virtualx-engine/core/math/transform.h

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/*  transform.h                                                          */
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#ifndef TRANSFORM_H
#define TRANSFORM_H

#include "core/math/aabb.h"
#include "core/math/basis.h"
#include "core/math/plane.h"

class Transform3D {
public:
	Basis basis;
	Vector3 origin;

	void invert();
	Transform3D inverse() const;

	void affine_invert();
	Transform3D affine_inverse() const;

	Transform3D rotated(const Vector3 &p_axis, real_t p_phi) const;

	void rotate(const Vector3 &p_axis, real_t p_phi);
	void rotate_basis(const Vector3 &p_axis, real_t p_phi);

	void set_look_at(const Vector3 &p_eye, const Vector3 &p_target, const Vector3 &p_up = Vector3(0, 1, 0));
	Transform3D looking_at(const Vector3 &p_target, const Vector3 &p_up = Vector3(0, 1, 0)) const;

	void scale(const Vector3 &p_scale);
	Transform3D scaled(const Vector3 &p_scale) const;
	void scale_basis(const Vector3 &p_scale);
	void translate(real_t p_tx, real_t p_ty, real_t p_tz);
	void translate(const Vector3 &p_translation);
	Transform3D translated(const Vector3 &p_translation) const;

	const Basis &get_basis() const { return basis; }
	void set_basis(const Basis &p_basis) { basis = p_basis; }

	const Vector3 &get_origin() const { return origin; }
	void set_origin(const Vector3 &p_origin) { origin = p_origin; }

	void orthonormalize();
	Transform3D orthonormalized() const;
	bool is_equal_approx(const Transform3D &p_transform) const;

	bool operator==(const Transform3D &p_transform) const;
	bool operator!=(const Transform3D &p_transform) const;

	_FORCE_INLINE_ Vector3 xform(const Vector3 &p_vector) const;
	_FORCE_INLINE_ Vector3 xform_inv(const Vector3 &p_vector) const;

	_FORCE_INLINE_ Plane xform(const Plane &p_plane) const;
	_FORCE_INLINE_ Plane xform_inv(const Plane &p_plane) const;

	_FORCE_INLINE_ AABB xform(const AABB &p_aabb) const;
	_FORCE_INLINE_ AABB xform_inv(const AABB &p_aabb) const;

	_FORCE_INLINE_ Vector<Vector3> xform(const Vector<Vector3> &p_array) const;
	_FORCE_INLINE_ Vector<Vector3> xform_inv(const Vector<Vector3> &p_array) const;

	void operator*=(const Transform3D &p_transform);
	Transform3D operator*(const Transform3D &p_transform) const;

	Transform3D interpolate_with(const Transform3D &p_transform, real_t p_c) const;

	_FORCE_INLINE_ Transform3D inverse_xform(const Transform3D &t) const {
		Vector3 v = t.origin - origin;
		return Transform3D(basis.transpose_xform(t.basis),
				basis.xform(v));
	}

	void set(real_t xx, real_t xy, real_t xz, real_t yx, real_t yy, real_t yz, real_t zx, real_t zy, real_t zz, real_t tx, real_t ty, real_t tz) {
		basis.set(xx, xy, xz, yx, yy, yz, zx, zy, zz);
		origin.x = tx;
		origin.y = ty;
		origin.z = tz;
	}

	operator String() const;

	Transform3D() {}
	Transform3D(const Basis &p_basis, const Vector3 &p_origin = Vector3());
	Transform3D(const Vector3 &p_x, const Vector3 &p_y, const Vector3 &p_z, const Vector3 &p_origin);
	Transform3D(real_t xx, real_t xy, real_t xz, real_t yx, real_t yy, real_t yz, real_t zx, real_t zy, real_t zz, real_t ox, real_t oy, real_t oz);
};

_FORCE_INLINE_ Vector3 Transform3D::xform(const Vector3 &p_vector) const {
	return Vector3(
			basis[0].dot(p_vector) + origin.x,
			basis[1].dot(p_vector) + origin.y,
			basis[2].dot(p_vector) + origin.z);
}

