411 lines
11 KiB
C++
411 lines
11 KiB
C++
/**************************************************************************/
|
||
/* rect2.cpp */
|
||
/**************************************************************************/
|
||
/* This file is part of: */
|
||
/* GODOT ENGINE */
|
||
/* https://godotengine.org */
|
||
/**************************************************************************/
|
||
/* Copyright (c) 2014-present Godot Engine contributors (see AUTHORS.md). */
|
||
/* Copyright (c) 2007-2014 Juan Linietsky, Ariel Manzur. */
|
||
/* */
|
||
/* Permission is hereby granted, free of charge, to any person obtaining */
|
||
/* a copy of this software and associated documentation files (the */
|
||
/* "Software"), to deal in the Software without restriction, including */
|
||
/* without limitation the rights to use, copy, modify, merge, publish, */
|
||
/* distribute, sublicense, and/or sell copies of the Software, and to */
|
||
/* permit persons to whom the Software is furnished to do so, subject to */
|
||
/* the following conditions: */
|
||
/* */
|
||
/* The above copyright notice and this permission notice shall be */
|
||
/* included in all copies or substantial portions of the Software. */
|
||
/* */
|
||
/* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, */
|
||
/* EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF */
|
||
/* MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. */
|
||
/* IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY */
|
||
/* CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, */
|
||
/* TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE */
|
||
/* SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. */
|
||
/**************************************************************************/
|
||
|
||
#include "rect2.h"
|
||
|
||
#include "core/math/rect2i.h"
|
||
#include "core/math/transform_2d.h"
|
||
#include "core/string/ustring.h"
|
||
|
||
bool Rect2::is_equal_approx(const Rect2 &p_rect) const {
|
||
return position.is_equal_approx(p_rect.position) && size.is_equal_approx(p_rect.size);
|
||
}
|
||
|
||
bool Rect2::is_same(const Rect2 &p_rect) const {
|
||
return position.is_same(p_rect.position) && size.is_same(p_rect.size);
|
||
}
|
||
|
||
bool Rect2::is_finite() const {
|
||
return position.is_finite() && size.is_finite();
|
||
}
|
||
|
||
bool Rect2::intersects_segment(const Point2 &p_from, const Point2 &p_to, Point2 *r_pos, Point2 *r_normal) const {
|
||
#ifdef MATH_CHECKS
|
||
if (unlikely(size.x < 0 || size.y < 0)) {
|
||
ERR_PRINT("Rect2 size is negative, this is not supported. Use Rect2.abs() to get a Rect2 with a positive size.");
|
||
}
|
||
#endif
|
||
real_t min = 0, max = 1;
|
||
int axis = 0;
|
||
real_t sign = 0;
|
||
|
||
for (int i = 0; i < 2; i++) {
|
||
real_t seg_from = p_from[i];
|
||
real_t seg_to = p_to[i];
|
||
real_t box_begin = position[i];
|
||
real_t box_end = box_begin + size[i];
|
||
real_t cmin, cmax;
