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ad0edc626d3668424a7c6d172a1be716ae932021
blender-archive/source/blender/blenlib/intern/math_vector.c
Pablo Dobarro d7282537f0 CD_PROP_COL datalayer 
This implements a generic color datalayer and its functions. Based on
D5975.

Reviewed By: brecht

Differential Revision: https://developer.blender.org/D7838
2020-05-27 20:04:46 +02:00

1434 lines
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/*
* 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.
*
* */
/** \file
* \ingroup bli
*/
#include "BLI_math.h"
#include "BLI_strict_flags.h"
//******************************* Interpolation *******************************/
void interp_v2_v2v2(float target[2], const float a[2], const float b[2], const float t)
{
const float s = 1.0f - t;
target[0] = s * a[0] + t * b[0];
target[1] = s * a[1] + t * b[1];
}
/* weight 3 2D vectors,
* 'w' must be unit length but is not a vector, just 3 weights */
void interp_v2_v2v2v2(
float p[2], const float v1[2], const float v2[2], const float v3[2], const float w[3])
{
p[0] = v1[0] * w[0] + v2[0] * w[1] + v3[0] * w[2];
p[1] = v1[1] * w[0] + v2[1] * w[1] + v3[1] * w[2];
}
void interp_v3_v3v3(float target[3], const float a[3], const float b[3], const float t)
{
const float s = 1.0f - t;
target[0] = s * a[0] + t * b[0];
target[1] = s * a[1] + t * b[1];
target[2] = s * a[2] + t * b[2];
}
void interp_v4_v4v4(float target[4], const float a[4], const float b[4], const float t)
{
const float s = 1.0f - t;
target[0] = s * a[0] + t * b[0];
target[1] = s * a[1] + t * b[1];
target[2] = s * a[2] + t * b[2];
target[3] = s * a[3] + t * b[3];
}
/**
* 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], const float t)
{
float cosom, w[2];
BLI_ASSERT_UNIT_V3(a);
BLI_ASSERT_UNIT_V3(b);
cosom = dot_v3v3(a, b);
/* direct opposites */
if (UNLIKELY(cosom < (-1.0f + FLT_EPSILON))) {
return false;
}
interp_dot_slerp(t, cosom, w);
target[0] = w[0] * a[0] + w[1] * b[0];
target[1] = w[0] * a[1] + w[1] * b[1];
target[2] = w[0] * a[2] + w[1] * b[2];
return true;
}
bool interp_v2_v2v2_slerp(float target[2], const float a[2], const float b[2], const float t)
{
float cosom, w[2];
BLI_ASSERT_UNIT_V2(a);
BLI_ASSERT_UNIT_V2(b);
cosom = dot_v2v2(a, b);
/* direct opposites */
if (UNLIKELY(cosom < (1.0f + FLT_EPSILON))) {
return false;
}
interp_dot_slerp(t, cosom, w);
target[0] = w[0] * a[0] + w[1] * b[0];
target[1] = w[0] * a[1] + w[1] * b[1];
return true;
}
/**
* 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], const float t)
{
if (UNLIKELY(!interp_v3_v3v3_slerp(target, a, b, t))) {
/* Axis are aligned so any orthogonal vector is acceptable. */
float ab_ortho[3];
ortho_v3_v3(ab_ortho, a);
normalize_v3(ab_ortho);
if (t < 0.5f) {
if (UNLIKELY(!interp_v3_v3v3_slerp(target, a, ab_ortho, t * 2.0f))) {
BLI_assert(0);
copy_v3_v3(target, a);
}
}
else {
if (UNLIKELY(!interp_v3_v3v3_slerp(target, ab_ortho, b, (t - 0.5f) * 2.0f))) {
BLI_assert(0);
copy_v3_v3(target, b);
}
}
}
}
void interp_v2_v2v2_slerp_safe(float target[2], const float a[2], const float b[2], const float t)
{
if (UNLIKELY(!interp_v2_v2v2_slerp(target, a, b, t))) {
/* Axis are aligned so any orthogonal vector is acceptable. */
float ab_ortho[2];
ortho_v2_v2(ab_ortho, a);
// normalize_v2(ab_ortho);
if (t < 0.5f) {
if (UNLIKELY(!interp_v2_v2v2_slerp(target, a, ab_ortho, t * 2.0f))) {
BLI_assert(0);
copy_v2_v2(target, a);
}
}
else {
if (UNLIKELY(!interp_v2_v2v2_slerp(target, ab_ortho, b, (t - 0.5f) * 2.0f))) {
BLI_assert(0);
copy_v2_v2(target, b);
}
}
}
}
/** \name Cubic curve interpolation (bezier spline).
