/*
* This program is free software; you can redistribute it and/or
* modify it under the terms of the GNU General Public License
* as published by the Free Software Foundation; either version 2
* of the License, or (at your option) any later version.
*
* This program is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
* GNU General Public License for more details.
*
* You should have received a copy of the GNU General Public License
* along with this program; if not, write to the Free Software Foundation,
* Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
*
* The Original Code is Copyright (C) 2001-2002 by NaN Holding BV.
* All rights reserved.
*
* The Original Code is: some of this file.
*/
#pragma once
/** \file
* \ingroup bli
*/
#include "BLI_compiler_attrs.h"
#include "BLI_math_inline.h"
#include "BLI_utildefines.h"
#ifdef __cplusplus
extern "C" {
#endif
/* -------------------------------------------------------------------- */
/** \name Init
* \{ */
#ifdef BLI_MATH_GCC_WARN_PRAGMA
# pragma GCC diagnostic push
# pragma GCC diagnostic ignored "-Wredundant-decls"
#endif
MINLINE void zero_v2(float r[2]);
MINLINE void zero_v3(float r[3]);
MINLINE void zero_v4(float r[4]);
MINLINE void copy_v2_v2(float r[2], const float a[2]);
MINLINE void copy_v3_v3(float r[3], const float a[3]);
MINLINE void copy_v4_v4(float r[4], const float a[4]);
MINLINE void copy_v2_fl(float r[2], float f);
MINLINE void copy_v3_fl(float r[3], float f);
MINLINE void copy_v4_fl(float r[4], float f);
MINLINE void swap_v2_v2(float a[2], float b[2]);
MINLINE void swap_v3_v3(float a[3], float b[3]);
MINLINE void swap_v4_v4(float a[4], float b[4]);
/* unsigned char */
MINLINE void copy_v2_v2_uchar(unsigned char r[2], const unsigned char a[2]);
MINLINE void copy_v3_v3_uchar(unsigned char r[3], const unsigned char a[3]);
MINLINE void copy_v4_v4_uchar(unsigned char r[4], const unsigned char a[4]);
MINLINE void copy_v2_uchar(unsigned char r[2], unsigned char a);
MINLINE void copy_v3_uchar(unsigned char r[3], unsigned char a);
MINLINE void copy_v4_uchar(unsigned char r[4], unsigned char a);
/* char */
MINLINE void copy_v2_v2_char(char r[2], const char a[2]);
MINLINE void copy_v3_v3_char(char r[3], const char a[3]);
MINLINE void copy_v4_v4_char(char r[4], const char a[4]);
/* short */
MINLINE void copy_v2_v2_short(short r[2], const short a[2]);
MINLINE void copy_v3_v3_short(short r[3], const short a[3]);
MINLINE void copy_v4_v4_short(short r[4], const short a[4]);
/* int */
MINLINE void zero_v3_int(int r[3]);
MINLINE void copy_v2_v2_int(int r[2], const int a[2]);
MINLINE void copy_v3_v3_int(int r[3], const int a[3]);
MINLINE void copy_v4_v4_int(int r[4], const int a[4]);
/* double */
MINLINE void zero_v3_db(double r[3]);
MINLINE void copy_v2_v2_db(double r[2], const double a[2]);
MINLINE void copy_v3_v3_db(double r[3], const double a[3]);
MINLINE void copy_v4_v4_db(double r[4], const double a[4]);
/* short -> float */
MINLINE void copy_v3fl_v3s(float r[3], const short a[3]);
/* int <-> float */
MINLINE void copy_v2fl_v2i(float r[2], const int a[2]);
/* int <-> float */
MINLINE void round_v2i_v2fl(int r[2], const float a[2]);
/* double -> float */
MINLINE void copy_v2fl_v2db(float r[2], const double a[2]);
MINLINE void copy_v3fl_v3db(float r[3], const double a[3]);
MINLINE void copy_v4fl_v4db(float r[4], const double a[4]);
/* float -> double */
MINLINE void copy_v2db_v2fl(double r[2], const float a[2]);
MINLINE void copy_v3db_v3fl(double r[3], const float a[3]);
MINLINE void copy_v4db_v4fl(double r[4], const float a[4]);
/* float args -> vec */
MINLINE void copy_v2_fl2(float v[2], float x, float y);
