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As many open source projects have started doing it, we're removing the current year from the copyright notice, so that we don't need to bump it every year. It seems like only the first year of publication is technically relevant for copyright notices, and even that seems to be something that many companies stopped listing altogether (in a version controlled codebase, the commits are a much better source of date of publication than a hardcoded copyright statement). We also now list Godot Engine contributors first as we're collectively the current maintainers of the project, and we clarify that the "exclusive" copyright of the co-founders covers the timespan before opensourcing (their further contributions are included as part of Godot Engine contributors). Also fixed "cf." Frenchism - it's meant as "refer to / see".
272 lines
11 KiB
C++
272 lines
11 KiB
C++
/**************************************************************************/
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/* transform_3d.h */
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/**************************************************************************/
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/* This file is part of: */
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/* GODOT ENGINE */
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/* https://godotengine.org */
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/**************************************************************************/
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/* Copyright (c) 2014-present Godot Engine contributors (see AUTHORS.md). */
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/* Copyright (c) 2007-2014 Juan Linietsky, Ariel Manzur. */
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/* */
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/* Permission is hereby granted, free of charge, to any person obtaining */
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/* a copy of this software and associated documentation files (the */
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/* "Software"), to deal in the Software without restriction, including */
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/* without limitation the rights to use, copy, modify, merge, publish, */
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/* distribute, sublicense, and/or sell copies of the Software, and to */
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/* permit persons to whom the Software is furnished to do so, subject to */
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/* the following conditions: */
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/* */
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/* The above copyright notice and this permission notice shall be */
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/* included in all copies or substantial portions of the Software. */
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/* */
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/* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, */
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/* EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF */
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/* MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. */
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/* IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY */
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/* CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, */
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/* TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE */
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/* SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. */
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/**************************************************************************/
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#ifndef TRANSFORM_3D_H
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#define TRANSFORM_3D_H
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#include "core/math/aabb.h"
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#include "core/math/basis.h"
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#include "core/math/plane.h"
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#include "core/templates/vector.h"
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struct _NO_DISCARD_ Transform3D {
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Basis basis;
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Vector3 origin;
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void invert();
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Transform3D inverse() const;
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void affine_invert();
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Transform3D affine_inverse() const;
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Transform3D rotated(const Vector3 &p_axis, real_t p_angle) const;
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Transform3D rotated_local(const Vector3 &p_axis, real_t p_angle) const;
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void rotate(const Vector3 &p_axis, real_t p_angle);
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void rotate_basis(const Vector3 &p_axis, real_t p_angle);
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void set_look_at(const Vector3 &p_eye, const Vector3 &p_target, const Vector3 &p_up = Vector3(0, 1, 0));
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Transform3D looking_at(const Vector3 &p_target, const Vector3 &p_up = Vector3(0, 1, 0)) const;
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void scale(const Vector3 &p_scale);
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Transform3D scaled(const Vector3 &p_scale) const;
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Transform3D scaled_local(const Vector3 &p_scale) const;
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void scale_basis(const Vector3 &p_scale);
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void translate_local(real_t p_tx, real_t p_ty, real_t p_tz);
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void translate_local(const Vector3 &p_translation);
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Transform3D translated(const Vector3 &p_translation) const;
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Transform3D translated_local(const Vector3 &p_translation) const;
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const Basis &get_basis() const { return basis; }
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void set_basis(const Basis &p_basis) { basis = p_basis; }
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const Vector3 &get_origin() const { return origin; }
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void set_origin(const Vector3 &p_origin) { origin = p_origin; }
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void orthonormalize();
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Transform3D orthonormalized() const;
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void orthogonalize();
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Transform3D orthogonalized() const;
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bool is_equal_approx(const Transform3D &p_transform) const;
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bool is_finite() const;
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bool operator==(const Transform3D &p_transform) const;
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bool operator!=(const Transform3D &p_transform) const;
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_FORCE_INLINE_ Vector3 xform(const Vector3 &p_vector) const;
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_FORCE_INLINE_ AABB xform(const AABB &p_aabb) const;
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_FORCE_INLINE_ Vector<Vector3> xform(const Vector<Vector3> &p_array) const;
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// NOTE: These are UNSAFE with non-uniform scaling, and will produce incorrect results.