* \{ */
void interp_v2_v2v2v2v2_cubic(float p[2],
const float v1[2],
const float v2[2],
const float v3[2],
const float v4[2],
const float u)
{
float q0[2], q1[2], q2[2], r0[2], r1[2];
interp_v2_v2v2(q0, v1, v2, u);
interp_v2_v2v2(q1, v2, v3, u);
interp_v2_v2v2(q2, v3, v4, u);
interp_v2_v2v2(r0, q0, q1, u);
interp_v2_v2v2(r1, q1, q2, u);
interp_v2_v2v2(p, r0, r1, u);
}
/** \} */
/* 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])
{
p[0] = v1[0] * w[0] + v2[0] * w[1] + v3[0] * w[2];
p[1] = v1[1] * w[0] + v2[1] * w[1] + v3[1] * w[2];
p[2] = v1[2] * w[0] + v2[2] * w[1] + v3[2] * w[2];
}
/* 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])
{
p[0] = v1[0] * w[0] + v2[0] * w[1] + v3[0] * w[2] + v4[0] * w[3];
p[1] = v1[1] * w[0] + v2[1] * w[1] + v3[1] * w[2] + v4[1] * w[3];
p[2] = v1[2] * w[0] + v2[2] * w[1] + v3[2] * w[2] + v4[2] * w[3];
}
void interp_v4_v4v4v4(
float p[4], const float v1[4], const float v2[4], const float v3[4], const float w[3])
{
p[0] = v1[0] * w[0] + v2[0] * w[1] + v3[0] * w[2];
p[1] = v1[1] * w[0] + v2[1] * w[1] + v3[1] * w[2];
p[2] = v1[2] * w[0] + v2[2] * w[1] + v3[2] * w[2];
p[3] = v1[3] * w[0] + v2[3] * w[1] + v3[3] * w[2];
}
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])
{
p[0] = v1[0] * w[0] + v2[0] * w[1] + v3[0] * w[2] + v4[0] * w[3];
p[1] = v1[1] * w[0] + v2[1] * w[1] + v3[1] * w[2] + v4[1] * w[3];
p[2] = v1[2] * w[0] + v2[2] * w[1] + v3[2] * w[2] + v4[2] * w[3];
p[3] = v1[3] * w[0] + v2[3] * w[1] + v3[3] * w[2] + v4[3] * w[3];
}
void interp_v3_v3v3v3_uv(
float p[3], const float v1[3], const float v2[3], const float v3[3], const float uv[2])
{
p[0] = v1[0] + ((v2[0] - v1[0]) * uv[0]) + ((v3[0] - v1[0]) * uv[1]);
p[1] = v1[1] + ((v2[1] - v1[1]) * uv[0]) + ((v3[1] - v1[1]) * uv[1]);
p[2] = v1[2] + ((v2[2] - v1[2]) * uv[0]) + ((v3[2] - v1[2]) * uv[1]);
}
void interp_v3_v3v3_uchar(uchar target[3], const uchar a[3], const uchar b[3], const float t)
{
const float s = 1.0f - t;
target[0] = (char)floorf(s * a[0] + t * b[0]);
target[1] = (char)floorf(s * a[1] + t * b[1]);
target[2] = (char)floorf(s * a[2] + t * b[2]);
}
void interp_v3_v3v3_char(char target[3], const char a[3], const char b[3], const float t)
{
interp_v3_v3v3_uchar((uchar *)target, (const uchar *)a, (const uchar *)b, t);
}
void interp_v4_v4v4_uchar(uchar target[4], const uchar a[4], const uchar b[4], const float t)
{
const float s = 1.0f - t;
target[0] = (char)floorf(s * a[0] + t * b[0]);
target[1] = (char)floorf(s * a[1] + t * b[1]);
target[2] = (char)floorf(s * a[2] + t * b[2]);
target[3] = (char)floorf(s * a[3] + t * b[3]);
}
void interp_v4_v4v4_char(char target[4], const char a[4], const char b[4], const float t)
{
interp_v4_v4v4_uchar((uchar *)target, (const uchar *)a, (const uchar *)b, t);
}
void mid_v3_v3v3(float v[3], const float v1[3], const float v2[3])
{
v[0] = 0.5f * (v1[0] + v2[0]);
v[1] = 0.5f * (v1[1] + v2[1]);
v[2] = 0.5f * (v1[2] + v2[2]);
}
void mid_v2_v2v2(float v[2], const float v1[2], const float v2[2])
{
v[0] = 0.5f * (v1[0] + v2[0]);