MINLINE void copy_v3_fl3(float v[3], float x, float y, float z);
MINLINE void copy_v4_fl4(float v[4], float x, float y, float z, float w);
/** \} */
/* -------------------------------------------------------------------- */
/** \name Arithmetic
* \{ */
MINLINE void add_v2_fl(float r[2], float f);
MINLINE void add_v3_fl(float r[3], float f);
MINLINE void add_v4_fl(float r[4], float f);
MINLINE void add_v2_v2(float r[2], const float a[2]);
MINLINE void add_v2_v2_db(double r[2], const double a[2]);
MINLINE void add_v2_v2v2(float r[2], const float a[2], const float b[2]);
MINLINE void add_v2_v2_int(int r[2], const int a[2]);
MINLINE void add_v2_v2v2_int(int r[2], const int a[2], const int b[2]);
MINLINE void add_v3_v3(float r[3], const float a[3]);
MINLINE void add_v3_v3_db(double r[3], const double a[3]);
MINLINE void add_v3_v3v3(float r[3], const float a[3], const float b[3]);
MINLINE void add_v4_v4(float r[4], const float a[4]);
MINLINE void add_v4_v4v4(float r[4], const float a[4], const float b[4]);
MINLINE void add_v3fl_v3fl_v3i(float r[3], const float a[3], const int b[3]);
MINLINE void sub_v2_v2(float r[2], const float a[2]);
MINLINE void sub_v2_v2v2(float r[2], const float a[2], const float b[2]);
MINLINE void sub_v2_v2v2_db(double r[2], const double a[2], const double b[2]);
MINLINE void sub_v2_v2v2_int(int r[2], const int a[2], const int b[2]);
MINLINE void sub_v3_v3(float r[3], const float a[3]);
MINLINE void sub_v3_v3v3(float r[3], const float a[3], const float b[3]);
MINLINE void sub_v3_v3v3_int(int r[3], const int a[3], const int b[3]);
MINLINE void sub_v3_v3v3_db(double r[3], const double a[3], const double b[3]);
MINLINE void sub_v4_v4(float r[4], const float a[4]);
MINLINE void sub_v4_v4v4(float r[4], const float a[4], const float b[4]);
MINLINE void sub_v2db_v2fl_v2fl(double r[2], const float a[2], const float b[2]);
MINLINE void sub_v3db_v3fl_v3fl(double r[3], const float a[3], const float b[3]);
MINLINE void mul_v2_fl(float r[2], float f);
MINLINE void mul_v2_v2fl(float r[2], const float a[2], float f);
MINLINE void mul_v3_fl(float r[3], float f);
MINLINE void mul_v3db_db(double r[3], double f);
MINLINE void mul_v3_v3fl(float r[3], const float a[3], float f);
MINLINE void mul_v3_v3db_db(double r[3], const double a[3], double f);
MINLINE void mul_v2_v2(float r[2], const float a[2]);
MINLINE void mul_v2_v2v2(float r[2], const float a[2], const float b[2]);
MINLINE void mul_v3_v3(float r[3], const float a[3]);
MINLINE void mul_v3_v3v3(float r[3], const float a[3], const float b[3]);
MINLINE void mul_v4_fl(float r[4], float f);
MINLINE void mul_v4_v4(float r[4], const float a[4]);
MINLINE void mul_v4_v4fl(float r[4], const float a[4], float f);
MINLINE void mul_v2_v2_cw(float r[2], const float mat[2], const float vec[2]);
MINLINE void mul_v2_v2_ccw(float r[2], const float mat[2], const float vec[2]);
/**
* Convenience function to get the projected depth of a position.
* This avoids creating a temporary 4D vector and multiplying it - only for the 4th component.
*
* Matches logic for:
*
* \code{.c}
* float co_4d[4] = {co[0], co[1], co[2], 1.0};
* mul_m4_v4(mat, co_4d);
* return co_4d[3];
* \endcode
*/
MINLINE float mul_project_m4_v3_zfac(const float mat[4][4],
const float co[3]) ATTR_WARN_UNUSED_RESULT;
/**
* Has the effect of #mul_m3_v3(), on a single axis.
*/
MINLINE float dot_m3_v3_row_x(const float M[3][3], const float a[3]) ATTR_WARN_UNUSED_RESULT;
MINLINE float dot_m3_v3_row_y(const float M[3][3], const float a[3]) ATTR_WARN_UNUSED_RESULT;
MINLINE float dot_m3_v3_row_z(const float M[3][3], const float a[3]) ATTR_WARN_UNUSED_RESULT;
/**
* Has the effect of #mul_mat3_m4_v3(), on a single axis.