|
||
real_t csign;
|
||
|
||
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;
|
||
csign = -1.0;
|
||
|
||
} 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;
|
||
csign = 1.0;
|
||
}
|
||
|
||
if (cmin > min) {
|
||
min = cmin;
|
||
axis = i;
|
||
sign = csign;
|
||
}
|
||
if (cmax < max) {
|
||
max = cmax;
|
||
}
|
||
if (max < min) {
|
||
return false;
|
||
}
|
||
}
|
||
|
||
Vector2 rel = p_to - p_from;
|
||
|
||
if (r_normal) {
|
||
Vector2 normal;
|
||
normal[axis] = sign;
|
||
*r_normal = normal;
|
||
}
|
||
|
||
if (r_pos) {
|
||
*r_pos = p_from + rel * min;
|
||
}
|
||
|
||
return true;
|
||
}
|
||
|
||
bool Rect2::intersects_transformed(const Transform2D &p_xform, const Rect2 &p_rect) const {
|
||
#ifdef MATH_CHECKS
|
||
if (unlikely(size.x < 0 || size.y < 0 || p_rect.size.x < 0 || p_rect.size.y < 0)) {
|
||
ERR_PRINT("Rect2 size is negative, this is not supported. Use Rect2.abs() to get a Rect2 with a positive size.");
|
||
}
|
||
#endif
|
||
//SAT intersection between local and transformed rect2
|
||
|
||
Vector2 xf_points[4] = {
|
||
p_xform.xform(p_rect.position),
|
||
p_xform.xform(Vector2(p_rect.position.x + p_rect.size.x, p_rect.position.y)),
|
||
p_xform.xform(Vector2(p_rect.position.x, p_rect.position.y + p_rect.size.y)),
|
||
p_xform.xform(Vector2(p_rect.position.x + p_rect.size.x, p_rect.position.y + p_rect.size.y)),
|
||
};
|
||
|
||
real_t low_limit;
|
||
|
||
//base rect2 first (faster)
|
||
|
||
if (xf_points[0].y > position.y) {
|
||
goto next1;
|
||
}
|
||
if (xf_points[1].y > position.y) {
|
||
goto next1;
|
||
}
|
||
if (xf_points[2].y > position.y) {
|
||
goto next1;
|
||
}
|
||
if (xf_points[3].y > position.y) {
|
||
goto next1;
|
||
}
|
||
|
||
return false;
|
||
|
||
next1:
|
||
|
||
low_limit = position.y + size.y;
|
||
|
||
if (xf_points[0].y < low_limit) {
|
||
goto next2;
|
||
}
|
||
if (xf_points[1].y < low_limit) {
|
||
goto next2;
|
||
}
|
||
if (xf_points[2].y < low_limit) {
|
||
goto next2;
|
||
}
|
||
if (xf_points[3].y < low_limit) {
|
||
goto next2;
|
||
}
|
||
|
||
return false;
|
||
|
||
next2:
|
||
|
||
if (xf_points[0].x > position.x) {
|
||
goto next3;
|
||
}
|
||
if (xf_points[1].x > position.x) {
|
||
goto next3;
|
||
}
|
||
if (xf_points[2].x > position.x) {
|
||
goto next3;
|
||
}
|
||
if (xf_points[3].x > position.x) {
|
||
goto next3;
|
||
}
|
||
|
||
return false;
|
||
|
||
next3:
|
||
|
||
low_limit = position.x + size.x;
|
||
|
||
if (xf_points[0].x < low_limit) {
|
||
goto next4;
|
||
}
|
||
if (xf_points[1].x < low_limit) {
|
||
goto next4;
|
||
}
|
||
if (xf_points[2].x < low_limit) {
|
||
goto next4;
|
||
}
|
||
if (xf_points[3].x < low_limit) {
|
||
goto next4;
|
||
}
|
||
|
||
return false;
|
||
|
||
next4:
|
||
|
||
Vector2 xf_points2[4] = {
|
||
position,
|
||
Vector2(position.x + size.x, position.y),
|
||
Vector2(position.x, position.y + size.y),
|
||
Vector2(position.x + size.x, position.y + size.y),
|
||
};
|
||
|
||