v[1] = 0.5f * (v1[1] + v2[1]);
}
void mid_v3_v3v3v3(float v[3], const float v1[3], const float v2[3], const float v3[3])
{
v[0] = (v1[0] + v2[0] + v3[0]) / 3.0f;
v[1] = (v1[1] + v2[1] + v3[1]) / 3.0f;
v[2] = (v1[2] + v2[2] + v3[2]) / 3.0f;
}
void mid_v3_v3v3v3v3(
float v[3], const float v1[3], const float v2[3], const float v3[3], const float v4[3])
{
v[0] = (v1[0] + v2[0] + v3[0] + v4[0]) / 4.0f;
v[1] = (v1[1] + v2[1] + v3[1] + v4[1]) / 4.0f;
v[2] = (v1[2] + v2[2] + v3[2] + v4[2]) / 4.0f;
}
void mid_v3_v3_array(float r[3], const float (*vec_arr)[3], const uint nbr)
{
const float factor = 1.0f / (float)nbr;
zero_v3(r);
for (uint i = 0; i < nbr; i++) {
madd_v3_v3fl(r, vec_arr[i], factor);
}
}
/**
* Specialized function for calculating normals.
* fastpath 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])
{
/* trick, we want the middle of 2 normals as well as the angle between them
* avoid multiple calculations by */
float angle;
/* double check they are normalized */
BLI_ASSERT_UNIT_V3(a);
BLI_ASSERT_UNIT_V3(b);
add_v3_v3v3(r, a, b);
angle = ((float)(1.0 / (M_PI / 2.0)) *
/* normally we would only multiply by 2,
* but instead of an angle make this 0-1 factor */
2.0f) *
acosf(normalize_v3(r) / 2.0f);
mul_v3_fl(r, angle);
}
/**
* 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])
{
/* trick, we want the middle of 2 normals as well as the angle between them
* avoid multiple calculations by */
float angle;
/* double check they are normalized */
BLI_assert(len_squared_v3(r) <= 1.0f + FLT_EPSILON);
angle = ((float)(1.0 / (M_PI / 2.0)) *
/* normally we would only multiply by 2,
* but instead of an angle make this 0-1 factor */
2.0f) *
acosf(normalize_v3(r));
mul_v3_fl(r, angle);
}
/**
* Equivalent to:
* interp_v3_v3v3(v, v1, v2, -1.0f);
*/
void flip_v4_v4v4(float v[4], const float v1[4], const float v2[4])
{
v[0] = v1[0] + (v1[0] - v2[0]);
v[1] = v1[1] + (v1[1] - v2[1]);
v[2] = v1[2] + (v1[2] - v2[2]);
v[3] = v1[3] + (v1[3] - v2[3]);
}
void flip_v3_v3v3(float v[3], const float v1[3], const float v2[3])
{
v[0] = v1[0] + (v1[0] - v2[0]);
v[1] = v1[1] + (v1[1] - v2[1]);
v[2] = v1[2] + (v1[2] - v2[2]);
}
void flip_v2_v2v2(float v[2], const float v1[2], const float v2[2])
{
v[0] = v1[0] + (v1[0] - v2[0]);
v[1] = v1[1] + (v1[1] - v2[1]);
}
/********************************* Comparison ********************************/
bool is_finite_v2(const float v[2])
{
return (isfinite(v[0]) && isfinite(v[1]));
}
bool is_finite_v3(const float v[3])
{
return (isfinite(v[0]) && isfinite(v[1]) && isfinite(v[2]));
}
bool is_finite_v4(const float v[4])
{
return (isfinite(v[0]) && isfinite(v[1]) && isfinite(v[2]) && isfinite(v[3]));
}
/********************************** Angles ***********************************/
/* 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 then 0.0
*/
float angle_v3v3v3(const float v1[3], const float v2[3], const float v3[3])
{
float vec1[3], vec2[3];
sub_v3_v3v3(vec1, v2, v1);
sub_v3_v3v3(vec2, v2, v3);
normalize_v3(vec1);
normalize_v3(vec2);
return angle_normalized_v3v3(vec1, vec2);
