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diff --git a/core/math/aabb.cpp b/core/math/aabb.cpp
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+/*************************************************************************/
+/* aabb.cpp */
+/*************************************************************************/
+/* This file is part of: */
+/* GODOT ENGINE */
+/* https://godotengine.org */
+/*************************************************************************/
+/* Copyright (c) 2007-2017 Juan Linietsky, Ariel Manzur. */
+/* Copyright (c) 2014-2017 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. */
+/*************************************************************************/
+#include "aabb.h"
+
+#include "print_string.h"
+
+real_t AABB::get_area() const {
+
+ return size.x * size.y * size.z;
+}
+
+bool AABB::operator==(const AABB &p_rval) const {
+
+ return ((position == p_rval.position) && (size == p_rval.size));
+}
+bool AABB::operator!=(const AABB &p_rval) const {
+
+ return ((position != p_rval.position) || (size != p_rval.size));
+}
+
+void AABB::merge_with(const AABB &p_aabb) {
+
+ Vector3 beg_1, beg_2;
+ Vector3 end_1, end_2;
+ Vector3 min, max;
+
+ beg_1 = position;
+ beg_2 = p_aabb.position;
+ end_1 = Vector3(size.x, size.y, size.z) + beg_1;
+ end_2 = Vector3(p_aabb.size.x, p_aabb.size.y, p_aabb.size.z) + beg_2;
+
+ min.x = (beg_1.x < beg_2.x) ? beg_1.x : beg_2.x;
+ min.y = (beg_1.y < beg_2.y) ? beg_1.y : beg_2.y;
+ min.z = (beg_1.z < beg_2.z) ? beg_1.z : beg_2.z;
+
+ max.x = (end_1.x > end_2.x) ? end_1.x : end_2.x;
+ max.y = (end_1.y > end_2.y) ? end_1.y : end_2.y;
+ max.z = (end_1.z > end_2.z) ? end_1.z : end_2.z;
+
+ position = min;
+ size = max - min;
+}
+
+AABB AABB::intersection(const AABB &p_aabb) const {
+
+ Vector3 src_min = position;
+ Vector3 src_max = position + size;
+ Vector3 dst_min = p_aabb.position;
+ Vector3 dst_max = p_aabb.position + p_aabb.size;
+
+ Vector3 min, max;
+
+ if (src_min.x > dst_max.x || src_max.x < dst_min.x)
+ return AABB();
+ else {
+
+ min.x = (src_min.x > dst_min.x) ? src_min.x : dst_min.x;
+ max.x = (src_max.x < dst_max.x) ? src_max.x : dst_max.x;
+ }
+
+ if (src_min.y > dst_max.y || src_max.y < dst_min.y)
+ return AABB();
+ else {
+
+ min.y = (src_min.y > dst_min.y) ? src_min.y : dst_min.y;
+ max.y = (src_max.y < dst_max.y) ? src_max.y : dst_max.y;
+ }
+
+ if (src_min.z > dst_max.z || src_max.z < dst_min.z)
+ return AABB();
+ else {
+
+ min.z = (src_min.z > dst_min.z) ? src_min.z : dst_min.z;
+ max.z = (src_max.z < dst_max.z) ? src_max.z : dst_max.z;
+ }
+
+ return AABB(min, max - min);
+}
+
+bool AABB::intersects_ray(const Vector3 &p_from, const Vector3 &p_dir, Vector3 *r_clip, Vector3 *r_normal) const {
+
+ Vector3 c1, c2;
+ Vector3 end = position + size;
+ real_t near = -1e20;
+ real_t far = 1e20;
+ int axis = 0;
+
+ for (int i = 0; i < 3; i++) {
+ if (p_dir[i] == 0) {
+ if ((p_from[i] < position[i]) || (p_from[i] > end[i])) {
+ return false;
+ }
+ } else { // ray not parallel to planes in this direction
+ c1[i] = (position[i] - p_from[i]) / p_dir[i];
+ c2[i] = (end[i] - p_from[i]) / p_dir[i];
+
+ if (c1[i] > c2[i]) {
+ SWAP(c1, c2);
+ }
+ if (c1[i] > near) {
+ near = c1[i];
+ axis = i;
+ }
+ if (c2[i] < far) {
+ far = c2[i];
+ }
+ if ((near > far) || (far < 0)) {
+ return false;
+ }
+ }
+ }
+
+ if (r_clip)
+ *r_clip = c1;
+ if (r_normal) {
+ *r_normal = Vector3();
+ (*r_normal)[axis] = p_dir[axis] ? -1 : 1;
+ }
+
+ return true;
+}
+
+bool AABB::intersects_segment(const Vector3 &p_from, const Vector3 &p_to, Vector3 *r_clip, Vector3 *r_normal) const {
+
+ real_t min = 0, max = 1;
+ int axis = 0;
+ real_t sign = 0;
+
+ for (int i = 0; i < 3; 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;
+ }
+
+ Vector3 rel = p_to - p_from;
+
+ if (r_normal) {
+ Vector3 normal;
+ normal[axis] = sign;
+ *r_normal = normal;
+ }
+
+ if (r_clip)
+ *r_clip = p_from + rel * min;
+
+ return true;
+}
+
+bool AABB::intersects_plane(const Plane &p_plane) const {
+
+ Vector3 points[8] = {
+ Vector3(position.x, position.y, position.z),
+ Vector3(position.x, position.y, position.z + size.z),
+ Vector3(position.x, position.y + size.y, position.z),