* (no adding translation)
*/
MINLINE float dot_m4_v3_row_x(const float M[4][4], const float a[3]) ATTR_WARN_UNUSED_RESULT;
MINLINE float dot_m4_v3_row_y(const float M[4][4], const float a[3]) ATTR_WARN_UNUSED_RESULT;
MINLINE float dot_m4_v3_row_z(const float M[4][4], const float a[3]) ATTR_WARN_UNUSED_RESULT;
MINLINE void madd_v2_v2fl(float r[2], const float a[2], float f);
MINLINE void madd_v3_v3fl(float r[3], const float a[3], float f);
MINLINE void madd_v3_v3v3(float r[3], const float a[3], const float b[3]);
MINLINE void madd_v2_v2v2fl(float r[2], const float a[2], const float b[2], float f);
MINLINE void madd_v3_v3v3fl(float r[3], const float a[3], const float b[3], float f);
MINLINE void madd_v3_v3v3db_db(double r[3], const double a[3], const double b[3], double f);
MINLINE void madd_v3_v3v3v3(float r[3], const float a[3], const float b[3], const float c[3]);
MINLINE void madd_v4_v4fl(float r[4], const float a[4], float f);
MINLINE void madd_v4_v4v4(float r[4], const float a[4], const float b[4]);
MINLINE void madd_v3fl_v3fl_v3fl_v3i(float r[3],
const float a[3],
const float b[3],
const int c[3]);
MINLINE void negate_v2(float r[2]);
MINLINE void negate_v2_v2(float r[2], const float a[2]);
MINLINE void negate_v3(float r[3]);
MINLINE void negate_v3_v3(float r[3], const float a[3]);
MINLINE void negate_v4(float r[4]);
MINLINE void negate_v4_v4(float r[4], const float a[4]);
/* could add more... */
MINLINE void negate_v3_short(short r[3]);
MINLINE void negate_v3_db(double r[3]);
MINLINE void invert_v2(float r[2]);
MINLINE void invert_v3(float r[3]);
/**
* Invert the vector, but leaves zero values as zero.
*/
MINLINE void invert_v3_safe(float r[3]);
MINLINE void abs_v2(float r[2]);
MINLINE void abs_v2_v2(float r[2], const float a[2]);
MINLINE void abs_v3(float r[3]);
MINLINE void abs_v3_v3(float r[3], const float a[3]);
MINLINE void abs_v4(float r[4]);
MINLINE void abs_v4_v4(float r[4], const float a[4]);
MINLINE float dot_v2v2(const float a[2], const float b[2]) ATTR_WARN_UNUSED_RESULT;
MINLINE double dot_v2v2_db(const double a[2], const double b[2]) ATTR_WARN_UNUSED_RESULT;
MINLINE float dot_v3v3(const float a[3], const float b[3]) ATTR_WARN_UNUSED_RESULT;
MINLINE float dot_v3v3v3(const float p[3],
const float a[3],
const float b[3]) ATTR_WARN_UNUSED_RESULT;
MINLINE float dot_v4v4(const float a[4], const float b[4]) ATTR_WARN_UNUSED_RESULT;
MINLINE double dot_v3db_v3fl(const double a[3], const float b[3]) ATTR_WARN_UNUSED_RESULT;
MINLINE double dot_v3v3_db(const double a[3], const double b[3]) ATTR_WARN_UNUSED_RESULT;
MINLINE float cross_v2v2(const float a[2], const float b[2]) ATTR_WARN_UNUSED_RESULT;
MINLINE double cross_v2v2_db(const double a[2], const double b[2]) ATTR_WARN_UNUSED_RESULT;
MINLINE void cross_v3_v3v3(float r[3], const float a[3], const float b[3]);
/**
* Cross product suffers from severe precision loss when vectors are
* nearly parallel or opposite; doing the computation in double helps a lot.
*/
MINLINE void cross_v3_v3v3_hi_prec(float r[3], const float a[3], const float b[3]);
MINLINE void cross_v3_v3v3_db(double r[3], const double a[3], const double b[3]);
/**
* Excuse this fairly specific function, its used for polygon normals all over the place
* (could use a better name).