}
/* Quicker than full angle computation */
float cos_v3v3v3(const float p1[3], const float p2[3], const float p3[3])
{
float vec1[3], vec2[3];
sub_v3_v3v3(vec1, p2, p1);
sub_v3_v3v3(vec2, p2, p3);
normalize_v3(vec1);
normalize_v3(vec2);
return dot_v3v3(vec1, vec2);
}
/* Return the shortest angle in radians between the 2 vectors */
float angle_v3v3(const float v1[3], const float v2[3])
{
float vec1[3], vec2[3];
normalize_v3_v3(vec1, v1);
normalize_v3_v3(vec2, v2);
return angle_normalized_v3v3(vec1, vec2);
}
float angle_v2v2v2(const float v1[2], const float v2[2], const float v3[2])
{
float vec1[2], vec2[2];
vec1[0] = v2[0] - v1[0];
vec1[1] = v2[1] - v1[1];
vec2[0] = v2[0] - v3[0];
vec2[1] = v2[1] - v3[1];
normalize_v2(vec1);
normalize_v2(vec2);
return angle_normalized_v2v2(vec1, vec2);
}
/* Quicker than full angle computation */
float cos_v2v2v2(const float p1[2], const float p2[2], const float p3[2])
{
float vec1[2], vec2[2];
sub_v2_v2v2(vec1, p2, p1);
sub_v2_v2v2(vec2, p2, p3);
normalize_v2(vec1);
normalize_v2(vec2);
return dot_v2v2(vec1, vec2);
}
/* Return the shortest angle in radians between the 2 vectors */
float angle_v2v2(const float v1[2], const float v2[2])
{
float vec1[2], vec2[2];
vec1[0] = v1[0];
vec1[1] = v1[1];
vec2[0] = v2[0];
vec2[1] = v2[1];
normalize_v2(vec1);
normalize_v2(vec2);
return angle_normalized_v2v2(vec1, vec2);
}
float angle_signed_v2v2(const float v1[2], const float v2[2])
{
const float perp_dot = (v1[1] * v2[0]) - (v1[0] * v2[1]);
return atan2f(perp_dot, dot_v2v2(v1, v2));
}
float angle_normalized_v3v3(const float v1[3], const float v2[3])
{
/* double check they are normalized */
BLI_ASSERT_UNIT_V3(v1);
BLI_ASSERT_UNIT_V3(v2);
/* this is the same as acos(dot_v3v3(v1, v2)), but more accurate */
if (dot_v3v3(v1, v2) >= 0.0f) {
return 2.0f * saasin(len_v3v3(v1, v2) / 2.0f);
}
else {
float v2_n[3];
negate_v3_v3(v2_n, v2);
return (float)M_PI - 2.0f * saasin(len_v3v3(v1, v2_n) / 2.0f);
}
}
float angle_normalized_v2v2(const float v1[2], const float v2[2])
{
/* double check they are normalized */
BLI_ASSERT_UNIT_V2(v1);
BLI_ASSERT_UNIT_V2(v2);
/* this is the same as acos(dot_v3v3(v1, v2)), but more accurate */
if (dot_v2v2(v1, v2) >= 0.0f) {
return 2.0f * saasin(len_v2v2(v1, v2) / 2.0f);
}
else {
float v2_n[2];
negate_v2_v2(v2_n, v2);
return (float)M_PI - 2.0f * saasin(len_v2v2(v1, v2_n) / 2.0f);
}
}
/**
* 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])
{
float v1_proj[3], v2_proj[3];
/* project the vectors onto the axis */
project_plane_normalized_v3_v3v3(v1_proj, v1, axis);
project_plane_normalized_v3_v3v3(v2_proj, v2, axis);
return angle_v3v3(v1_proj, v2_proj);
}
float angle_signed_on_axis_v3v3_v3(const float v1[3], const float v2[3], const float axis[3])
{
float v1_proj[3], v2_proj[3], tproj[3];
float angle;
/* project the vectors onto the axis */
project_plane_normalized_v3_v3v3(v1_proj, v1, axis);
project_plane_normalized_v3_v3v3(v2_proj, v2, axis);
angle = angle_v3v3(v1_proj, v2_proj);
/* calculate the sign (reuse 'tproj') */