+ Vector3(position.x, position.y + size.y, position.z + size.z),
+ Vector3(position.x + size.x, position.y, position.z),
+ Vector3(position.x + size.x, position.y, position.z + size.z),
+ Vector3(position.x + size.x, position.y + size.y, position.z),
+ Vector3(position.x + size.x, position.y + size.y, position.z + size.z),
+ };
+
+ bool over = false;
+ bool under = false;
+
+ for (int i = 0; i < 8; i++) {
+
+ if (p_plane.distance_to(points[i]) > 0)
+ over = true;
+ else
+ under = true;
+ }
+
+ return under && over;
+}
+
+Vector3 AABB::get_longest_axis() const {
+
+ Vector3 axis(1, 0, 0);
+ real_t max_size = size.x;
+
+ if (size.y > max_size) {
+ axis = Vector3(0, 1, 0);
+ max_size = size.y;
+ }
+
+ if (size.z > max_size) {
+ axis = Vector3(0, 0, 1);
+ max_size = size.z;
+ }
+
+ return axis;
+}
+int AABB::get_longest_axis_index() const {
+
+ int axis = 0;
+ real_t max_size = size.x;
+
+ if (size.y > max_size) {
+ axis = 1;
+ max_size = size.y;
+ }
+
+ if (size.z > max_size) {
+ axis = 2;
+ max_size = size.z;
+ }
+
+ return axis;
+}
+
+Vector3 AABB::get_shortest_axis() const {
+
+ Vector3 axis(1, 0, 0);
+ real_t max_size = size.x;
+
+ if (size.y < max_size) {
+ axis = Vector3(0, 1, 0);
+ max_size = size.y;
+ }
+
+ if (size.z < max_size) {
+ axis = Vector3(0, 0, 1);
+ max_size = size.z;
+ }
+
+ return axis;
+}
+int AABB::get_shortest_axis_index() const {
+
+ int axis = 0;
+ real_t max_size = size.x;
+
+ if (size.y < max_size) {
+ axis = 1;
+ max_size = size.y;
+ }
+
+ if (size.z < max_size) {
+ axis = 2;
+ max_size = size.z;
+ }
+
+ return axis;
+}
+
+AABB AABB::merge(const AABB &p_with) const {
+
+ AABB aabb = *this;
+ aabb.merge_with(p_with);
+ return aabb;
+}
+AABB AABB::expand(const Vector3 &p_vector) const {
+ AABB aabb = *this;
+ aabb.expand_to(p_vector);
+ return aabb;
+}
+AABB AABB::grow(real_t p_by) const {
+
+ AABB aabb = *this;
+ aabb.grow_by(p_by);
+ return aabb;
+}
+
+void AABB::get_edge(int p_edge, Vector3 &r_from, Vector3 &r_to) const {
+
+ ERR_FAIL_INDEX(p_edge, 12);
+ switch (p_edge) {
+
+ case 0: {
+
+ r_from = Vector3(position.x + size.x, position.y, position.z);
+ r_to = Vector3(position.x, position.y, position.z);
+ } break;
+ case 1: {
+
+ r_from = Vector3(position.x + size.x, position.y, position.z + size.z);
+ r_to = Vector3(position.x + size.x, position.y, position.z);
+ } break;
+ case 2: {
+ r_from = Vector3(position.x, position.y, position.z + size.z);
+ r_to = Vector3(position.x + size.x, position.y, position.z + size.z);
+
+ } break;
+ case 3: {
+
+ r_from = Vector3(position.x, position.y, position.z);
+ r_to = Vector3(position.x, position.y, position.z + size.z);
+
+ } break;
+ case 4: {
+
+ r_from = Vector3(position.x, position.y + size.y, position.z);
+ r_to = Vector3(position.x + size.x, position.y + size.y, position.z);
+ } break;
+ case 5: {
+
+ r_from = Vector3(position.x + size.x, position.y + size.y, position.z);
+ r_to = Vector3(position.x + size.x, position.y + size.y, position.z + size.z);
+ } break;
+ case 6: {
+ r_from = Vector3(position.x + size.x, position.y + size.y, position.z + size.z);
+ r_to = Vector3(position.x, position.y + size.y, position.z + size.z);
+
+ } break;
+ case 7: {
+
+ r_from = Vector3(position.x, position.y + size.y, position.z + size.z);
+ r_to = Vector3(position.x, position.y + size.y, position.z);
+
+ } break;
+ case 8: {
+
+ r_from = Vector3(position.x, position.y, position.z + size.z);
+ r_to = Vector3(position.x, position.y + size.y, position.z + size.z);
+
+ } break;
+ case 9: {
+
+ r_from = Vector3(position.x, position.y, position.z);
+ r_to = Vector3(position.x, position.y + size.y, position.z);
+
+ } break;
+ case 10: {
+
+ r_from = Vector3(position.x + size.x, position.y, position.z);
+ r_to = Vector3(position.x + size.x, position.y + size.y, position.z);
+
+ } break;
+ case 11: {
+
+ r_from = Vector3(position.x + size.x, position.y, position.z + size.z);
+ r_to = Vector3(position.x + size.x, position.y + size.y, position.z + size.z);
+
+ } break;
+ }
+}
+
+AABB::operator String() const {
+
+ return String() + position + " - " + size;
+}
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