271 lines
11 KiB
C++
271 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) 2007-2022 Juan Linietsky, Ariel Manzur. */
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/* Copyright (c) 2014-2022 Godot Engine contributors (cf. AUTHORS.md). */
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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 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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