godot/core/math/plane.cpp

/*************************************************************************/
/*  plane.cpp                                                            */
/*************************************************************************/
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/*                           GODOT ENGINE                                */
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/* Copyright (c) 2007-2021 Juan Linietsky, Ariel Manzur.                 */
/* Copyright (c) 2014-2021 Godot Engine contributors (cf. AUTHORS.md).   */
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#include "plane.h"

#include "core/math/math_funcs.h"
#include "core/variant/variant.h"

void Plane::set_normal(const Vector3 &p_normal) {
	normal = p_normal;
}

void Plane::normalize() {
	real_t l = normal.length();
	if (l == 0) {
		*this = Plane(0, 0, 0, 0);
		return;
	}
	normal /= l;
	d /= l;
}

Plane Plane::normalized() const {
	Plane p = *this;
	p.normalize();
	return p;
}

Vector3 Plane::get_any_perpendicular_normal() const {
	static const Vector3 p1 = Vector3(1, 0, 0);
	static const Vector3 p2 = Vector3(0, 1, 0);
	Vector3 p;

	if (ABS(normal.dot(p1)) > 0.99) { // if too similar to p1
		p = p2; // use p2
	} else {
		p = p1; // use p1
	}

	p -= normal * normal.dot(p);
	p.normalize();

	return p;
}

/* intersections */

bool Plane::intersect_3(const Plane &p_plane1, const Plane &p_plane2, Vector3 *r_result) const {
	const Plane &p_plane0 = *this;
	Vector3 normal0 = p_plane0.normal;
	Vector3 normal1 = p_plane1.normal;
	Vector3 normal2 = p_plane2.normal;

	real_t denom = vec3_cross(normal0, normal1).dot(normal2);

	if (Math::is_zero_approx(denom)) {
		return false;
	}

	if (r_result) {
		*r_result = ((vec3_cross(normal1, normal2) * p_plane0.d) +
							(vec3_cross(normal2, normal0) * p_plane1.d) +
							(vec3_cross(normal0, normal1) * p_plane2.d)) /
					denom;
	}

	return true;
}

bool Plane::intersects_ray(const Vector3 &p_from, const Vector3 &p_dir, Vector3 *p_intersection) const {
	Vector3 segment = p_dir;
	real_t den = normal.dot(segment);

	//printf("den is %i\n",den);
	if (Math::is_zero_approx(den)) {
		return false;
	}

	real_t dist = (normal.dot(p_from) - d) / den;
	//printf("dist is %i\n",dist);

	if (dist > CMP_EPSILON) { //this is a ray, before the emitting pos (p_from) doesn't exist

		return false;
	}

	dist = -dist;
	*p_intersection = p_from + segment * dist;

	return true;
}

bool Plane::intersects_segment(const Vector3 &p_begin, const Vector3 &p_end, Vector3 *p_intersection) const {
	Vector3 segment = p_begin - p_end;
	real_t den = normal.dot(segment);

	//printf("den is %i\n",den);
	if (Math::is_zero_approx(den)) {
		return false;
	}

	real_t dist = (normal.dot(p_begin) - d) / den;
	//printf("dist is %i\n",dist);

	if (dist < -CMP_EPSILON || dist > (1.0 + CMP_EPSILON)) {
		return false;
	}

	dist = -dist;
	*p_intersection = p_begin + segment * dist;

	return true;
}

Variant Plane::intersect_3_bind(const Plane &p_plane1, const Plane &p_plane2) const {
	Vector3 inters;
	if (intersect_3(p_plane1, p_plane2, &inters)) {
		return inters;
	} else {
		return Variant();
	}
}
Variant Plane::intersects_ray_bind(const Vector3 &p_from, const Vector3 &p_dir) const {
	Vector3 inters;
	if (intersects_ray(p_from, p_dir, &inters)) {
		return inters;
	} else {
		return Variant();
	}
}
Variant Plane::intersects_segment_bind(const Vector3 &p_begin, const Vector3 &p_end) const {
	Vector3 inters;
	if (intersects_segment(p_begin, p_end, &inters)) {
		return inters;
	} else {
		return Variant();
	}
}

/* misc */

bool Plane::is_equal_approx_any_side(const Plane &p_plane) const {
	return (normal.is_equal_approx(p_plane.normal) && Math::is_equal_approx(d, p_plane.d)) || (normal.is_equal_approx(-p_plane.normal) && Math::is_equal_approx(d, -p_plane.d));
}

bool Plane::is_equal_approx(const Plane &p_plane) const {
	return normal.is_equal_approx(p_plane.normal) && Math::is_equal_approx(d, p_plane.d);
}

Plane::operator String() const {
	return "[N: " + normal.operator String() + ", D: " + String::num_real(d, false) + "]";
}