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// They use the transpose.
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// For safe inverse transforms, xform by the affine_inverse.
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_FORCE_INLINE_ Vector3 xform_inv(const Vector3 &p_vector) const;
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_FORCE_INLINE_ AABB xform_inv(const AABB &p_aabb) const;
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_FORCE_INLINE_ Vector<Vector3> xform_inv(const Vector<Vector3> &p_array) const;
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// Safe with non-uniform scaling (uses affine_inverse).
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_FORCE_INLINE_ Plane xform(const Plane &p_plane) const;
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_FORCE_INLINE_ Plane xform_inv(const Plane &p_plane) const;
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// These fast versions use precomputed affine inverse, and should be used in bottleneck areas where
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// multiple planes are to be transformed.
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_FORCE_INLINE_ Plane xform_fast(const Plane &p_plane, const Basis &p_basis_inverse_transpose) const;
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static _FORCE_INLINE_ Plane xform_inv_fast(const Plane &p_plane, const Transform3D &p_inverse, const Basis &p_basis_transpose);
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void operator*=(const Transform3D &p_transform);
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Transform3D operator*(const Transform3D &p_transform) const;
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void operator*=(const real_t p_val);
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Transform3D operator*(const real_t p_val) const;
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Transform3D interpolate_with(const Transform3D &p_transform, real_t p_c) const;
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_FORCE_INLINE_ Transform3D inverse_xform(const Transform3D &t) const {
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Vector3 v = t.origin - origin;
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return Transform3D(basis.transpose_xform(t.basis),
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basis.xform(v));
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}
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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) {
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basis.set(xx, xy, xz, yx, yy, yz, zx, zy, zz);
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origin.x = tx;
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origin.y = ty;
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origin.z = tz;
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}
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operator String() const;
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Transform3D() {}
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Transform3D(const Basis &p_basis, const Vector3 &p_origin = Vector3());
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Transform3D(const Vector3 &p_x, const Vector3 &p_y, const Vector3 &p_z, const Vector3 &p_origin);
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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);
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};
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_FORCE_INLINE_ Vector3 Transform3D::xform(const Vector3 &p_vector) const {
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return Vector3(
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basis[0].dot(p_vector) + origin.x,
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basis[1].dot(p_vector) + origin.y,
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basis[2].dot(p_vector) + origin.z);
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}
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_FORCE_INLINE_ Vector3 Transform3D::xform_inv(const Vector3 &p_vector) const {
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Vector3 v = p_vector - origin;
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return Vector3(
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(basis.rows[0][0] * v.x) + (basis.rows[1][0] * v.y) + (basis.rows[2][0] * v.z),
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(basis.rows[0][1] * v.x) + (basis.rows[1][1] * v.y) + (basis.rows[2][1] * v.z),
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(basis.rows[0][2] * v.x) + (basis.rows[1][2] * v.y) + (basis.rows[2][2] * v.z));
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}
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// Neither the plane regular xform or xform_inv are particularly efficient,
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// as they do a basis inverse. For xforming a large number
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// of planes it is better to pre-calculate the inverse transpose basis once
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// and reuse it for each plane, by using the 'fast' version of the functions.