*/
MINLINE void add_newell_cross_v3_v3v3(float n[3], const float v_prev[3], const float v_curr[3]);
MINLINE void star_m3_v3(float rmat[3][3], const float a[3]);
/** \} */
/* -------------------------------------------------------------------- */
/** \name Length
* \{ */
MINLINE float len_squared_v2(const float v[2]) ATTR_WARN_UNUSED_RESULT;
MINLINE float len_squared_v3(const float v[3]) ATTR_WARN_UNUSED_RESULT;
MINLINE float len_manhattan_v2(const float v[2]) ATTR_WARN_UNUSED_RESULT;
MINLINE int len_manhattan_v2_int(const int v[2]) ATTR_WARN_UNUSED_RESULT;
MINLINE float len_manhattan_v3(const float v[3]) ATTR_WARN_UNUSED_RESULT;
MINLINE float len_v2(const float a[2]) ATTR_WARN_UNUSED_RESULT;
MINLINE double len_v2_db(const double v[2]) ATTR_WARN_UNUSED_RESULT;
MINLINE float len_v2v2(const float a[2], const float b[2]) ATTR_WARN_UNUSED_RESULT;
MINLINE double len_v2v2_db(const double a[2], const double b[2]) ATTR_WARN_UNUSED_RESULT;
MINLINE float len_v2v2_int(const int v1[2], const int v2[2]);
MINLINE float len_squared_v2v2(const float a[2], const float b[2]) ATTR_WARN_UNUSED_RESULT;
MINLINE double len_squared_v2v2_db(const double a[2], const double b[2]) ATTR_WARN_UNUSED_RESULT;
MINLINE float len_squared_v3v3(const float a[3], const float b[3]) ATTR_WARN_UNUSED_RESULT;
MINLINE float len_squared_v4v4(const float a[4], const float b[4]) ATTR_WARN_UNUSED_RESULT;
MINLINE float len_manhattan_v2v2(const float a[2], const float b[2]) ATTR_WARN_UNUSED_RESULT;
MINLINE int len_manhattan_v2v2_int(const int a[2], const int b[2]) ATTR_WARN_UNUSED_RESULT;
MINLINE float len_manhattan_v3v3(const float a[3], const float b[3]) ATTR_WARN_UNUSED_RESULT;
MINLINE float len_v3(const float a[3]) ATTR_WARN_UNUSED_RESULT;
MINLINE float len_v3v3(const float a[3], const float b[3]) ATTR_WARN_UNUSED_RESULT;
MINLINE double len_v3_db(const double a[3]) ATTR_WARN_UNUSED_RESULT;
MINLINE double len_squared_v3_db(const double v[3]) ATTR_WARN_UNUSED_RESULT;
MINLINE float normalize_v2_length(float r[2], float unit_scale);
/**
* \note any vectors containing `nan` will be zeroed out.
*/
MINLINE float normalize_v2_v2_length(float r[2], const float a[2], float unit_scale);
MINLINE float normalize_v3_length(float r[3], float unit_scale);
/**
* \note any vectors containing `nan` will be zeroed out.
*/
MINLINE float normalize_v3_v3_length(float r[3], const float a[3], float unit_scale);
MINLINE double normalize_v3_length_db(double n[3], double unit_scale);
MINLINE double normalize_v3_v3_length_db(double r[3], const double a[3], double unit_scale);
MINLINE float normalize_v2(float r[2]);
MINLINE float normalize_v2_v2(float r[2], const float a[2]);
MINLINE float normalize_v3(float r[3]);
MINLINE float normalize_v3_v3(float r[3], const float a[3]);
MINLINE double normalize_v3_v3_db(double r[3], const double a[3]);
MINLINE double normalize_v3_db(double n[3]);
/** \} */
/* -------------------------------------------------------------------- */
/** \name Interpolation
* \{ */
void interp_v2_v2v2(float r[2], const float a[2], const float b[2], float t);
void interp_v2_v2v2_db(double target[2], const double a[2], const double b[2], double t);
/**
* Weight 3 2D vectors,
* 'w' must be unit length but is not a vector, just 3 weights.
*/
void interp_v2_v2v2v2(
float r[2], const float a[2], const float b[2], const float c[2], const float t[3]);
void interp_v3_v3v3(float r[3], const float a[3], const float b[3], float t);
void interp_v3_v3v3_db(double target[3], const double a[3], const double b[3], double t);
/**
* Weight 3 vectors,
* 'w' must be unit length but is not a vector, just 3 weights.
*/
void interp_v3_v3v3v3(
float p[3], const float v1[3], const float v2[3], const float v3[3], const float w[3]);
/**
* Weight 3 vectors,
* 'w' must be unit length but is not a vector, just 4 weights.
