BLI_math_matrix.h

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/* SPDX-FileCopyrightText: 2001-2002 NaN Holding BV. All rights reserved.
 *
 * SPDX-License-Identifier: GPL-2.0-or-later */
 
#pragma once
 
#include "BLI_compiler_attrs.h"
#include "BLI_sys_types.h"
 
#ifdef __cplusplus
extern "C" {
#endif
 
/* -------------------------------------------------------------------- */
void zero_m2(float m[2][2]);
void zero_m3(float m[3][3]);
void zero_m4(float m[4][4]);
 
void unit_m2(float m[2][2]);
void unit_m3(float m[3][3]);
void unit_m4(float m[4][4]);
void unit_m4_db(double m[4][4]);
 
void copy_m2_m2(float m1[2][2], const float m2[2][2]);
void copy_m3_m3(float m1[3][3], const float m2[3][3]);
void copy_m4_m4(float m1[4][4], const float m2[4][4]);
void copy_m3_m4(float m1[3][3], const float m2[4][4]);
void copy_m4_m3(float m1[4][4], const float m2[3][3]);
void copy_m3_m2(float m1[3][3], const float m2[2][2]);
void copy_m4_m2(float m1[4][4], const float m2[2][2]);
 
void copy_m4_m4_db(double m1[4][4], const double m2[4][4]);
 
/* double->float */
 
void copy_m3_m3d(float m1[3][3], const double m2[3][3]);
 
/* float->double */
 
void copy_m3d_m3(double m1[3][3], const float m2[3][3]);
void copy_m4d_m4(double m1[4][4], const float m2[4][4]);
 
void swap_m3m3(float m1[3][3], float m2[3][3]);
void swap_m4m4(float m1[4][4], float m2[4][4]);
 
void shuffle_m4(float R[4][4], const int index[4]);
 
/* -------------------------------------------------------------------- */
void add_m3_m3m3(float R[3][3], const float A[3][3], const float B[3][3]);
void add_m4_m4m4(float R[4][4], const float A[4][4], const float B[4][4]);
 
void madd_m3_m3m3fl(float R[3][3], const float A[3][3], const float B[3][3], float f);
void madd_m4_m4m4fl(float R[4][4], const float A[4][4], const float B[4][4], float f);
 
void sub_m3_m3m3(float R[3][3], const float A[3][3], const float B[3][3]);
void sub_m4_m4m4(float R[4][4], const float A[4][4], const float B[4][4]);
 
void mul_m3_m3m3(float R[3][3], const float A[3][3], const float B[3][3]);
void mul_m4_m3m4(float R[4][4], const float A[3][3], const float B[4][4]);
void mul_m4_m4m3(float R[4][4], const float A[4][4], const float B[3][3]);
void mul_m4_m4m4(float R[4][4], const float A[4][4], const float B[4][4]);
void mul_m3_m3m4(float R[3][3], const float A[3][3], const float B[4][4]);
void mul_m3_m4m3(float R[3][3], const float A[4][4], const float B[3][3]);
void mul_m3_m4m4(float R[3][3], const float A[4][4], const float B[4][4]);
 
void mul_m3_m3_pre(float R[3][3], const float A[3][3]);
void mul_m3_m3_post(float R[3][3], const float B[3][3]);
void mul_m4db_m4db_m4fl(double R[4][4], const double A[4][4], const float B[4][4]);
void mul_m4_m4_pre(float R[4][4], const float A[4][4]);
void mul_m4_m4_post(float R[4][4], const float B[4][4]);
 
