D = p_to_b - p_from_a;
real_t ABlen = B.dot(B);
if (ABlen <= 0) {
return false;
}
Vector2 Bn = B / ABlen;
C = Vector2(C.x * Bn.x + C.y * Bn.y, C.y * Bn.x - C.x * Bn.y);
D = Vector2(D.x * Bn.x + D.y * Bn.y, D.y * Bn.x - D.x * Bn.y);
if ((C.y < 0 && D.y < 0) || (C.y >= 0 && D.y >= 0)) {
return false;
}
real_t ABpos = D.x + (C.x - D.x) * D.y / (D.y - C.y);
// Fail if segment C-D crosses line A-B outside of segment A-B.
if (ABpos < 0 || ABpos > 1.0) {
return false;
}
// (4) Apply the discovered position to line A-B in the original coordinate system.
if (r_result) {
*r_result = p_from_a + B * ABpos;
}
return true;
}
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 (Geometry::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 bool is_point_in_circle(const Vector2 &p_point, const Vector2 &p_circle_pos, real_t p_circle_radius) {
return p_point.distance_squared_to(p_circle_pos) <= p_circle_radius * p_circle_radius;
}
static real_t segment_intersects_circle(const Vector2 &p_from, const Vector2 &p_to, const Vector2 &p_circle_pos, real_t p_circle_radius) {
Vector2 line_vec = p_to - p_from;
Vector2 vec_to_line = p_from - p_circle_pos;
// Create a quadratic formula of the form ax^2 + bx + c = 0
real_t a, b, c;
a = line_vec.dot(line_vec);
b = 2 * vec_to_line.dot(line_vec);
c = vec_to_line.dot(vec_to_line) - p_circle_radius * p_circle_radius;
// Solve for t.
real_t sqrtterm = b * b - 4 * a * c;
// If the term we intend to square root is less than 0 then the answer won't be real,
// so it definitely won't be t in the range 0 to 1.
if (sqrtterm < 0) {
return -1;
}
// If we can assume that the line segment starts outside the circle (e.g. for continuous time collision detection)
// then the following can be skipped and we can just return the equivalent of res1.
sqrtterm = Math::sqrt(sqrtterm);
real_t res1 = (-b - sqrtterm) / (2 * a);
real_t res2 = (-b + sqrtterm) / (2 * a);
if (res1 >= 0 && res1 <= 1) {
return res1;
}
if (res2 >= 0 && res2 <= 1) {
return res2;
}
return -1;
}
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 < -CMP_POINT_IN_PLANE_EPSILON) {
location_cache[a] = LOC_INSIDE;
inside_count++;
} else {
if (dist > 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;
}
enum PolyBooleanOperation {
OPERATION_UNION,
OPERATION_DIFFERENCE,
OPERATION_INTERSECTION,
OPERATION_XOR
};
enum PolyJoinType {
JOIN_SQUARE,
JOIN_ROUND,
JOIN_MITER
};
enum PolyEndType {
END_POLYGON,
END_JOINED,
END_BUTT,
END_SQUARE,
END_ROUND
};
static Vector<Vector<Point2>> merge_polygons_2d(const Vector<Point2> &p_polygon_a, const Vector<Point2> &p_polygon_b) {
return _polypaths_do_operation(OPERATION_UNION, p_polygon_a, p_polygon_b);
}
static Vector<Vector<Point2>> clip_polygons_2d(const Vector<Point2> &p_polygon_a, const Vector<Point2> &p_polygon_b) {
return _polypaths_do_operation(OPERATION_DIFFERENCE, p_polygon_a, p_polygon_b);
}
static Vector<Vector<Point2>> intersect_polygons_2d(const Vector<Point2> &p_polygon_a, const Vector<Point2> &p_polygon_b) {
return _polypaths_do_operation(OPERATION_INTERSECTION, p_polygon_a, p_polygon_b);
}
static Vector<Vector<Point2>> exclude_polygons_2d(const Vector<Point2> &p_polygon_a, const Vector<Point2> &p_polygon_b) {
return _polypaths_do_operation(OPERATION_XOR, p_polygon_a, p_polygon_b);
}
static Vector<Vector<Point2>> clip_polyline_with_polygon_2d(const Vector<Vector2> &p_polyline, const Vector<Vector2> &p_polygon) {
return _polypaths_do_operation(OPERATION_DIFFERENCE, p_polyline, p_polygon, true);
}
static Vector<Vector<Point2>> intersect_polyline_with_polygon_2d(const Vector<Vector2> &p_polyline, const Vector<Vector2> &p_polygon) {
return _polypaths_do_operation(OPERATION_INTERSECTION, p_polyline, p_polygon, true);
}
static Vector<Vector<Point2>> offset_polygon_2d(const Vector<Vector2> &p_polygon, real_t p_delta, PolyJoinType p_join_type) {
return _polypath_offset(p_polygon, p_delta, p_join_type, END_POLYGON);
}
static Vector<Vector<Point2>> offset_polyline_2d(const Vector<Vector2> &p_polygon, real_t p_delta, PolyJoinType p_join_type, PolyEndType p_end_type) {
ERR_FAIL_COND_V_MSG(p_end_type == END_POLYGON, Vector<Vector<Point2>>(), "Attempt to offset a polyline like a polygon (use offset_polygon_2d instead).");
return _polypath_offset(p_polygon, p_delta, p_join_type, p_end_type);
}
static Vector<int> triangulate_delaunay_2d(const Vector<Vector2> &p_points) {
Vector<Delaunay2D::Triangle> tr = Delaunay2D::triangulate(p_points);
Vector<int> triangles;
for (int i = 0; i < tr.size(); i++) {
triangles.push_back(tr[i].points[0]);
triangles.push_back(tr[i].points[1]);
triangles.push_back(tr[i].points[2]);
}
return triangles;
}
static Vector<int> triangulate_polygon(const Vector<Vector2> &p_polygon) {
Vector<int> triangles;
if (!Triangulate::triangulate(p_polygon, triangles)) {
return Vector<int>(); //fail
}
return triangles;
}
static bool is_polygon_clockwise(const Vector<Vector2> &p_polygon) {
int c = p_polygon.size();
if (c < 3) {
return false;
}
const Vector2 *p = p_polygon.ptr();
real_t sum = 0;
for (int i = 0; i < c; i++) {
const Vector2 &v1 = p[i];
const Vector2 &v2 = p[(i + 1) % c];
sum += (v2.x - v1.x) * (v2.y + v1.y);
}
return sum > 0.0f;
}
// Alternate implementation that should be faster.
