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503 lines
17 KiB
C++
503 lines
17 KiB
C++
/**************************************************************************/
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/* geometry_2d.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_2D_H
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#define GEOMETRY_2D_H
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#include "core/math/delaunay_2d.h"
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#include "core/math/math_funcs.h"
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#include "core/math/triangulate.h"
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#include "core/math/vector2.h"
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#include "core/math/vector2i.h"
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#include "core/math/vector3.h"
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#include "core/math/vector3i.h"
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#include "core/templates/vector.h"
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class Geometry2D {
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public:
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static real_t get_closest_points_between_segments(const Vector2 &p1, const Vector2 &q1, const Vector2 &p2, const Vector2 &q2, Vector2 &c1, Vector2 &c2) {
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Vector2 d1 = q1 - p1; // Direction vector of segment S1.
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Vector2 d2 = q2 - p2; // Direction vector of segment S2.
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Vector2 r = p1 - p2;
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real_t a = d1.dot(d1); // Squared length of segment S1, always nonnegative.
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real_t e = d2.dot(d2); // Squared length of segment S2, always nonnegative.
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real_t f = d2.dot(r);
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real_t s, t;
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// Check if either or both segments degenerate into points.
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if (a <= (real_t)CMP_EPSILON && e <= (real_t)CMP_EPSILON) {
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// Both segments degenerate into points.
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c1 = p1;
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c2 = p2;
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return Math::sqrt((c1 - c2).dot(c1 - c2));
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}
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if (a <= (real_t)CMP_EPSILON) {
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// First segment degenerates into a point.
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s = 0.0;
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t = f / e; // s = 0 => t = (b*s + f) / e = f / e
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t = CLAMP(t, 0.0f, 1.0f);
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} else {
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real_t c = d1.dot(r);
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if (e <= (real_t)CMP_EPSILON) {
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// Second segment degenerates into a point.
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t = 0.0;
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s = CLAMP(-c / a, 0.0f, 1.0f); // t = 0 => s = (b*t - c) / a = -c / a
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} else {
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// The general nondegenerate case starts here.
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real_t b = d1.dot(d2);
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real_t denom = a * e - b * b; // Always nonnegative.
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// If segments not parallel, compute closest point on L1 to L2 and
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// clamp to segment S1. Else pick arbitrary s (here 0).
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if (denom != 0.0f) {
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s = CLAMP((b * f - c * e) / denom, 0.0f, 1.0f);
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} else {
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s = 0.0;
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}
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// Compute point on L2 closest to S1(s) using
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// t = Dot((P1 + D1*s) - P2,D2) / Dot(D2,D2) = (b*s + f) / e
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t = (b * s + f) / e;
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//If t in [0,1] done. Else clamp t, recompute s for the new value
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// of t using s = Dot((P2 + D2*t) - P1,D1) / Dot(D1,D1)= (t*b - c) / a
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// and clamp s to [0, 1].
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if (t < 0.0f) {
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t = 0.0;
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s = CLAMP(-c / a, 0.0f, 1.0f);
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} else if (t > 1.0f) {
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t = 1.0;
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s = CLAMP((b - c) / a, 0.0f, 1.0f);
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}
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}
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}
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c1 = p1 + d1 * s;
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c2 = p2 + d2 * t;
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return Math::sqrt((c1 - c2).dot(c1 - c2));
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}
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static Vector2 get_closest_point_to_segment(const Vector2 &p_point, const Vector2 *p_segment) {
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Vector2 p = p_point - p_segment[0];
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Vector2 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 real_t get_distance_to_segment(const Vector2 &p_point, const Vector2 *p_segment) {
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return p_point.distance_to(get_closest_point_to_segment(p_point, p_segment));
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}
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static bool is_point_in_triangle(const Vector2 &s, const Vector2 &a, const Vector2 &b, const Vector2 &c) {
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Vector2 an = a - s;
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Vector2 bn = b - s;
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Vector2 cn = c - s;
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bool orientation = an.cross(bn) > 0;
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if ((bn.cross(cn) > 0) != orientation) {
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return false;
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}
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return (cn.cross(an) > 0) == orientation;
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}
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static Vector2 get_closest_point_to_segment_uncapped(const Vector2 &p_point, const Vector2 *p_segment) {
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Vector2 p = p_point - p_segment[0];
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Vector2 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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// Disable False Positives in MSVC compiler; we correctly check for 0 here to prevent a division by 0.