/* Implement #mul_m3_series macro. */
 
void _va_mul_m3_series_3(float r[3][3], const float m1[3][3], const float m2[3][3]) ATTR_NONNULL();
void _va_mul_m3_series_4(float r[3][3],
                         const float m1[3][3],
                         const float m2[3][3],
                         const float m3[3][3]) ATTR_NONNULL();
void _va_mul_m3_series_5(float r[3][3],
                         const float m1[3][3],
                         const float m2[3][3],
                         const float m3[3][3],
                         const float m4[3][3]) ATTR_NONNULL();
void _va_mul_m3_series_6(float r[3][3],
                         const float m1[3][3],
                         const float m2[3][3],
                         const float m3[3][3],
                         const float m4[3][3],
                         const float m5[3][3]) ATTR_NONNULL();
void _va_mul_m3_series_7(float r[3][3],
                         const float m1[3][3],
                         const float m2[3][3],
                         const float m3[3][3],
                         const float m4[3][3],
                         const float m5[3][3],
                         const float m6[3][3]) ATTR_NONNULL();
void _va_mul_m3_series_8(float r[3][3],
                         const float m1[3][3],
                         const float m2[3][3],
                         const float m3[3][3],
                         const float m4[3][3],
                         const float m5[3][3],
                         const float m6[3][3],
                         const float m7[3][3]) ATTR_NONNULL();
void _va_mul_m3_series_9(float r[3][3],
                         const float m1[3][3],
                         const float m2[3][3],
                         const float m3[3][3],
                         const float m4[3][3],
                         const float m5[3][3],
                         const float m6[3][3],
                         const float m7[3][3],
                         const float m8[3][3]) ATTR_NONNULL();
 
/* Implement #mul_m4_series macro. */
 
void _va_mul_m4_series_3(float r[4][4], const float m1[4][4], const float m2[4][4]) ATTR_NONNULL();
void _va_mul_m4_series_4(float r[4][4],
                         const float m1[4][4],
                         const float m2[4][4],
                         const float m3[4][4]) ATTR_NONNULL();
void _va_mul_m4_series_5(float r[4][4],
                         const float m1[4][4],
                         const float m2[4][4],
                         const float m3[4][4],
                         const float m4[4][4]) ATTR_NONNULL();
void _va_mul_m4_series_6(float r[4][4],
                         const float m1[4][4],
                         const float m2[4][4],
                         const float m3[4][4],
                         const float m4[4][4],
                         const float m5[4][4]) ATTR_NONNULL();
void _va_mul_m4_series_7(float r[4][4],
                         const float m1[4][4],
                         const float m2[4][4],
                         const float m3[4][4],
                         const float m4[4][4],
                         const float m5[4][4],
                         const float m6[4][4]) ATTR_NONNULL();
void _va_mul_m4_series_8(float r[4][4],
                         const float m1[4][4],
                         const float m2[4][4],
                         const float m3[4][4],
                         const float m4[4][4],
                         const float m5[4][4],
                         const float m6[4][4],
                         const float m7[4][4]) ATTR_NONNULL();
void _va_mul_m4_series_9(float r[4][4],
                         const float m1[4][4],
                         const float m2[4][4],
                         const float m3[4][4],
                         const float m4[4][4],
                         const float m5[4][4],
                         const float m6[4][4],
                         const float m7[4][4],
                         const float m8[4][4]) ATTR_NONNULL();
 
#define mul_m3_series(...) VA_NARGS_CALL_OVERLOAD(_va_mul_m3_series_, __VA_ARGS__)
#define mul_m4_series(...) VA_NARGS_CALL_OVERLOAD(_va_mul_m4_series_, __VA_ARGS__)
 