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_FORCE_INLINE_ Plane Transform3D::xform(const Plane &p_plane) const {
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Basis b = basis.inverse();
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b.transpose();
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return xform_fast(p_plane, b);
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}
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_FORCE_INLINE_ Plane Transform3D::xform_inv(const Plane &p_plane) const {
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Transform3D inv = affine_inverse();
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Basis basis_transpose = basis.transposed();
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return xform_inv_fast(p_plane, inv, basis_transpose);
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}
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_FORCE_INLINE_ AABB Transform3D::xform(const AABB &p_aabb) const {
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/* https://dev.theomader.com/transform-bounding-boxes/ */
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Vector3 min = p_aabb.position;
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Vector3 max = p_aabb.position + p_aabb.size;
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Vector3 tmin, tmax;
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for (int i = 0; i < 3; i++) {
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tmin[i] = tmax[i] = origin[i];
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for (int j = 0; j < 3; j++) {
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real_t e = basis[i][j] * min[j];
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real_t f = basis[i][j] * max[j];
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if (e < f) {
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tmin[i] += e;
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tmax[i] += f;
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} else {
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tmin[i] += f;
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tmax[i] += e;
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}
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}
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}
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AABB r_aabb;
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r_aabb.position = tmin;
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r_aabb.size = tmax - tmin;
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return r_aabb;
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}
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_FORCE_INLINE_ AABB Transform3D::xform_inv(const AABB &p_aabb) const {
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/* define vertices */
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Vector3 vertices[8] = {
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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),
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Vector3(p_aabb.position.x + p_aabb.size.x, p_aabb.position.y + p_aabb.size.y, p_aabb.position.z),
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Vector3(p_aabb.position.x + p_aabb.size.x, p_aabb.position.y, p_aabb.position.z + p_aabb.size.z),
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Vector3(p_aabb.position.x + p_aabb.size.x, p_aabb.position.y, p_aabb.position.z),
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Vector3(p_aabb.position.x, p_aabb.position.y + p_aabb.size.y, p_aabb.position.z + p_aabb.size.z),
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Vector3(p_aabb.position.x, p_aabb.position.y + p_aabb.size.y, p_aabb.position.z),
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Vector3(p_aabb.position.x, p_aabb.position.y, p_aabb.position.z + p_aabb.size.z),
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Vector3(p_aabb.position.x, p_aabb.position.y, p_aabb.position.z)
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};
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AABB ret;
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ret.position = xform_inv(vertices[0]);
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for (int i = 1; i < 8; i++) {
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ret.expand_to(xform_inv(vertices[i]));
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}
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return ret;
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}
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Vector<Vector3> Transform3D::xform(const Vector<Vector3> &p_array) const {
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Vector<Vector3> array;
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array.resize(p_array.size());
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const Vector3 *r = p_array.ptr();
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Vector3 *w = array.ptrw();
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for (int i = 0; i < p_array.size(); ++i) {
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w[i] = xform(r[i]);
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}
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return array;
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}
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Vector<Vector3> Transform3D::xform_inv(const Vector<Vector3> &p_array) const {
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Vector<Vector3> array;
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array.resize(p_array.size());
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const Vector3 *r = p_array.ptr();
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Vector3 *w = array.ptrw();
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for (int i = 0; i < p_array.size(); ++i) {
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w[i] = xform_inv(r[i]);
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}
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return array;
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}
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_FORCE_INLINE_ Plane Transform3D::xform_fast(const Plane &p_plane, const Basis &p_basis_inverse_transpose) const {
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// Transform a single point on the plane.
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Vector3 point = p_plane.normal * p_plane.d;
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point = xform(point);
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// Use inverse transpose for correct normals with non-uniform scaling.
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Vector3 normal = p_basis_inverse_transpose.xform(p_plane.normal);
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normal.normalize();
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real_t d = normal.dot(point);
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return Plane(normal, d);
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}
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_FORCE_INLINE_ Plane Transform3D::xform_inv_fast(const Plane &p_plane, const Transform3D &p_inverse, const Basis &p_basis_transpose) {
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// Transform a single point on the plane.
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Vector3 point = p_plane.normal * p_plane.d;
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point = p_inverse.xform(point);
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// Note that instead of precalculating the transpose, an alternative
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// would be to use the transpose for the basis transform.
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// However that would be less SIMD friendly (requiring a swizzle).
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// So the cost is one extra precalced value in the calling code.
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// This is probably worth it, as this could be used in bottleneck areas. And
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// where it is not a bottleneck, the non-fast method is fine.
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// Use transpose for correct normals with non-uniform scaling.
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Vector3 normal = p_basis_transpose.xform(p_plane.normal);
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normal.normalize();
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real_t d = normal.dot(point);
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return Plane(normal, d);
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}
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#endif // TRANSFORM_3D_H
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