godot/core/math/aabb.cpp

/**************************************************************************/
/*  aabb.cpp                                                              */
/**************************************************************************/
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/*                             GODOT ENGINE                               */
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/* Copyright (c) 2014-present Godot Engine contributors (see AUTHORS.md). */
/* Copyright (c) 2007-2014 Juan Linietsky, Ariel Manzur.                  */
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#include "aabb.h"

#include "core/string/ustring.h"
#include "core/variant/variant.h"

real_t AABB::get_volume() const {
	return size.x * size.y * size.z;
}

void AABB::merge_with(const AABB &p_aabb) {
#ifdef MATH_CHECKS
	if (unlikely(size.x < 0 || size.y < 0 || size.z < 0 || p_aabb.size.x < 0 || p_aabb.size.y < 0 || p_aabb.size.z < 0)) {
		ERR_PRINT("AABB size is negative, this is not supported. Use AABB.abs() to get an AABB with a positive size.");
	}
#endif
	Vector3 beg_1, beg_2;
	Vector3 end_1, end_2;
	Vector3 min, max;

	beg_1 = position;
	beg_2 = p_aabb.position;
	end_1 = size + beg_1;
	end_2 = p_aabb.size + 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;
}

bool AABB::is_equal_approx(const AABB &p_aabb) const {
	return position.is_equal_approx(p_aabb.position) && size.is_equal_approx(p_aabb.size);
}

bool AABB::is_same(const AABB &p_aabb) const {
	return position.is_same(p_aabb.position) && size.is_same(p_aabb.size);
}

bool AABB::is_finite() const {
	return position.is_finite() && size.is_finite();
}

AABB AABB::intersection(const AABB &p_aabb) const {
#ifdef MATH_CHECKS
	if (unlikely(size.x < 0 || size.y < 0 || size.z < 0 || p_aabb.size.x < 0 || p_aabb.size.y < 0 || p_aabb.size.z < 0)) {
		ERR_PRINT("AABB size is negative, this is not supported. Use AABB.abs() to get an AABB with a positive size.");
	}
#endif
	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);
}

// Note that this routine returns the BACKTRACKED (i.e. behind the ray origin)
// intersection point + normal if INSIDE the AABB.
// The caller can therefore decide when INSIDE whether to use the
// backtracked intersection, or use p_from as the intersection, and
// carry on progressing without e.g. reflecting against the normal.
bool AABB::find_intersects_ray(const Vector3 &p_from, const Vector3 &p_dir, bool &r_inside, Vector3 *r_intersection_point, Vector3 *r_normal) const {
#ifdef MATH_CHECKS
	if (unlikely(size.x < 0 || size.y < 0 || size.z < 0)) {
		ERR_PRINT("AABB size is negative, this is not supported. Use AABB.abs() to get an AABB with a positive size.");
	}
#endif
	Vector3 end = position + size;
	real_t tmin = -1e20;
	real_t tmax = 1e20;
	int axis = 0;

	// Make sure r_inside is always initialized,
	// to prevent reading uninitialized data in the client code.
	r_inside = false;

	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
			real_t t1 = (position[i] - p_from[i]) / p_dir[i];
			real_t t2 = (end[i] - p_from[i]) / p_dir[i];

			if (t1 > t2) {
				SWAP(t1, t2);
			}
			if (t1 >= tmin) {
				tmin = t1;
				axis = i;
			}
			if (t2 < tmax) {
				if (t2 < 0) {
					return false;
				}
				tmax = t2;
			}
			if (tmin > tmax) {
				return false;
			}
		}
	}

	// Did the ray start from inside the box?
	// In which case the intersection returned is the point of entry
	// (behind the ray start) or the calling routine can use the ray origin as intersection point.
	r_inside = tmin < 0;

	if (r_intersection_point) {
		*r_intersection_point = p_from + p_dir * tmin;

		// Prevent float error by making sure the point is exactly
		// on the AABB border on the relevant axis.
		r_intersection_point->coord[axis] = (p_dir[axis] >= 0) ? position.coord[axis] : end.coord[axis];
	}
	if (r_normal) {
		*r_normal = Vector3();
		(*r_normal)[axis] = (p_dir[axis] >= 0) ? -1 : 1;
	}

	return true;
}

bool AABB::intersects_segment(const Vector3 &p_from, const Vector3 &p_to, Vector3 *r_intersection_point, Vector3 *r_normal) const {
#ifdef MATH_CHECKS
	if (unlikely(size.x < 0 || size.y < 0 || size.z < 0)) {
		ERR_PRINT("AABB size is negative, this is not supported. Use AABB.abs() to get an AABB with a positive size.");
	}
#endif
	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_intersection_point) {
		*r_intersection_point = 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);
	}

	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;
	}

	return axis;
}

Vector3 AABB::get_shortest_axis() const {
	Vector3 axis(1, 0, 0);
	real_t min_size = size.x;

	if (size.y < min_size) {
		axis = Vector3(0, 1, 0);
		min_size = size.y;
	}

	if (size.z < min_size) {
		axis = Vector3(0, 0, 1);
	}

	return axis;
}

int AABB::get_shortest_axis_index() const {
	int axis = 0;
	real_t min_size = size.x;

	if (size.y < min_size) {
		axis = 1;
		min_size = size.y;
	}

	if (size.z < min_size) {
		axis = 2;
	}

	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;
	}
}

Variant AABB::intersects_segment_bind(const Vector3 &p_from, const Vector3 &p_to) const {
	Vector3 inters;
	if (intersects_segment(p_from, p_to, &inters)) {
		return inters;
	}
	return Variant();
}

Variant AABB::intersects_ray_bind(const Vector3 &p_from, const Vector3 &p_dir) const {
	Vector3 inters;
	bool inside = false;

	if (find_intersects_ray(p_from, p_dir, inside, &inters)) {
		// When inside the intersection point may be BEHIND the ray,
		// so for general use we return the ray origin.
		if (inside) {
			return p_from;
		}

		return inters;
	}
	return Variant();
}

AABB::operator String() const {
	return "[P: " + position.operator String() + ", S: " + size + "]";
}