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// See: https://github.com/godotengine/godot/pull/44274
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#ifdef _MSC_VER
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#pragma warning(disable : 4723)
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#endif
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static bool line_intersects_line(const Vector2 &p_from_a, const Vector2 &p_dir_a, const Vector2 &p_from_b, const Vector2 &p_dir_b, Vector2 &r_result) {
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// See http://paulbourke.net/geometry/pointlineplane/
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const real_t denom = p_dir_b.y * p_dir_a.x - p_dir_b.x * p_dir_a.y;
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if (Math::is_zero_approx(denom)) { // Parallel?
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return false;
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}
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const Vector2 v = p_from_a - p_from_b;
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const real_t t = (p_dir_b.x * v.y - p_dir_b.y * v.x) / denom;
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r_result = p_from_a + t * p_dir_a;
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return true;
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}
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// Re-enable division by 0 warning
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#ifdef _MSC_VER
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#pragma warning(default : 4723)
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#endif
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static bool segment_intersects_segment(const Vector2 &p_from_a, const Vector2 &p_to_a, const Vector2 &p_from_b, const Vector2 &p_to_b, Vector2 *r_result) {
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Vector2 B = p_to_a - p_from_a;
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Vector2 C = p_from_b - p_from_a;
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Vector2 D = p_to_b - p_from_a;
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real_t ABlen = B.dot(B);
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if (ABlen <= 0) {
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return false;
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}
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Vector2 Bn = B / ABlen;
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C = Vector2(C.x * Bn.x + C.y * Bn.y, C.y * Bn.x - C.x * Bn.y);
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D = Vector2(D.x * Bn.x + D.y * Bn.y, D.y * Bn.x - D.x * Bn.y);
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// Fail if C x B and D x B have the same sign (segments don't intersect).
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if ((C.y < (real_t)-CMP_EPSILON && D.y < (real_t)-CMP_EPSILON) || (C.y > (real_t)CMP_EPSILON && D.y > (real_t)CMP_EPSILON)) {
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return false;
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}
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// Fail if segments are parallel or colinear.
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// (when A x B == zero, i.e (C - D) x B == zero, i.e C x B == D x B)
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if (Math::is_equal_approx(C.y, D.y)) {
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return false;
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}
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real_t ABpos = D.x + (C.x - D.x) * D.y / (D.y - C.y);
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// Fail if segment C-D crosses line A-B outside of segment A-B.
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if ((ABpos < 0) || (ABpos > 1)) {
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return false;
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}
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// Apply the discovered position to line A-B in the original coordinate system.
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if (r_result) {
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*r_result = p_from_a + B * ABpos;
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}
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return true;
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}
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static inline bool is_point_in_circle(const Vector2 &p_point, const Vector2 &p_circle_pos, real_t p_circle_radius) {
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return p_point.distance_squared_to(p_circle_pos) <= p_circle_radius * p_circle_radius;
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}
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static real_t segment_intersects_circle(const Vector2 &p_from, const Vector2 &p_to, const Vector2 &p_circle_pos, real_t p_circle_radius) {
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Vector2 line_vec = p_to - p_from;
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Vector2 vec_to_line = p_from - p_circle_pos;
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// Create a quadratic formula of the form ax^2 + bx + c = 0
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real_t a, b, c;
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a = line_vec.dot(line_vec);
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b = 2 * vec_to_line.dot(line_vec);
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c = vec_to_line.dot(vec_to_line) - p_circle_radius * p_circle_radius;
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// Solve for t.
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real_t sqrtterm = b * b - 4 * a * c;
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// If the term we intend to square root is less than 0 then the answer won't be real,
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// so it definitely won't be t in the range 0 to 1.
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if (sqrtterm < 0) {
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return -1;
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}
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// If we can assume that the line segment starts outside the circle (e.g. for continuous time collision detection)
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// then the following can be skipped and we can just return the equivalent of res1.
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sqrtterm = Math::sqrt(sqrtterm);
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real_t res1 = (-b - sqrtterm) / (2 * a);
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real_t res2 = (-b + sqrtterm) / (2 * a);
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if (res1 >= 0 && res1 <= 1) {
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return res1;
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}
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if (res2 >= 0 && res2 <= 1) {
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return res2;
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}
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return -1;
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}
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static bool segment_intersects_rect(const Vector2 &p_from, const Vector2 &p_to, const Rect2 &p_rect) {
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if (p_rect.has_point(p_from) || p_rect.has_point(p_to)) {
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return true;
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}
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const Vector2 rect_points[4] = {
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p_rect.position,
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p_rect.position + Vector2(p_rect.size.x, 0),
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p_rect.position + p_rect.size,
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p_rect.position + Vector2(0, p_rect.size.y)
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};
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// Check if any of the rect's edges intersect the segment.