*/
void interp_v3_v3v3v3v3(float p[3],
const float v1[3],
const float v2[3],
const float v3[3],
const float v4[3],
const float w[4]);
void interp_v4_v4v4(float r[4], const float a[4], const float b[4], float t);
void interp_v4_v4v4v4(
float p[4], const float v1[4], const float v2[4], const float v3[4], const float w[3]);
void interp_v4_v4v4v4v4(float p[4],
const float v1[4],
const float v2[4],
const float v3[4],
const float v4[4],
const float w[4]);
void interp_v3_v3v3v3_uv(
float p[3], const float v1[3], const float v2[3], const float v3[3], const float uv[2]);
/**
* slerp, treat vectors as spherical coordinates
* \see #interp_qt_qtqt
*
* \return success
*/
bool interp_v3_v3v3_slerp(float target[3], const float a[3], const float b[3], float t)
ATTR_WARN_UNUSED_RESULT;
bool interp_v2_v2v2_slerp(float target[2], const float a[2], const float b[2], float t)
ATTR_WARN_UNUSED_RESULT;
/**
* Same as #interp_v3_v3v3_slerp but uses fallback values for opposite vectors.
*/
void interp_v3_v3v3_slerp_safe(float target[3], const float a[3], const float b[3], float t);
void interp_v2_v2v2_slerp_safe(float target[2], const float a[2], const float b[2], float t);
void interp_v2_v2v2v2v2_cubic(float p[2],
const float v1[2],
const float v2[2],
const float v3[2],
const float v4[2],
float u);
void interp_v3_v3v3_char(char target[3], const char a[3], const char b[3], float t);
void interp_v3_v3v3_uchar(unsigned char target[3],
const unsigned char a[3],
const unsigned char b[3],
float t);
void interp_v4_v4v4_char(char target[4], const char a[4], const char b[4], float t);
void interp_v4_v4v4_uchar(unsigned char target[4],
const unsigned char a[4],
const unsigned char b[4],
float t);
void mid_v3_v3v3(float r[3], const float a[3], const float b[3]);
void mid_v2_v2v2(float r[2], const float a[2], const float b[2]);
void mid_v3_v3v3v3(float v[3], const float v1[3], const float v2[3], const float v3[3]);
void mid_v2_v2v2v2(float v[2], const float v1[2], const float v2[2], const float v3[2]);
void mid_v3_v3v3v3v3(
float v[3], const float v1[3], const float v2[3], const float v3[3], const float v4[3]);
void mid_v3_v3_array(float r[3], const float (*vec_arr)[3], unsigned int nbr);
/**
* Specialized function for calculating normals.
* Fast-path for:
*
* \code{.c}
* add_v3_v3v3(r, a, b);
* normalize_v3(r)
* mul_v3_fl(r, angle_normalized_v3v3(a, b) / M_PI_2);
* \endcode
*
* We can use the length of (a + b) to calculate the angle.
*/
void mid_v3_v3v3_angle_weighted(float r[3], const float a[3], const float b[3]);
/**
* Same as mid_v3_v3v3_angle_weighted
* but \a r is assumed to be accumulated normals, divided by their total.
*/
void mid_v3_angle_weighted(float r[3]);
void flip_v4_v4v4(float v[4], const float v1[4], const float v2[4]);
void flip_v3_v3v3(float v[3], const float v1[3], const float v2[3]);
void flip_v2_v2v2(float v[2], const float v1[2], const float v2[2]);
/** \} */
/* -------------------------------------------------------------------- */
/** \name Comparison
* \{ */
MINLINE bool is_zero_v2(const float a[2]) ATTR_WARN_UNUSED_RESULT;
MINLINE bool is_zero_v3(const float a[3]) ATTR_WARN_UNUSED_RESULT;
MINLINE bool is_zero_v4(const float a[4]) ATTR_WARN_UNUSED_RESULT;
MINLINE bool is_zero_v2_db(const double a[2]) ATTR_WARN_UNUSED_RESULT;
MINLINE bool is_zero_v3_db(const double a[3]) ATTR_WARN_UNUSED_RESULT;
MINLINE bool is_zero_v4_db(const double a[4]) ATTR_WARN_UNUSED_RESULT;
bool is_finite_v2(const float a[2]) ATTR_WARN_UNUSED_RESULT;
bool is_finite_v3(const float a[3]) ATTR_WARN_UNUSED_RESULT;
bool is_finite_v4(const float a[4]) ATTR_WARN_UNUSED_RESULT;
MINLINE bool is_one_v3(const float a[3]) ATTR_WARN_UNUSED_RESULT;