real_t maxa = p_xform.columns[0].dot(xf_points2[0]);
|
||
real_t mina = maxa;
|
||
|
||
real_t dp = p_xform.columns[0].dot(xf_points2[1]);
|
||
maxa = MAX(dp, maxa);
|
||
mina = MIN(dp, mina);
|
||
|
||
dp = p_xform.columns[0].dot(xf_points2[2]);
|
||
maxa = MAX(dp, maxa);
|
||
mina = MIN(dp, mina);
|
||
|
||
dp = p_xform.columns[0].dot(xf_points2[3]);
|
||
maxa = MAX(dp, maxa);
|
||
mina = MIN(dp, mina);
|
||
|
||
real_t maxb = p_xform.columns[0].dot(xf_points[0]);
|
||
real_t minb = maxb;
|
||
|
||
dp = p_xform.columns[0].dot(xf_points[1]);
|
||
maxb = MAX(dp, maxb);
|
||
minb = MIN(dp, minb);
|
||
|
||
dp = p_xform.columns[0].dot(xf_points[2]);
|
||
maxb = MAX(dp, maxb);
|
||
minb = MIN(dp, minb);
|
||
|
||
dp = p_xform.columns[0].dot(xf_points[3]);
|
||
maxb = MAX(dp, maxb);
|
||
minb = MIN(dp, minb);
|
||
|
||
if (mina > maxb) {
|
||
return false;
|
||
}
|
||
if (minb > maxa) {
|
||
return false;
|
||
}
|
||
|
||
maxa = p_xform.columns[1].dot(xf_points2[0]);
|
||
mina = maxa;
|
||
|
||
dp = p_xform.columns[1].dot(xf_points2[1]);
|
||
maxa = MAX(dp, maxa);
|
||
mina = MIN(dp, mina);
|
||
|
||
dp = p_xform.columns[1].dot(xf_points2[2]);
|
||
maxa = MAX(dp, maxa);
|
||
mina = MIN(dp, mina);
|
||
|
||
dp = p_xform.columns[1].dot(xf_points2[3]);
|
||
maxa = MAX(dp, maxa);
|
||
mina = MIN(dp, mina);
|
||
|
||
maxb = p_xform.columns[1].dot(xf_points[0]);
|
||
minb = maxb;
|
||
|
||
dp = p_xform.columns[1].dot(xf_points[1]);
|
||
maxb = MAX(dp, maxb);
|
||
minb = MIN(dp, minb);
|
||
|
||
dp = p_xform.columns[1].dot(xf_points[2]);
|
||
maxb = MAX(dp, maxb);
|
||
minb = MIN(dp, minb);
|
||
|
||
dp = p_xform.columns[1].dot(xf_points[3]);
|
||
maxb = MAX(dp, maxb);
|
||
minb = MIN(dp, minb);
|
||
|
||
if (mina > maxb) {
|
||
return false;
|
||
}
|
||
if (minb > maxa) {
|
||
return false;
|
||
}
|
||
|
||
return true;
|
||
}
|
||
|
||
Rect2 Rect2::intersection_transformed(const Transform2D &p_xform, const Rect2 &p_rect) const {
|
||
#ifdef MATH_CHECKS
|
||
if (unlikely(size.x < 0 || size.y < 0 || p_rect.size.x < 0 || p_rect.size.y < 0)) {
|
||
ERR_PRINT("Rect2 size is negative, this is not supported. Use Rect2.abs() to get a Rect2 with a positive size.");
|
||
}
|
||
#endif
|
||
|
||
if ((Math::is_zero_approx(p_xform.columns[0].y) && Math::is_zero_approx(p_xform.columns[1].x)) ||
|
||
(Math::is_zero_approx(p_xform.columns[0].x) && Math::is_zero_approx(p_xform.columns[1].y))) {
|
||
return intersection(p_xform.xform(p_rect));
|
||
}
|
||
|
||
if (!intersects_transformed(p_xform, p_rect)) {
|
||
return Rect2();
|
||
}
|
||
|
||
const Vector2 xf_points[4] = {
|
||
p_xform.xform(p_rect.position),
|
||
p_xform.xform(Vector2(p_rect.position.x + p_rect.size.x, p_rect.position.y)),
|
||
p_xform.xform(Vector2(p_rect.position.x + p_rect.size.x, p_rect.position.y + p_rect.size.y)),
|
||
p_xform.xform(Vector2(p_rect.position.x, p_rect.position.y + p_rect.size.y)),
|
||
};
|
||
|
||
// Use Sutherland–Hodgman algorithm.
