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godot/core/math/transform_3d.h

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/*************************************************************************/
/* transform_3d.h */
/*************************************************************************/
/* This file is part of: */
/* GODOT ENGINE */
/* https://godotengine.org */
/*************************************************************************/
/* Copyright (c) 2007-2022 Juan Linietsky, Ariel Manzur. */
/* Copyright (c) 2014-2022 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. */
/*************************************************************************/
#ifndef TRANSFORM_H
#define TRANSFORM_H
#include "core/math/aabb.h"
#include "core/math/basis.h"
#include "core/math/plane.h"
class _NO_DISCARD_ 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;
void orthogonalize();
Transform3D orthogonalized() 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_ AABB xform(const AABB &p_aabb) const;
_FORCE_INLINE_ Vector<Vector3> xform(const Vector<Vector3> &p_array) const;
// NOTE: These are UNSAFE with non-uniform scaling, and will produce incorrect results.
// They use the transpose.
// For safe inverse transforms, xform by the affine_inverse.
_FORCE_INLINE_ Vector3 xform_inv(const Vector3 &p_vector) const;
_FORCE_INLINE_ AABB xform_inv(const AABB &p_aabb) const;
_FORCE_INLINE_ Vector<Vector3> xform_inv(const Vector<Vector3> &p_array) const;
// Safe with non-uniform scaling (uses affine_inverse).
_FORCE_INLINE_ Plane xform(const Plane &p_plane) const;
_FORCE_INLINE_ Plane xform_inv(const Plane &p_plane) const;
// These fast versions use precomputed affine inverse, and should be used in bottleneck areas where
// multiple planes are to be transformed.
_FORCE_INLINE_ Plane xform_fast(const Plane &p_plane, const Basis &p_basis_inverse_transpose) const;
static _FORCE_INLINE_ Plane xform_inv_fast(const Plane &p_plane, const Transform3D &p_inverse, const Basis &p_basis_transpose);
void operator*=(const Transform3D &p_transform);
Transform3D operator*(const Transform3D &p_transform) const;
void operator*=(const real_t p_val);
Transform3D operator*(const real_t p_val) const;
Transform3D sphere_interpolate_with(const Transform3D &p_transform, real_t p_c) 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));
}
// Neither the plane regular xform or xform_inv are particularly efficient,
// as they do a basis inverse. For xforming a large number
// of planes it is better to pre-calculate the inverse transpose basis once
// and reuse it for each plane, by using the 'fast' version of the functions.
_FORCE_INLINE_ Plane Transform3D::xform(const Plane &p_plane) const {
Basis b = basis.inverse();
b.transpose();
return xform_fast(p_plane, b);
}
_FORCE_INLINE_ Plane Transform3D::xform_inv(const Plane &p_plane) const {
Transform3D inv = affine_inverse();
Basis basis_transpose = basis.transposed();
return xform_inv_fast(p_plane, inv, basis_transpose);
}
_FORCE_INLINE_ AABB Transform3D::xform(const AABB &p_aabb) const {
/* https://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;
}
_FORCE_INLINE_ Plane Transform3D::xform_fast(const Plane &p_plane, const Basis &p_basis_inverse_transpose) const {
// Transform a single point on the plane.
Vector3 point = p_plane.normal * p_plane.d;
point = xform(point);
// Use inverse transpose for correct normals with non-uniform scaling.
Vector3 normal = p_basis_inverse_transpose.xform(p_plane.normal);
normal.normalize();
real_t d = normal.dot(point);
return Plane(normal, d);
}
_FORCE_INLINE_ Plane Transform3D::xform_inv_fast(const Plane &p_plane, const Transform3D &p_inverse, const Basis &p_basis_transpose) {
// Transform a single point on the plane.
Vector3 point = p_plane.normal * p_plane.d;
point = p_inverse.xform(point);
// Note that instead of precalculating the transpose, an alternative
// would be to use the transpose for the basis transform.
// However that would be less SIMD friendly (requiring a swizzle).
// So the cost is one extra precalced value in the calling code.
// This is probably worth it, as this could be used in bottleneck areas. And
// where it is not a bottleneck, the non-fast method is fine.
// Use transpose for correct normals with non-uniform scaling.
Vector3 normal = p_basis_transpose.xform(p_plane.normal);
normal.normalize();
real_t d = normal.dot(point);
return Plane(normal, d);
}
#endif // TRANSFORM_H
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