MINLINE bool equals_v2v2(const float v1[2], const float v2[2]) ATTR_WARN_UNUSED_RESULT;
MINLINE bool equals_v3v3(const float a[3], const float b[3]) ATTR_WARN_UNUSED_RESULT;
MINLINE bool equals_v4v4(const float a[4], const float b[4]) ATTR_WARN_UNUSED_RESULT;
MINLINE bool equals_v2v2_int(const int v1[2], const int v2[2]) ATTR_WARN_UNUSED_RESULT;
MINLINE bool equals_v3v3_int(const int v1[3], const int v2[3]) ATTR_WARN_UNUSED_RESULT;
MINLINE bool equals_v4v4_int(const int v1[4], const int v2[4]) ATTR_WARN_UNUSED_RESULT;
MINLINE bool compare_v2v2(const float a[2], const float b[2], float limit) ATTR_WARN_UNUSED_RESULT;
MINLINE bool compare_v3v3(const float a[3], const float b[3], float limit) ATTR_WARN_UNUSED_RESULT;
MINLINE bool compare_v4v4(const float a[4], const float b[4], float limit) ATTR_WARN_UNUSED_RESULT;
MINLINE bool compare_v2v2_relative(const float a[2], const float b[2], float limit, int max_ulps)
ATTR_WARN_UNUSED_RESULT;
MINLINE bool compare_v3v3_relative(const float a[3], const float b[3], float limit, int max_ulps)
ATTR_WARN_UNUSED_RESULT;
MINLINE bool compare_v4v4_relative(const float a[4], const float b[4], float limit, int max_ulps)
ATTR_WARN_UNUSED_RESULT;
MINLINE bool compare_len_v3v3(const float a[3],
const float b[3],
float limit) ATTR_WARN_UNUSED_RESULT;
MINLINE bool compare_size_v3v3(const float a[3],
const float b[3],
float limit) ATTR_WARN_UNUSED_RESULT;
/**
*
* + l1
* |
* neg <- | -> pos
* |
* + l2
*
*
* \return Positive value when 'pt' is left-of-line
* (looking from 'l1' -> 'l2').
*/
MINLINE float line_point_side_v2(const float l1[2],
const float l2[2],
const float pt[2]) ATTR_WARN_UNUSED_RESULT;
/** \} */
/* -------------------------------------------------------------------- */
/** \name Angles
* \{ */
/* - angle with 2 arguments is angle between vector.
* - angle with 3 arguments is angle between 3 points at the middle point.
* - angle_normalized_* is faster equivalent if vectors are normalized.
*/
/**
* Return the shortest angle in radians between the 2 vectors.
*/
float angle_v2v2(const float a[2], const float b[2]) ATTR_WARN_UNUSED_RESULT;
float angle_signed_v2v2(const float v1[2], const float v2[2]) ATTR_WARN_UNUSED_RESULT;
float angle_v2v2v2(const float a[2], const float b[2], const float c[2]) ATTR_WARN_UNUSED_RESULT;
float angle_normalized_v2v2(const float a[2], const float b[2]) ATTR_WARN_UNUSED_RESULT;
/**
* Return the shortest angle in radians between the 2 vectors.
*/
float angle_v3v3(const float a[3], const float b[3]) ATTR_WARN_UNUSED_RESULT;
/**
* Return the angle in radians between vecs 1-2 and 2-3 in radians
* If v1 is a shoulder, v2 is the elbow and v3 is the hand,
* this would return the angle at the elbow.
*
* note that when v1/v2/v3 represent 3 points along a straight line
* that the angle returned will be pi (180deg), rather than 0.0.
*/
float angle_v3v3v3(const float a[3], const float b[3], const float c[3]) ATTR_WARN_UNUSED_RESULT;
/**
* Quicker than full angle computation.
*/
float cos_v3v3v3(const float p1[3], const float p2[3], const float p3[3]) ATTR_WARN_UNUSED_RESULT;
/**
* Quicker than full angle computation.
*/
float cos_v2v2v2(const float p1[2], const float p2[2], const float p3[2]) ATTR_WARN_UNUSED_RESULT;
/**
* Angle between 2 vectors, about an axis (axis can be considered a plane).
*/
float angle_on_axis_v3v3_v3(const float v1[3],
const float v2[3],
const float axis[3]) ATTR_WARN_UNUSED_RESULT;
float angle_signed_on_axis_v3v3_v3(const float v1[3],
const float v2[3],
const float axis[3]) ATTR_WARN_UNUSED_RESULT;
float angle_normalized_v3v3(const float v1[3], const float v2[3]) ATTR_WARN_UNUSED_RESULT;
/**
* Angle between 2 vectors defined by 3 coords, about an axis (axis can be considered a plane).
