/*************************************************************************/ /* basis.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 BASIS_H #define BASIS_H #include "core/math/quat.h" #include "core/math/vector3.h" class _NO_DISCARD_CLASS_ Basis { public: Vector3 elements[3] = { Vector3(1, 0, 0), Vector3(0, 1, 0), Vector3(0, 0, 1) }; _FORCE_INLINE_ const Vector3 &operator[](int axis) const { return elements[axis]; } _FORCE_INLINE_ Vector3 &operator[](int axis) { return elements[axis]; } void invert(); void transpose(); Basis inverse() const; Basis transposed() const; _FORCE_INLINE_ real_t determinant() const; void from_z(const Vector3 &p_z); _FORCE_INLINE_ Vector3 get_axis(int p_axis) const { // get actual basis axis (elements is transposed for performance) return Vector3(elements[0][p_axis], elements[1][p_axis], elements[2][p_axis]); } _FORCE_INLINE_ void set_axis(int p_axis, const Vector3 &p_value) { // get actual basis axis (elements is transposed for performance) elements[0][p_axis] = p_value.x; elements[1][p_axis] = p_value.y; elements[2][p_axis] = p_value.z; } void rotate(const Vector3 &p_axis, real_t p_phi); Basis rotated(const Vector3 &p_axis, real_t p_phi) const; void rotate_local(const Vector3 &p_axis, real_t p_phi); Basis rotated_local(const Vector3 &p_axis, real_t p_phi) const; void rotate(const Vector3 &p_euler); Basis rotated(const Vector3 &p_euler) const; void rotate(const Quat &p_quat); Basis rotated(const Quat &p_quat) const; Vector3 get_rotation_euler() const; void get_rotation_axis_angle(Vector3 &p_axis, real_t &p_angle) const; void get_rotation_axis_angle_local(Vector3 &p_axis, real_t &p_angle) const; Quat get_rotation_quat() const; Vector3 get_rotation() const { return get_rotation_euler(); }; Vector3 rotref_posscale_decomposition(Basis &rotref) const; Vector3 get_euler_xyz() const; void set_euler_xyz(const Vector3 &p_euler); Vector3 get_euler_xzy() const; void set_euler_xzy(const Vector3 &p_euler); Vector3 get_euler_yzx() const; void set_euler_yzx(const Vector3 &p_euler); Vector3 get_euler_yxz() const; void set_euler_yxz(const Vector3 &p_euler); Vector3 get_euler_zxy() const; void set_euler_zxy(const Vector3 &p_euler); Vector3 get_euler_zyx() const; void set_euler_zyx(const Vector3 &p_euler); Quat get_quat() const; void set_quat(const Quat &p_quat); Vector3 get_euler() const { return get_euler_yxz(); } void set_euler(const Vector3 &p_euler) { set_euler_yxz(p_euler); } void get_axis_angle(Vector3 &r_axis, real_t &r_angle) const; void set_axis_angle(const Vector3 &p_axis, real_t p_phi); void scale(const Vector3 &p_scale); Basis scaled(const Vector3 &p_scale) const; void scale_local(const Vector3 &p_scale); Basis scaled_local(const Vector3 &p_scale) const; Vector3 get_scale() const; Vector3 get_scale_abs() const; Vector3 get_scale_local() const; void set_axis_angle_scale(const Vector3 &p_axis, real_t p_phi, const Vector3 &p_scale); void set_euler_scale(const Vector3 &p_euler, const Vector3 &p_scale); void set_quat_scale(const Quat &p_quat, const Vector3 &p_scale); // transposed dot products _FORCE_INLINE_ real_t tdotx(const Vector3 &v) const { return elements[0][0] * v[0] + elements[1][0] * v[1] + elements[2][0] * v[2]; } _FORCE_INLINE_ real_t tdoty(const Vector3 &v) const { return elements[0][1] * v[0] + elements[1][1] * v[1] + elements[2][1] * v[2]; } _FORCE_INLINE_ real_t tdotz(const Vector3 &v) const { return elements[0][2] * v[0] + elements[1][2] * v[1] + elements[2][2] * v[2]; } bool is_equal_approx(const Basis &p_basis) const; // For complicated reasons, the second argument is always discarded. See #45062. bool is_equal_approx(const Basis &a, const Basis &b) const { return is_equal_approx(a); } bool is_equal_approx_ratio(const Basis &a, const Basis &b, real_t p_epsilon = UNIT_EPSILON) const; bool operator==(const Basis &p_matrix) const; bool operator!