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for (int i = 0; i < 4; i++) {
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if (segment_intersects_segment(p_from, p_to, rect_points[i], rect_points[(i + 1) % 4], nullptr)) {
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return true;
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}
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}
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return false;
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}
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enum PolyBooleanOperation {
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OPERATION_UNION,
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OPERATION_DIFFERENCE,
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OPERATION_INTERSECTION,
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OPERATION_XOR
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};
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enum PolyJoinType {
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JOIN_SQUARE,
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JOIN_ROUND,
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JOIN_MITER
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};
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enum PolyEndType {
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END_POLYGON,
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END_JOINED,
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END_BUTT,
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END_SQUARE,
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END_ROUND
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};
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static Vector<Vector<Point2>> merge_polygons(const Vector<Point2> &p_polygon_a, const Vector<Point2> &p_polygon_b) {
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return _polypaths_do_operation(OPERATION_UNION, p_polygon_a, p_polygon_b);
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}
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static Vector<Vector<Point2>> clip_polygons(const Vector<Point2> &p_polygon_a, const Vector<Point2> &p_polygon_b) {
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return _polypaths_do_operation(OPERATION_DIFFERENCE, p_polygon_a, p_polygon_b);
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}
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static Vector<Vector<Point2>> intersect_polygons(const Vector<Point2> &p_polygon_a, const Vector<Point2> &p_polygon_b) {
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return _polypaths_do_operation(OPERATION_INTERSECTION, p_polygon_a, p_polygon_b);
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}
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static Vector<Vector<Point2>> exclude_polygons(const Vector<Point2> &p_polygon_a, const Vector<Point2> &p_polygon_b) {
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return _polypaths_do_operation(OPERATION_XOR, p_polygon_a, p_polygon_b);
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}
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static Vector<Vector<Point2>> clip_polyline_with_polygon(const Vector<Vector2> &p_polyline, const Vector<Vector2> &p_polygon) {
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return _polypaths_do_operation(OPERATION_DIFFERENCE, p_polyline, p_polygon, true);
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}
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static Vector<Vector<Point2>> intersect_polyline_with_polygon(const Vector<Vector2> &p_polyline, const Vector<Vector2> &p_polygon) {
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return _polypaths_do_operation(OPERATION_INTERSECTION, p_polyline, p_polygon, true);
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}
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static Vector<Vector<Point2>> offset_polygon(const Vector<Vector2> &p_polygon, real_t p_delta, PolyJoinType p_join_type) {
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return _polypath_offset(p_polygon, p_delta, p_join_type, END_POLYGON);
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}
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static Vector<Vector<Point2>> offset_polyline(const Vector<Vector2> &p_polygon, real_t p_delta, PolyJoinType p_join_type, PolyEndType p_end_type) {
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ERR_FAIL_COND_V_MSG(p_end_type == END_POLYGON, Vector<Vector<Point2>>(), "Attempt to offset a polyline like a polygon (use offset_polygon instead).");
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return _polypath_offset(p_polygon, p_delta, p_join_type, p_end_type);
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}
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static Vector<int> triangulate_delaunay(const Vector<Vector2> &p_points) {
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Vector<Delaunay2D::Triangle> tr = Delaunay2D::triangulate(p_points);
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Vector<int> triangles;
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triangles.resize(3 * tr.size());
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int *ptr = triangles.ptrw();
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for (int i = 0; i < tr.size(); i++) {
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*ptr++ = tr[i].points[0];
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*ptr++ = tr[i].points[1];
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*ptr++ = tr[i].points[2];
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}
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return triangles;
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}
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static Vector<int> triangulate_polygon(const Vector<Vector2> &p_polygon) {
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Vector<int> triangles;
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if (!Triangulate::triangulate(p_polygon, triangles)) {
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return Vector<int>(); //fail
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}
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return triangles;
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}
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// Assumes cartesian coordinate system with +x to the right, +y up.
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// If using screen coordinates (+x to the right, +y down) the result will need to be flipped.
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static bool is_polygon_clockwise(const Vector<Vector2> &p_polygon) {
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int c = p_polygon.size();
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if (c < 3) {
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return false;
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}
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const Vector2 *p = p_polygon.ptr();
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real_t sum = 0;
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for (int i = 0; i < c; i++) {
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const Vector2 &v1 = p[i];
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const Vector2 &v2 = p[(i + 1) % c];
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sum += (v2.x - v1.x) * (v2.y + v1.y);
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}
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return sum > 0.0f;
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}
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// Alternate implementation that should be faster.