*/
float angle_on_axis_v3v3v3_v3(const float v1[3],
const float v2[3],
const float v3[3],
const float axis[3]) ATTR_WARN_UNUSED_RESULT;
float angle_signed_on_axis_v3v3v3_v3(const float v1[3],
const float v2[3],
const float v3[3],
const float axis[3]) ATTR_WARN_UNUSED_RESULT;
void angle_tri_v3(float angles[3], const float v1[3], const float v2[3], const float v3[3]);
void angle_quad_v3(
float angles[4], const float v1[3], const float v2[3], const float v3[3], const float v4[3]);
void angle_poly_v3(float *angles, const float *verts[3], int len);
/** \} */
/* -------------------------------------------------------------------- */
/** \name Geometry
* \{ */
/**
* Project \a p onto \a v_proj
*/
void project_v2_v2v2(float out[2], const float p[2], const float v_proj[2]);
/**
* Project \a p onto \a v_proj
*/
void project_v3_v3v3(float out[3], const float p[3], const float v_proj[3]);
void project_v3_v3v3_db(double out[3], const double p[3], const double v_proj[3]);
/**
* Project \a p onto a unit length \a v_proj
*/
void project_v2_v2v2_normalized(float out[2], const float p[2], const float v_proj[2]);
/**
* Project \a p onto a unit length \a v_proj
*/
void project_v3_v3v3_normalized(float out[3], const float p[3], const float v_proj[3]);
/**
* In this case plane is a 3D vector only (no 4th component).
*
* Projecting will make \a out a copy of \a p orthogonal to \a v_plane.
*
* \note If \a p is exactly perpendicular to \a v_plane, \a out will just be a copy of \a p.
*
* \note This function is a convenience to call:
* \code{.c}
* project_v3_v3v3(out, p, v_plane);
* sub_v3_v3v3(out, p, out);
* \endcode
*/
void project_plane_v3_v3v3(float out[3], const float p[3], const float v_plane[3]);
void project_plane_v2_v2v2(float out[2], const float p[2], const float v_plane[2]);
void project_plane_normalized_v3_v3v3(float out[3], const float p[3], const float v_plane[3]);
void project_plane_normalized_v2_v2v2(float out[2], const float p[2], const float v_plane[2]);
/**
* Project a vector on a plane defined by normal and a plane point p.
*/
void project_v3_plane(float out[3], const float plane_no[3], const float plane_co[3]);
/**
* Returns a reflection vector from a vector and a normal vector
* reflect = vec - ((2 * dot(vec, mirror)) * mirror).
*
*
* v
* + ^
* \ |
* \|
* + normal: axis of reflection
* /
* /
* +
* out: result (negate for a 'bounce').
*
*/
void reflect_v3_v3v3(float out[3], const float vec[3], const float normal[3]);
void reflect_v3_v3v3_db(double out[3], const double vec[3], const double normal[3]);
/**
* Takes a vector and computes 2 orthogonal directions.
*
* \note if \a n is n unit length, computed values will be too.
*/
void ortho_basis_v3v3_v3(float r_n1[3], float r_n2[3], const float n[3]);
/**
* Calculates \a p - a perpendicular vector to \a v
*
* \note return vector won't maintain same length.
*/
void ortho_v3_v3(float out[3], const float v[3]);
/**
* no brainer compared to v3, just have for consistency.
*/
void ortho_v2_v2(float out[2], const float v[2]);
/**
* Returns a vector bisecting the angle at b formed by a, b and c.
*/
void bisect_v3_v3v3v3(float r[3], const float a[3], const float b[3], const float c[3]);
/**
* Rotate a point \a p by \a angle around origin (0, 0)
*/
void rotate_v2_v2fl(float r[2], const float p[2], float angle);
void rotate_v3_v3v3fl(float r[3], const float p[3], const float axis[3], float angle);
/**
* Rotate a point \a p by \a angle around an arbitrary unit length \a axis.