=(const Basis &p_matrix) const; _FORCE_INLINE_ Vector3 xform(const Vector3 &p_vector) const; _FORCE_INLINE_ Vector3 xform_inv(const Vector3 &p_vector) const; _FORCE_INLINE_ void operator*=(const Basis &p_matrix); _FORCE_INLINE_ Basis operator*(const Basis &p_matrix) const; _FORCE_INLINE_ void operator+=(const Basis &p_matrix); _FORCE_INLINE_ Basis operator+(const Basis &p_matrix) const; _FORCE_INLINE_ void operator-=(const Basis &p_matrix); _FORCE_INLINE_ Basis operator-(const Basis &p_matrix) const; _FORCE_INLINE_ void operator*=(real_t p_val); _FORCE_INLINE_ Basis operator*(real_t p_val) const; int get_orthogonal_index() const; void set_orthogonal_index(int p_index); void set_diagonal(const Vector3 &p_diag); bool is_orthogonal() const; bool is_diagonal() const; bool is_rotation() const; Basis slerp(const Basis &p_to, const real_t &p_weight) const; _FORCE_INLINE_ Basis lerp(const Basis &p_to, const real_t &p_weight) const; operator String() const; /* create / set */ _FORCE_INLINE_ 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) { elements[0][0] = xx; elements[0][1] = xy; elements[0][2] = xz; elements[1][0] = yx; elements[1][1] = yy; elements[1][2] = yz; elements[2][0] = zx; elements[2][1] = zy; elements[2][2] = zz; } _FORCE_INLINE_ void set(const Vector3 &p_x, const Vector3 &p_y, const Vector3 &p_z) { set_axis(0, p_x); set_axis(1, p_y); set_axis(2, p_z); } _FORCE_INLINE_ Vector3 get_column(int i) const { return Vector3(elements[0][i], elements[1][i], elements[2][i]); } _FORCE_INLINE_ Vector3 get_row(int i) const { return Vector3(elements[i][0], elements[i][1], elements[i][2]); } _FORCE_INLINE_ Vector3 get_main_diagonal() const { return Vector3(elements[0][0], elements[1][1], elements[2][2]); } _FORCE_INLINE_ void set_row(int i, const Vector3 &p_row) { elements[i][0] = p_row.x; elements[i][1] = p_row.y; elements[i][2] = p_row.z; } _FORCE_INLINE_ void set_zero() { elements[0].zero(); elements[1].zero(); elements[2].zero(); } _FORCE_INLINE_ Basis transpose_xform(const Basis &m) const { return Basis( elements[0].x * m[0].x + elements[1].x * m[1].x + elements[2].x * m[2].x, elements[0].x * m[0].y + elements[1].x * m[1].y + elements[2].x * m[2].y, elements[0].x * m[0].z + elements[1].x * m[1].z + elements[2].x * m[2].z, elements[0].y * m[0].x + elements[1].y * m[1].x + elements[2].y * m[2].x, elements[0].y * m[0].y + elements[1].y * m[1].y + elements[2].y * m[2].y, elements[0].y * m[0].z + elements[1].y * m[1].z + elements[2].y * m[2].z, elements[0].z * m[0].x + elements[1].z * m[1].x + elements[2].z * m[2].x, elements[0].z * m[0].y + elements[1].z * m[1].y + elements[2].z * m[2].y, elements[0].z * m[0].z + elements[1].z * m[1].z + elements[2].z * m[2].z); } Basis(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) { set(xx, xy, xz, yx, yy, yz, zx, zy, zz); } void orthonormalize(); Basis orthonormalized() const; bool is_symmetric() const; Basis diagonalize(); // The following normal xform functions are correct for non-uniform scales. // Use these two functions in combination to xform a series of normals. // First use get_normal_xform_basis() to precalculate the inverse transpose. // Then apply xform_normal_fast() multiple times using the inverse transpose basis. Basis get_normal_xform_basis() const { return inverse().transposed(); } // N.B. This only does a normal transform if the basis used is the inverse transpose! // Otherwise use xform_normal(). Vector3 xform_normal_fast(const Vector3 &p_vector) const { return