void mul_m4_v3(const float M[4][4], float r[3]);
void mul_v3_m4v3(float r[3], const float mat[4][4], const float vec[3]);
void mul_v3_m4v3_db(double r[3], const double mat[4][4], const double vec[3]);
void mul_v4_m4v3_db(double r[4], const double mat[4][4], const double vec[3]);
void mul_v2_m4v3(float r[2], const float mat[4][4], const float vec[3]);
void mul_v2_m2v2(float r[2], const float mat[2][2], const float vec[2]);
void mul_m2_v2(const float mat[2][2], float vec[2]);
void mul_mat3_m4_v3(const float mat[4][4], float r[3]);
void mul_v3_mat3_m4v3(float r[3], const float mat[4][4], const float vec[3]);
void mul_v3_mat3_m4v3_db(double r[3], const double mat[4][4], const double vec[3]);
void mul_m4_v4(const float mat[4][4], float r[4]);
void mul_v4_m4v4(float r[4], const float mat[4][4], const float v[4]);
void mul_v4_m4v3(float r[4], const float M[4][4], const float v[3]); /* v has implicit w = 1.0f */
void mul_project_m4_v3(const float mat[4][4], float vec[3]);
void mul_v3_project_m4_v3(float r[3], const float mat[4][4], const float vec[3]);
void mul_v2_project_m4_v3(float r[2], const float mat[4][4], const float vec[3]);
 
void mul_m3_v2(const float m[3][3], float r[2]);
void mul_v2_m3v2(float r[2], const float m[3][3], const float v[2]);
void mul_m3_v3(const float M[3][3], float r[3]);
void mul_v3_m3v3(float r[3], const float M[3][3], const float a[3]);
void mul_v2_m3v3(float r[2], const float M[3][3], const float a[3]);
void mul_transposed_m3_v3(const float M[3][3], float r[3]);
void mul_transposed_mat3_m4_v3(const float M[4][4], float r[3]);
void mul_m3_v3_double(const float M[3][3], double r[3]);
 
void mul_m4_m4m4_aligned_scale(float R[4][4], const float A[4][4], const float B[4][4]);
void mul_m4_m4m4_split_channels(float R[4][4], const float A[4][4], const float B[4][4]);
 
void mul_m3_fl(float R[3][3], float f);
void mul_m4_fl(float R[4][4], float f);
void mul_mat3_m4_fl(float R[4][4], float f);
 
void negate_m3(float R[3][3]);
void negate_mat3_m4(float R[4][4]);
void negate_m4(float R[4][4]);
 
bool invert_m3_ex(float mat[3][3], float epsilon);
bool invert_m3_m3_ex(float inverse[3][3], const float mat[3][3], float epsilon);
 
bool invert_m3(float mat[3][3]);
bool invert_m2_m2(float inverse[2][2], const float mat[2][2]);
bool invert_m3_m3(float inverse[3][3], const float mat[3][3]);
bool invert_m4(float mat[4][4]);
bool invert_m4_m4(float inverse[4][4], const float mat[4][4]);
bool invert_m4_m4_fallback(float inverse[4][4], const float mat[4][4]);
 
/* Double arithmetic (mixed float/double). */
 
void mul_m4_v4d(const float mat[4][4], double r[4]);
void mul_v4d_m4v4d(double r[4], const float mat[4][4], const double v[4]);
 
/* Double matrix functions (no mixing types). */
 
void mul_v3_m3v3_db(double r[3], const double M[3][3], const double a[3]);
void mul_m3_v3_db(const double M[3][3], double r[3]);
 
/* -------------------------------------------------------------------- */
void transpose_m3(float R[3][3]);
void transpose_m3_m3(float R[3][3], const float M[3][3]);
void transpose_m3_m4(float R[3][3], const float M[4][4]);
void transpose_m4(float R[4][4]);
void transpose_m4_m4(float R[4][4], const float M[4][4]);
 
bool compare_m4m4(const float mat1[4][4], const float mat2[4][4], float limit);
 