* http://local.wasp.uwa.edu.au/~pbourke/geometry/
*/
void rotate_normalized_v3_v3v3fl(float out[3], const float p[3], const float axis[3], float angle);
/** \} */
/* -------------------------------------------------------------------- */
/** \name Other
* \{ */
void print_v2(const char *str, const float v[2]);
void print_v3(const char *str, const float v[3]);
void print_v4(const char *str, const float v[4]);
void print_vn(const char *str, const float v[], int n);
#define print_v2_id(v) print_v2(STRINGIFY(v), v)
#define print_v3_id(v) print_v3(STRINGIFY(v), v)
#define print_v4_id(v) print_v4(STRINGIFY(v), v)
#define print_vn_id(v, n) print_vn(STRINGIFY(v), v, n)
MINLINE void normal_float_to_short_v2(short r[2], const float n[2]);
MINLINE void normal_short_to_float_v3(float r[3], const short n[3]);
MINLINE void normal_float_to_short_v3(short r[3], const float n[3]);
MINLINE void normal_float_to_short_v4(short r[4], const float n[4]);
void minmax_v4v4_v4(float min[4], float max[4], const float vec[4]);
void minmax_v3v3_v3(float min[3], float max[3], const float vec[3]);
void minmax_v2v2_v2(float min[2], float max[2], const float vec[2]);
void minmax_v3v3_v3_array(float r_min[3], float r_max[3], const float (*vec_arr)[3], int nbr);
/** ensure \a v1 is \a dist from \a v2 */
void dist_ensure_v3_v3fl(float v1[3], const float v2[3], float dist);
void dist_ensure_v2_v2fl(float v1[2], const float v2[2], float dist);
void axis_sort_v3(const float axis_values[3], int r_axis_order[3]);
MINLINE void clamp_v2(float vec[2], float min, float max);
MINLINE void clamp_v3(float vec[3], float min, float max);
MINLINE void clamp_v4(float vec[4], float min, float max);
MINLINE void clamp_v2_v2v2(float vec[2], const float min[2], const float max[2]);
MINLINE void clamp_v3_v3v3(float vec[3], const float min[3], const float max[3]);
MINLINE void clamp_v4_v4v4(float vec[4], const float min[4], const float max[4]);
/** \} */
/* -------------------------------------------------------------------- */
/** \name Array Functions
* \{ */
/**
* Follow fixed length vector function conventions.
*/
double dot_vn_vn(const float *array_src_a,
const float *array_src_b,
int size) ATTR_WARN_UNUSED_RESULT;
double len_squared_vn(const float *array, int size) ATTR_WARN_UNUSED_RESULT;
float normalize_vn_vn(float *array_tar, const float *array_src, int size);
float normalize_vn(float *array_tar, int size);
void range_vn_i(int *array_tar, int size, int start);
void range_vn_u(unsigned int *array_tar, int size, unsigned int start);
void range_vn_fl(float *array_tar, int size, float start, float step);
void negate_vn(float *array_tar, int size);
void negate_vn_vn(float *array_tar, const float *array_src, int size);
void mul_vn_vn(float *array_tar, const float *array_src, int size);
void mul_vn_vnvn(float *array_tar, const float *array_src_a, const float *array_src_b, int size);
void mul_vn_fl(float *array_tar, int size, float f);
void mul_vn_vn_fl(float *array_tar, const float *array_src, int size, float f);
void add_vn_vn(float *array_tar, const float *array_src, int size);
void add_vn_vnvn(float *array_tar, const float *array_src_a, const float *array_src_b, int size);
void madd_vn_vn(float *array_tar, const float *array_src, float f, int size);
void madd_vn_vnvn(
float *array_tar, const float *array_src_a, const float *array_src_b, float f, int size);
void sub_vn_vn(float *array_tar, const float *array_src, int size);
void sub_vn_vnvn(float *array_tar, const float *array_src_a, const float *array_src_b, int size);
void msub_vn_vn(float *array_tar, const float *array_src, float f, int size);
void msub_vn_vnvn(
float *array_tar, const float *array_src_a, const float *array_src_b, float f, int size);
void interp_vn_vn(float *array_tar, const float *array_src, float t, int size);
void copy_vn_i(int *array_tar, int size, int val);
void copy_vn_short(short *array_tar, int size, short val);
void copy_vn_ushort(unsigned short *array_tar, int size, unsigned short val);
void copy_vn_uchar(unsigned char *array_tar, int size, unsigned char val);
void copy_vn_fl(float *array_tar, int size, float val);
void add_vn_vn_d(double *array_tar, const double *array_src, int size);
void add_vn_vnvn_d(double *array_tar,
const double *array_src_a,
const double *array_src_b,
int size);
void mul_vn_db(double *array_tar, int size, double f);
/** \} */
/* -------------------------------------------------------------------- */
/** \name Inline Definitions
* \{ */
#if BLI_MATH_DO_INLINE
# include "intern/math_vector_inline.c"
#endif
#ifdef BLI_MATH_GCC_WARN_PRAGMA
# pragma GCC diagnostic pop
#endif
/** \} */
#ifdef __cplusplus
}
#endif