|
||
|
||
Vector2 subject[8];
|
||
int subject_count = 4;
|
||
subject[0] = xf_points[0];
|
||
subject[1] = xf_points[1];
|
||
subject[2] = xf_points[2];
|
||
subject[3] = xf_points[3];
|
||
|
||
const Vector2 min = position;
|
||
const Vector2 max = position + size;
|
||
Vector2 intersected;
|
||
|
||
for (int edge = 0; edge < 4; edge++) {
|
||
const int axis = edge % 2;
|
||
const int another_axis = 1 - axis;
|
||
const bool is_min = (edge < 2);
|
||
intersected[axis] = is_min ? min[axis] : max[axis];
|
||
|
||
Vector2 output[8];
|
||
int output_count = 0;
|
||
|
||
Vector2 prev = subject[subject_count - 1];
|
||
bool prev_in_halfplane = is_min ? (prev[axis] >= intersected[axis]) : (prev[axis] <= intersected[axis]);
|
||
|
||
for (int i = 0; i < subject_count; i++) {
|
||
const Vector2 &curr = subject[i];
|
||
bool curr_in_halfplane = is_min ? (curr[axis] >= intersected[axis]) : (curr[axis] <= intersected[axis]);
|
||
if (prev_in_halfplane != curr_in_halfplane) {
|
||
// Entering/exiting the half-plane.
|
||
real_t t = (intersected[axis] - prev[axis]) / (curr[axis] - prev[axis]);
|
||
intersected[another_axis] = prev[another_axis] + (curr[another_axis] - prev[another_axis]) * t;
|
||
output[output_count++] = intersected;
|
||
}
|
||
if (curr_in_halfplane) {
|
||
output[output_count++] = curr;
|
||
}
|
||
prev = curr;
|
||
prev_in_halfplane = curr_in_halfplane;
|
||
}
|
||
|
||
for (int i = 0; i < output_count; i++) {
|
||
subject[i] = output[i];
|
||
}
|
||
|
||
subject_count = output_count;
|
||
if (subject_count == 0) {
|
||
break;
|
||
}
|
||
}
|
||
|
||
if (subject_count > 0) {
|
||
return Rect2::from_points(subject, subject_count);
|
||
}
|
||
|
||
// Perform a reverse containment test; the current rect may be inside the transformed rect.
|
||
|
||
const Vector2 corners[4] = {
|
||
position,
|
||
Vector2(max.x, min.y),
|
||
max,
|
||
Vector2(min.x, max.y)
|
||
};
|
||
|
||
Vector2 inside_points[4];
|
||
int inside_count = 0;
|
||
|
||
for (int point_idx = 0; point_idx < 4; point_idx++) {
|
||
bool has_pos = false;
|
||
bool has_neg = false;
|
||
for (int idx = 0; idx < 4; idx++) {
|
||
const int next_idx = (idx + 1) % 4;
|
||
Vector2 v0 = xf_points[next_idx] - xf_points[idx];
|
||
Vector2 v1 = corners[point_idx] - xf_points[idx];
|
||
real_t cross = v0.cross(v1);
|
||
if (cross > CMP_EPSILON) {
|
||
has_pos = true;
|
||
}
|
||
if (cross < -CMP_EPSILON) {
|
||
has_neg = true;
|
||
}
|
||
if (has_pos && has_neg) {
|
||
break;
|
||
}
|
||
}
|
||
if (!(has_pos && has_neg)) {
|
||
inside_points[inside_count++] = corners[point_idx];
|
||
}
|
||
}
|
||
|
||
return inside_count > 0 ? Rect2::from_points(inside_points, inside_count) : Rect2();
|
||
}
|
||
|
||
Rect2::operator String() const {
|
||
return "[P: " + position.operator String() + ", S: " + size.operator String() + "]";
|
||
}
|
||
|
||
Rect2::operator Rect2i() const {
|
||
return Rect2i(position, size);
|
||
}
|