_FORCE_INLINE_ Vector3 Transform3D::xform_inv(const Vector3 &p_vector) const {
	Vector3 v = p_vector - origin;

	return Vector3(
			(basis.elements[0][0] * v.x) + (basis.elements[1][0] * v.y) + (basis.elements[2][0] * v.z),
			(basis.elements[0][1] * v.x) + (basis.elements[1][1] * v.y) + (basis.elements[2][1] * v.z),
			(basis.elements[0][2] * v.x) + (basis.elements[1][2] * v.y) + (basis.elements[2][2] * v.z));
}

_FORCE_INLINE_ Plane Transform3D::xform(const Plane &p_plane) const {
	Vector3 point = p_plane.normal * p_plane.d;
	Vector3 point_dir = point + p_plane.normal;
	point = xform(point);
	point_dir = xform(point_dir);

	Vector3 normal = point_dir - point;
	normal.normalize();
	real_t d = normal.dot(point);

	return Plane(normal, d);
}

_FORCE_INLINE_ Plane Transform3D::xform_inv(const Plane &p_plane) const {
	Vector3 point = p_plane.normal * p_plane.d;
	Vector3 point_dir = point + p_plane.normal;
	point = xform_inv(point);
	point_dir = xform_inv(point_dir);

	Vector3 normal = point_dir - point;
	normal.normalize();
	real_t d = normal.dot(point);

	return Plane(normal, d);
}

_FORCE_INLINE_ AABB Transform3D::xform(const AABB &p_aabb) const {
	/* http://dev.theomader.com/transform-bounding-boxes/ */
	Vector3 min = p_aabb.position;
	Vector3 max = p_aabb.position + p_aabb.size;
	Vector3 tmin, tmax;
	for (int i = 0; i < 3; i++) {
		tmin[i] = tmax[i] = origin[i];
		for (int j = 0; j < 3; j++) {
			real_t e = basis[i][j] * min[j];
			real_t f = basis[i][j] * max[j];
			if (e < f) {
				tmin[i] += e;
				tmax[i] += f;
			} else {
				tmin[i] += f;
				tmax[i] += e;
			}
		}
	}
	AABB r_aabb;
	r_aabb.position = tmin;
	r_aabb.size = tmax - tmin;
	return r_aabb;
}

_FORCE_INLINE_ AABB Transform3D::xform_inv(const AABB &p_aabb) const {
	/* define vertices */
	Vector3 vertices[8] = {
		Vector3(p_aabb.position.x + p_aabb.size.x, p_aabb.position.y + p_aabb.size.y, p_aabb.position.z + p_aabb.size.z),
		Vector3(p_aabb.position.x + p_aabb.size.x, p_aabb.position.y + p_aabb.size.y, p_aabb.position.z),
		Vector3(p_aabb.position.x + p_aabb.size.x, p_aabb.position.y, p_aabb.position.z + p_aabb.size.z),
		Vector3(p_aabb.position.x + p_aabb.size.x, p_aabb.position.y, p_aabb.position.z),
		Vector3(p_aabb.position.x, p_aabb.position.y + p_aabb.size.y, p_aabb.position.z + p_aabb.size.z),
		Vector3(p_aabb.position.x, p_aabb.position.y + p_aabb.size.y, p_aabb.position.z),
		Vector3(p_aabb.position.x, p_aabb.position.y, p_aabb.position.z + p_aabb.size.z),
		Vector3(p_aabb.position.x, p_aabb.position.y, p_aabb.position.z)
	};

	AABB ret;

	ret.position = xform_inv(vertices[0]);

	for (int i = 1; i < 8; i++) {
		ret.expand_to(xform_inv(vertices[i]));
	}

	return ret;
}

Vector<Vector3> Transform3D::xform(const Vector<Vector3> &p_array) const {
	Vector<Vector3> array;
	array.resize(p_array.size());

	const Vector3 *r = p_array.ptr();
	Vector3 *w = array.ptrw();

	for (int i = 0; i < p_array.size(); ++i) {
		w[i] = xform(r[i]);
	}
	return array;
}

Vector<Vector3> Transform3D::xform_inv(const Vector<Vector3> &p_array) const {
	Vector<Vector3> array;
	array.resize(p_array.size());

	const Vector3 *r = p_array.ptr();
	Vector3 *w = array.ptrw();

	for (int i = 0; i < p_array.size(); ++i) {
		w[i] = xform_inv(r[i]);
	}
	return array;
}

#endif // TRANSFORM_H