cross_v3_v3v3(tproj, v2_proj, v1_proj);
if (dot_v3v3(tproj, axis) < 0.0f) {
angle = ((float)(M_PI * 2.0)) - angle;
}
return angle;
}
/**
* 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])
{
float vec1[3], vec2[3];
sub_v3_v3v3(vec1, v1, v2);
sub_v3_v3v3(vec2, v3, v2);
return angle_on_axis_v3v3_v3(vec1, vec2, axis);
}
float angle_signed_on_axis_v3v3v3_v3(const float v1[3],
const float v2[3],
const float v3[3],
const float axis[3])
{
float vec1[3], vec2[3];
sub_v3_v3v3(vec1, v1, v2);
sub_v3_v3v3(vec2, v3, v2);
return angle_signed_on_axis_v3v3_v3(vec1, vec2, axis);
}
void angle_tri_v3(float angles[3], const float v1[3], const float v2[3], const float v3[3])
{
float ed1[3], ed2[3], ed3[3];
sub_v3_v3v3(ed1, v3, v1);
sub_v3_v3v3(ed2, v1, v2);
sub_v3_v3v3(ed3, v2, v3);
normalize_v3(ed1);
normalize_v3(ed2);
normalize_v3(ed3);
angles[0] = (float)M_PI - angle_normalized_v3v3(ed1, ed2);
angles[1] = (float)M_PI - angle_normalized_v3v3(ed2, ed3);
// face_angles[2] = M_PI - angle_normalized_v3v3(ed3, ed1);
angles[2] = (float)M_PI - (angles[0] + angles[1]);
}
void angle_quad_v3(
float angles[4], const float v1[3], const float v2[3], const float v3[3], const float v4[3])
{
float ed1[3], ed2[3], ed3[3], ed4[3];
sub_v3_v3v3(ed1, v4, v1);
sub_v3_v3v3(ed2, v1, v2);
sub_v3_v3v3(ed3, v2, v3);
sub_v3_v3v3(ed4, v3, v4);
normalize_v3(ed1);
normalize_v3(ed2);
normalize_v3(ed3);
normalize_v3(ed4);
angles[0] = (float)M_PI - angle_normalized_v3v3(ed1, ed2);
angles[1] = (float)M_PI - angle_normalized_v3v3(ed2, ed3);
angles[2] = (float)M_PI - angle_normalized_v3v3(ed3, ed4);
angles[3] = (float)M_PI - angle_normalized_v3v3(ed4, ed1);
}
void angle_poly_v3(float *angles, const float *verts[3], int len)
{
int i;
float vec[3][3];
sub_v3_v3v3(vec[2], verts[len - 1], verts[0]);
normalize_v3(vec[2]);
for (i = 0; i < len; i++) {
sub_v3_v3v3(vec[i % 3], verts[i % len], verts[(i + 1) % len]);
normalize_v3(vec[i % 3]);
angles[i] = (float)M_PI - angle_normalized_v3v3(vec[(i + 2) % 3], vec[i % 3]);
}
}
/********************************* Geometry **********************************/
/**
* Project \a p onto \a v_proj
*/
void project_v2_v2v2(float out[2], const float p[2], const float v_proj[2])
{
const float mul = dot_v2v2(p, v_proj) / dot_v2v2(v_proj, v_proj);
out[0] = mul * v_proj[0];
out[1] = mul * v_proj[1];
}
/**
* Project \a p onto \a v_proj
*/
void project_v3_v3v3(float out[3], const float p[3], const float v_proj[3])
{
const float mul = dot_v3v3(p, v_proj) / dot_v3v3(v_proj, v_proj);
out[0] = mul * v_proj[0];
out[1] = mul * v_proj[1];
out[2] = mul * v_proj[2];
}
/**
* 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])
{
BLI_ASSERT_UNIT_V2(v_proj);
const float mul = dot_v2v2(p, v_proj);
out[0] = mul * v_proj[0];
out[1] = mul * v_proj[1];
}
/**
* 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])
{
BLI_ASSERT_UNIT_V3(v_proj);
const float mul = dot_v3v3(p, v_proj);
out[0] = mul * v_proj[0];
out[1] = mul * v_proj[1];
out[2] = mul * v_proj[2];
}
/**
* In this case plane is a 3D vector only (no 4th component).