void normalize_m2_ex(float R[2][2], float r_scale[2]) ATTR_NONNULL();
void normalize_m2(float R[2][2]) ATTR_NONNULL();
void normalize_m2_m2_ex(float R[2][2], const float M[2][2], float r_scale[2]) ATTR_NONNULL();
void normalize_m2_m2(float R[2][2], const float M[2][2]) ATTR_NONNULL();
void normalize_m3_ex(float R[3][3], float r_scale[3]) ATTR_NONNULL();
void normalize_m3(float R[3][3]) ATTR_NONNULL();
void normalize_m3_m3_ex(float R[3][3], const float M[3][3], float r_scale[3]) ATTR_NONNULL();
void normalize_m3_m3(float R[3][3], const float M[3][3]) ATTR_NONNULL();
void normalize_m4_ex(float R[4][4], float r_scale[3]) ATTR_NONNULL();
void normalize_m4(float R[4][4]) ATTR_NONNULL();
void normalize_m4_m4_ex(float rmat[4][4], const float mat[4][4], float r_scale[3]) ATTR_NONNULL();
void normalize_m4_m4(float rmat[4][4], const float mat[4][4]) ATTR_NONNULL();
 
void orthogonalize_m3(float R[3][3], int axis);
void orthogonalize_m4(float R[4][4], int axis);
 
void orthogonalize_m3_stable(float R[3][3], int axis, bool normalize);
void orthogonalize_m4_stable(float R[4][4], int axis, bool normalize);
 
bool orthogonalize_m3_zero_axes(float m[3][3], float unit_length);
bool orthogonalize_m4_zero_axes(float m[4][4], float unit_length);
 
bool is_orthogonal_m3(const float m[3][3]);
bool is_orthogonal_m4(const float m[4][4]);
bool is_orthonormal_m3(const float m[3][3]);
bool is_orthonormal_m4(const float m[4][4]);
 
bool is_uniform_scaled_m3(const float m[3][3]);
bool is_uniform_scaled_m4(const float m[4][4]);
 
/* NOTE: 'adjoint' here means the adjugate (adjunct, "classical adjoint") matrix!
 * Nowadays 'adjoint' usually refers to the conjugate transpose,
 * which for real-valued matrices is simply the transpose. */
 
void adjoint_m2_m2(float R[2][2], const float M[2][2]);
void adjoint_m3_m3(float R[3][3], const float M[3][3]);
void adjoint_m4_m4(float R[4][4], const float M[4][4]);
 
float determinant_m2(float a, float b, float c, float d);
float determinant_m3(
    float a1, float a2, float a3, float b1, float b2, float b3, float c1, float c2, float c3);
float determinant_m3_array(const float m[3][3]);
float determinant_m4_mat3_array(const float m[4][4]);
double determinant_m3_array_db(const double m[3][3]);
float determinant_m4(const float m[4][4]);
 
#define PSEUDOINVERSE_EPSILON 1e-8f
 
void svd_m4(float U[4][4], float s[4], float V[4][4], float A_[4][4]);
void pseudoinverse_m4_m4(float inverse[4][4], const float mat[4][4], float epsilon);
void pseudoinverse_m3_m3(float inverse[3][3], const float mat[3][3], float epsilon);
 
bool has_zero_axis_m4(const float matrix[4][4]);
void zero_axis_bias_m4(float mat[4][4]);
 
void invert_m4_m4_safe(float inverse[4][4], const float mat[4][4]);
 
void invert_m3_m3_safe_ortho(float inverse[3][3], const float mat[3][3]);
void invert_m4_m4_safe_ortho(float inverse[4][4], const float mat[4][4]);
 
/* -------------------------------------------------------------------- */
void scale_m3_fl(float R[3][3], float scale);
void scale_m4_fl(float R[4][4], float scale);
void scale_m4_v2(float R[4][4], const float scale[2]);
 
float mat3_to_volume_scale(const float mat[3][3]);
float mat4_to_volume_scale(const float mat[4][4]);
 
float mat3_to_scale(const float mat[3][3]);
float mat4_to_scale(const float mat[4][4]);
float mat4_to_xy_scale(const float mat[4][4]);
 
void size_to_mat3(float R[3][3], const float size[3]);
void size_to_mat4(float R[4][4], const float size[3]);
 
void mat3_to_size_2d(float size[2], const float M[3][3]);
void mat3_to_size(float size[3], const float M[3][3]);
void mat4_to_size(float size[3], const float M[4][4]);
 