xform(p_vector).normalized(); } // This function does the above but for a single normal vector. It is considerably slower, so should usually // only be used in cases of single normals, or when the basis changes each time. Vector3 xform_normal(const Vector3 &p_vector) const { return get_normal_xform_basis().xform_normal_fast(p_vector); } operator Quat() const { return get_quat(); } Basis(const Quat &p_quat) { set_quat(p_quat); } Basis(const Quat &p_quat, const Vector3 &p_scale) { set_quat_scale(p_quat, p_scale); } Basis(const Vector3 &p_euler) { set_euler(p_euler); } Basis(const Vector3 &p_euler, const Vector3 &p_scale) { set_euler_scale(p_euler, p_scale); } Basis(const Vector3 &p_axis, real_t p_phi) { set_axis_angle(p_axis, p_phi); } Basis(const Vector3 &p_axis, real_t p_phi, const Vector3 &p_scale) { set_axis_angle_scale(p_axis, p_phi, p_scale); } _FORCE_INLINE_ Basis(const Vector3 &row0, const Vector3 &row1, const Vector3 &row2) { elements[0] = row0; elements[1] = row1; elements[2] = row2; } _FORCE_INLINE_ Basis() {} }; _FORCE_INLINE_ void Basis::operator*=(const Basis &p_matrix) { set( p_matrix.tdotx(elements[0]), p_matrix.tdoty(elements[0]), p_matrix.tdotz(elements[0]), p_matrix.tdotx(elements[1]), p_matrix.tdoty(elements[1]), p_matrix.tdotz(elements[1]), p_matrix.tdotx(elements[2]), p_matrix.tdoty(elements[2]), p_matrix.tdotz(elements[2])); } _FORCE_INLINE_ Basis Basis::operator*(const Basis &p_matrix) const { return Basis( p_matrix.tdotx(elements[0]), p_matrix.tdoty(elements[0]), p_matrix.tdotz(elements[0]), p_matrix.tdotx(elements[1]), p_matrix.tdoty(elements[1]), p_matrix.tdotz(elements[1]), p_matrix.tdotx(elements[2]), p_matrix.tdoty(elements[2]), p_matrix.tdotz(elements[2])); } _FORCE_INLINE_ void Basis::operator+=(const Basis &p_matrix) { elements[0] += p_matrix.elements[0]; elements[1] += p_matrix.elements[1]; elements[2] += p_matrix.elements[2]; } _FORCE_INLINE_ Basis Basis::operator+(const Basis &p_matrix) const { Basis ret(*this); ret += p_matrix; return ret; } _FORCE_INLINE_ void Basis::operator-=(const Basis &p_matrix) { elements[0] -= p_matrix.elements[0]; elements[1] -= p_matrix.elements[1]; elements[2] -= p_matrix.elements[2]; } _FORCE_INLINE_ Basis Basis::operator-(const Basis &p_matrix) const { Basis ret(*this); ret -= p_matrix; return ret; } _FORCE_INLINE_ void Basis::operator*=(real_t p_val) { elements[0] *= p_val; elements[1] *= p_val; elements[2] *= p_val; } _FORCE_INLINE_ Basis Basis::operator*(real_t p_val) const { Basis ret(*this); ret *= p_val; return ret; } Vector3 Basis::xform(const Vector3 &p_vector) const { return Vector3( elements[0].dot(p_vector), elements[1].dot(p_vector), elements[2].dot(p_vector)); } Vector3 Basis::xform_inv(const Vector3 &p_vector) const { return Vector3( (elements[0][0] * p_vector.x) + (elements[1][0] * p_vector.y) + (elements[2][0] * p_vector.z), (elements[0][1] * p_vector.x) + (elements[1][1] * p_vector.y) + (elements[2][1] * p_vector.z), (elements[0][2] * p_vector.x) + (elements[1][2] * p_vector.y) + (elements[2][2] * p_vector.z)); } real_t Basis::determinant() const { return elements[0][0] * (elements[1][1] * elements[2][2] - elements[2][1] * elements[1][2]) - elements[1][0] * (elements[0][1] * elements[2][2] - elements[2][1] * elements[0][2]) + elements[2][0] * (elements[0][1] * elements[1][2] - elements[1][1] * elements[0][2]); } Basis Basis::lerp(const Basis &p_to, const real_t &p_weight) const { Basis b; b.elements[0] = elements[0].linear_interpolate(p_to.elements[0], p_weight); b.elements[1] = elements[1].linear_interpolate(p_to.elements[1], p_weight); b.elements[2] = elements[2].linear_interpolate(p_to.elements[2], p_weight); return b; } #endif // BASIS_H