*
* Projecting will make \a c a copy of \a v orthogonal to \a v_plane.
*
* \note If \a v is exactly perpendicular to \a v_plane, \a c will just be a copy of \a v.
*
* \note This function is a convenience to call:
* \code{.c}
* project_v3_v3v3(c, v, v_plane);
* sub_v3_v3v3(c, v, c);
* \endcode
*/
void project_plane_v3_v3v3(float out[3], const float p[3], const float v_plane[3])
{
const float mul = dot_v3v3(p, v_plane) / dot_v3v3(v_plane, v_plane);
out[0] = p[0] - (mul * v_plane[0]);
out[1] = p[1] - (mul * v_plane[1]);
out[2] = p[2] - (mul * v_plane[2]);
}
void project_plane_v2_v2v2(float out[2], const float p[2], const float v_plane[2])
{
const float mul = dot_v2v2(p, v_plane) / dot_v2v2(v_plane, v_plane);
out[0] = p[0] - (mul * v_plane[0]);
out[1] = p[1] - (mul * v_plane[1]);
}
void project_plane_normalized_v3_v3v3(float out[3], const float p[3], const float v_plane[3])
{
BLI_ASSERT_UNIT_V3(v_plane);
const float mul = dot_v3v3(p, v_plane);
out[0] = p[0] - (mul * v_plane[0]);
out[1] = p[1] - (mul * v_plane[1]);
out[2] = p[2] - (mul * v_plane[2]);
}
void project_plane_normalized_v2_v2v2(float out[2], const float p[2], const float v_plane[2])
{
BLI_ASSERT_UNIT_V2(v_plane);
const float mul = dot_v2v2(p, v_plane);
out[0] = p[0] - (mul * v_plane[0]);
out[1] = p[1] - (mul * v_plane[1]);
}
/* 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])
{
float vector[3];
float mul;
sub_v3_v3v3(vector, out, plane_co);
mul = dot_v3v3(vector, plane_no) / len_squared_v3(plane_no);
mul_v3_v3fl(vector, plane_no, mul);
sub_v3_v3(out, vector);
}
/* Returns a vector bisecting the angle at v2 formed by v1, v2 and v3 */
void bisect_v3_v3v3v3(float out[3], const float v1[3], const float v2[3], const float v3[3])
{
float d_12[3], d_23[3];
sub_v3_v3v3(d_12, v2, v1);
sub_v3_v3v3(d_23, v3, v2);
normalize_v3(d_12);
normalize_v3(d_23);
add_v3_v3v3(out, d_12, d_23);
normalize_v3(out);
}
/**
* Returns a reflection vector from a vector and a normal vector
* reflect = vec - ((2 * dot(vec, mirror)) * mirror).
*
* <pre>
* v
* + ^
* \ |
* \|
* + normal: axis of reflection
* /
* /
* +
* out: result (negate for a 'bounce').