float mat3_to_size_max_axis(const float M[3][3]);
float mat4_to_size_max_axis(const float M[4][4]);
 
void mat4_to_size_fix_shear(float size[3], const float M[4][4]);
 
void translate_m4(float mat[4][4], float Tx, float Ty, float Tz);
void rotate_m4(float mat[4][4], char axis, float angle);
void rescale_m4(float mat[4][4], const float scale[3]);
void transform_pivot_set_m4(float mat[4][4], const float pivot[3]);
 
void mat4_to_rot(float rot[3][3], const float wmat[4][4]);
 
void mat3_to_rot_size(float rot[3][3], float size[3], const float mat3[3][3]);
void mat4_to_loc_rot_size(float loc[3], float rot[3][3], float size[3], const float wmat[4][4]);
void mat4_to_loc_quat(float loc[3], float quat[4], const float wmat[4][4]);
void mat4_decompose(float loc[3], float quat[4], float size[3], const float wmat[4][4]);
 
void mat3_polar_decompose(const float mat3[3][3], float r_U[3][3], float r_P[3][3]);
 
void loc_rot_size_to_mat4(float R[4][4],
                          const float loc[3],
                          const float rot[3][3],
                          const float size[3]);
void loc_eul_size_to_mat4(float R[4][4],
                          const float loc[3],
                          const float eul[3],
                          const float size[3]);
void loc_eulO_size_to_mat4(
    float R[4][4], const float loc[3], const float eul[3], const float size[3], short order);
void loc_quat_size_to_mat4(float R[4][4],
                           const float loc[3],
                           const float quat[4],
                           const float size[3]);
void loc_axisangle_size_to_mat4(
    float R[4][4], const float loc[3], const float axis[3], float angle, const float size[3]);
 
void blend_m3_m3m3(float out[3][3], const float dst[3][3], const float src[3][3], float srcweight);
void blend_m4_m4m4(float out[4][4], const float dst[4][4], const float src[4][4], float srcweight);
 
void interp_m3_m3m3(float R[3][3], const float A[3][3], const float B[3][3], float t);
void interp_m4_m4m4(float R[4][4], const float A[4][4], const float B[4][4], float t);
 
bool is_negative_m3(const float mat[3][3]);
bool is_negative_m4(const float mat[4][4]);
 
bool is_zero_m3(const float mat[3][3]);
bool is_zero_m4(const float mat[4][4]);
 
bool equals_m3m3(const float mat1[3][3], const float mat2[3][3]);
bool equals_m4m4(const float mat1[4][4], const float mat2[4][4]);
 
typedef struct SpaceTransform {
  float local2target[4][4];
  float target2local[4][4];
 
} SpaceTransform;
 
void BLI_space_transform_from_matrices(struct SpaceTransform *data,
                                       const float local[4][4],
                                       const float target[4][4]);
void BLI_space_transform_global_from_matrices(struct SpaceTransform *data,
                                              const float local[4][4],
                                              const float target[4][4]);
void BLI_space_transform_apply(const struct SpaceTransform *data, float co[3]);
void BLI_space_transform_invert(const struct SpaceTransform *data, float co[3]);
void BLI_space_transform_apply_normal(const struct SpaceTransform *data, float no[3]);
void BLI_space_transform_invert_normal(const struct SpaceTransform *data, float no[3]);
 
#define BLI_SPACE_TRANSFORM_SETUP(data, local, target) \
  BLI_space_transform_from_matrices( \
      (data), (local)->object_to_world().ptr(), (target)->object_to_world().ptr())
 
/* -------------------------------------------------------------------- */
void print_m3(const char *str, const float m[3][3]);
void print_m4(const char *str, const float m[4][4]);
 
#define print_m3_id(M) print_m3(STRINGIFY(M), M)
#define print_m4_id(M) print_m4(STRINGIFY(M), M)
 
#ifdef __cplusplus
}
#endif