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static bool is_point_in_polygon(const Vector2 &p_point, const Vector<Vector2> &p_polygon) {
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int c = p_polygon.size();
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if (c < 3) {
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return false;
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}
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const Vector2 *p = p_polygon.ptr();
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Vector2 further_away(-1e20, -1e20);
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Vector2 further_away_opposite(1e20, 1e20);
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for (int i = 0; i < c; i++) {
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further_away = further_away.max(p[i]);
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further_away_opposite = further_away_opposite.min(p[i]);
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}
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// Make point outside that won't intersect with points in segment from p_point.
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further_away += (further_away - further_away_opposite) * Vector2(1.221313, 1.512312);
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int intersections = 0;
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for (int i = 0; i < c; i++) {
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const Vector2 &v1 = p[i];
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const Vector2 &v2 = p[(i + 1) % c];
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Vector2 res;
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if (segment_intersects_segment(v1, v2, p_point, further_away, &res)) {
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intersections++;
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if (res.is_equal_approx(p_point)) {
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// Point is in one of the polygon edges.
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return true;
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}
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}
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}
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return (intersections & 1);
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}
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static bool is_segment_intersecting_polygon(const Vector2 &p_from, const Vector2 &p_to, const Vector<Vector2> &p_polygon) {
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int c = p_polygon.size();
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const Vector2 *p = p_polygon.ptr();
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for (int i = 0; i < c; i++) {
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const Vector2 &v1 = p[i];
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const Vector2 &v2 = p[(i + 1) % c];
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if (segment_intersects_segment(p_from, p_to, v1, v2, nullptr)) {
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return true;
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}
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}
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return false;
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}
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static real_t vec2_cross(const Point2 &O, const Point2 &A, const Point2 &B) {
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return (real_t)(A.x - O.x) * (B.y - O.y) - (real_t)(A.y - O.y) * (B.x - O.x);
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}
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// Returns a list of points on the convex hull in counter-clockwise order.
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// Note: the last point in the returned list is the same as the first one.
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static Vector<Point2> convex_hull(Vector<Point2> P) {
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int n = P.size(), k = 0;
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Vector<Point2> H;
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H.resize(2 * n);
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// Sort points lexicographically.
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P.sort();
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// Build lower hull.
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for (int i = 0; i < n; ++i) {
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while (k >= 2 && vec2_cross(H[k - 2], H[k - 1], P[i]) <= 0) {
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k--;
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}
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H.write[k++] = P[i];
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}
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// Build upper hull.
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for (int i = n - 2, t = k + 1; i >= 0; i--) {
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while (k >= t && vec2_cross(H[k - 2], H[k - 1], P[i]) <= 0) {
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k--;
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}
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H.write[k++] = P[i];
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}
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H.resize(k);
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return H;
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}
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static Vector<Point2i> bresenham_line(const Point2i &p_start, const Point2i &p_end) {
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Vector<Point2i> points;
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Vector2i delta = (p_end - p_start).abs() * 2;
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Vector2i step = (p_end - p_start).sign();
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Vector2i current = p_start;
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if (delta.x > delta.y) {
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int err = delta.x / 2;
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for (; current.x != p_end.x; current.x += step.x) {
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points.push_back(current);
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err -= delta.y;
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if (err < 0) {
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current.y += step.y;
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err += delta.x;
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}
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}
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} else {
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int err = delta.y / 2;
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for (; current.y != p_end.y; current.y += step.y) {
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points.push_back(current);
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err -= delta.x;
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if (err < 0) {
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current.x += step.x;
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err += delta.y;
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}
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}
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}
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points.push_back(current);
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return points;
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}
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static Vector<Vector<Vector2>> decompose_polygon_in_convex(const Vector<Point2> &polygon);
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static void make_atlas(const Vector<Size2i> &p_rects, Vector<Point2i> &r_result, Size2i &r_size);
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static Vector<Vector3i> partial_pack_rects(const Vector<Vector2i> &p_sizes, const Size2i &p_atlas_size);
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private:
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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);
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static Vector<Vector<Point2>> _polypath_offset(const Vector<Point2> &p_polypath, real_t p_delta, PolyJoinType p_join_type, PolyEndType p_end_type);
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};
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#endif // GEOMETRY_2D_H
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