static bool is_point_in_polygon(const Vector2 &p_point, const Vector<Vector2> &p_polygon) {
int c = p_polygon.size();
if (c < 3) {
return false;
}
const Vector2 *p = p_polygon.ptr();
Vector2 further_away(-1e20, -1e20);
Vector2 further_away_opposite(1e20, 1e20);
for (int i = 0; i < c; i++) {
further_away.x = MAX(p[i].x, further_away.x);
further_away.y = MAX(p[i].y, further_away.y);
further_away_opposite.x = MIN(p[i].x, further_away_opposite.x);
further_away_opposite.y = MIN(p[i].y, further_away_opposite.y);
}
// Make point outside that won't intersect with points in segment from p_point.
further_away += (further_away - further_away_opposite) * Vector2(1.221313, 1.512312);
int intersections = 0;
for (int i = 0; i < c; i++) {
const Vector2 &v1 = p[i];
const Vector2 &v2 = p[(i + 1) % c];
if (segment_intersects_segment_2d(v1, v2, p_point, further_away, nullptr)) {
intersections++;
}
}
return (intersections & 1);
}
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();
};
_FORCE_INLINE_ static int get_uv84_normal_bit(const Vector3 &p_vector) {
int lat = Math::fast_ftoi(Math::floor(Math::acos(p_vector.dot(Vector3(0, 1, 0))) * 4.0 / Math_PI + 0.5));
if (lat == 0) {
return 24;
} else if (lat == 4) {
return 25;
}
int lon = Math::fast_ftoi(Math::floor((Math_PI + Math::atan2(p_vector.x, p_vector.z)) * 8.0 / (Math_PI * 2.0) + 0.5)) % 8;
return lon + (lat - 1) * 8;
}
_FORCE_INLINE_ static int get_uv84_normal_bit_neighbors(int p_idx) {
if (p_idx == 24) {
return 1 | 2 | 4 | 8;
} else if (p_idx == 25) {
return (1 << 23) | (1 << 22) | (1 << 21) | (1 << 20);
} else {
int ret = 0;
if ((p_idx % 8) == 0) {
ret |= (1 << (p_idx + 7));
} else {
ret |= (1 << (p_idx - 1));
}
if ((p_idx % 8) == 7) {
ret |= (1 << (p_idx - 7));
} else {
ret |= (1 << (p_idx + 1));
}
int mask = ret | (1 << p_idx);
if (p_idx < 8) {
ret |= 24;
} else {
ret |= mask >> 8;
}
if (p_idx >= 16) {
ret |= 25;
} else {
ret |= mask << 8;
}
return ret;
}
}
static real_t vec2_cross(const Point2 &O, const Point2 &A, const Point2 &B) {
return (real_t)(A.x - O.x) * (B.y - O.y) - (real_t)(A.y - O.y) * (B.x - O.x);
}
// Returns a list of points on the convex hull in counter-clockwise order.
// Note: the last point in the returned list is the same as the first one.
static Vector<Point2> convex_hull_2d(Vector<Point2> P) {
int n = P.size(), k = 0;
Vector<Point2> H;
H.resize(2 * n);
// Sort points lexicographically.
P.sort();
// Build lower hull.
for (int i = 0; i < n; ++i) {
while (k >= 2 && vec2_cross(H[k - 2], H[k - 1], P[i]) <= 0) {
k--;
}
H.write[k++] = P[i];
}
// Build upper hull.
for (int i = n - 2, t = k + 1; i >= 0; i--) {
while (k >= t && vec2_cross(H[k - 2], H[k - 1], P[i]) <= 0) {
k--;
}
H.write[k++] = P[i];
}
H.resize(k);
return H;
}
static Vector<Vector<Vector2>> decompose_polygon_in_convex(Vector<Point2> polygon);
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 void make_atlas(const Vector<Size2i> &p_rects, Vector<Point2i> &r_result, Size2i &r_size);
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<Point2i> pack_rects(const Vector<Size2i> &p_sizes, const Size2i &p_atlas_size);
static Vector<Vector3i> partial_pack_rects(const Vector<Vector2i> &p_sizes, const Size2i &p_atlas_size);
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
}
private:
static Vector<Vector<Point2>> _polypaths_do_operation(PolyBooleanOperation p_op, const Vector<Point2> &p_polypath_a, const Vector<Point2> &p_polypath_b, bool is_a_open = false);
static Vector<Vector<Point2>> _polypath_offset(const Vector<Point2> &p_polypath, real_t p_delta, PolyJoinType p_join_type, PolyEndType p_end_type);
};
#endif // GEOMETRY_H
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