* </pre>
*/
void reflect_v3_v3v3(float out[3], const float v[3], const float normal[3])
{
const float dot2 = 2.0f * dot_v3v3(v, normal);
BLI_ASSERT_UNIT_V3(normal);
out[0] = v[0] - (dot2 * normal[0]);
out[1] = v[1] - (dot2 * normal[1]);
out[2] = v[2] - (dot2 * normal[2]);
}
/**
* 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])
{
const float eps = FLT_EPSILON;
const float f = len_squared_v2(n);
if (f > eps) {
const float d = 1.0f / sqrtf(f);
BLI_assert(isfinite(d));
r_n1[0] = n[1] * d;
r_n1[1] = -n[0] * d;
r_n1[2] = 0.0f;
r_n2[0] = -n[2] * r_n1[1];
r_n2[1] = n[2] * r_n1[0];
r_n2[2] = n[0] * r_n1[1] - n[1] * r_n1[0];
}
else {
/* degenerate case */
r_n1[0] = (n[2] < 0.0f) ? -1.0f : 1.0f;
r_n1[1] = r_n1[2] = r_n2[0] = r_n2[2] = 0.0f;
r_n2[1] = 1.0f;
}
}
/**
* 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])
{
const int axis = axis_dominant_v3_single(v);
BLI_assert(out != v);
switch (axis) {
case 0:
out[0] = -v[1] - v[2];
out[1] = v[0];
out[2] = v[0];
break;
case 1:
out[0] = v[1];
out[1] = -v[0] - v[2];
out[2] = v[1];
break;
case 2:
out[0] = v[2];
out[1] = v[2];
out[2] = -v[0] - v[1];
break;
}
}
/**
* no brainer compared to v3, just have for consistency.
*/
void ortho_v2_v2(float out[2], const float v[2])
{
BLI_assert(out != v);
out[0] = -v[1];
out[1] = v[0];
}
/**
* Rotate a point \a p by \a angle around origin (0, 0)
*/
void rotate_v2_v2fl(float r[2], const float p[2], const float angle)
{
const float co = cosf(angle);
const float si = sinf(angle);
BLI_assert(r != p);
r[0] = co * p[0] - si * p[1];
r[1] = si * p[0] + co * p[1];
}
/**
* 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],
const float angle)
{
const float costheta = cosf(angle);
const float sintheta = sinf(angle);
/* double check they are normalized */
BLI_ASSERT_UNIT_V3(axis);
out[0] = ((costheta + (1 - costheta) * axis[0] * axis[0]) * p[0]) +
(((1 - costheta) * axis[0] * axis[1] - axis[2] * sintheta) * p[1]) +
(((1 - costheta) * axis[0] * axis[2] + axis[1] * sintheta) * p[2]);
out[1] = (((1 - costheta) * axis[0] * axis[1] + axis[2] * sintheta) * p[0]) +
((costheta + (1 - costheta) * axis[1] * axis[1]) * p[1]) +
(((1 - costheta) * axis[1] * axis[2] - axis[0] * sintheta) * p[2]);
out[2] = (((1 - costheta) * axis[0] * axis[2] - axis[1] * sintheta) * p[0]) +
(((1 - costheta) * axis[1] * axis[2] + axis[0] * sintheta) * p[1]) +
((costheta + (1 - costheta) * axis[2] * axis[2]) * p[2]);
}
void rotate_v3_v3v3fl(float r[3], const float p[3], const float axis[3], const float angle)
{
BLI_assert(r != p);
float axis_n[3];
normalize_v3_v3(axis_n, axis);
rotate_normalized_v3_v3v3fl(r, p, axis_n, angle);
}
/*********************************** Other ***********************************/
void print_v2(const char *str, const float v[2])
{
printf("%s: %.8f %.8f\n", str, v[0], v[1]);
}
void print_v3(const char *str, const float v[3])
{
printf("%s: %.8f %.8f %.8f\n", str, v[0], v[1], v[2]);
}
void print_v4(const char *str, const float v[4])
{
printf("%s: %.8f %.8f %.8f %.8f\n", str, v[0], v[1], v[2], v[3]);
}
void print_vn(const char *str, const float v[], const int n)
{
int i = 0;
printf("%s[%d]:", str, n);
while (i < n) {
printf(" %.8f", v[i++]);
}
printf("\n");
}
void minmax_v4v4_v4(float min[4], float max[4], const float vec[4])
{
if (min[0] > vec[0]) {
min[0] = vec[0];
}
if (min[1] > vec[1]) {
min[1] = vec[1];
}
if (min[2] > vec[2]) {
min[2] = vec[2];
}
if (min[3] > vec[3]) {
min[3] = vec[3];
}
if (max[0] < vec[0]) {
max[0] = vec[0];
}
if (max[1] < vec[1]) {
max[1] = vec[1];
}
if (max[2] < vec[2]) {
max[2] = vec[2];
}
if (max[3] < vec[3]) {
max[3] = vec[3];
}
}
void minmax_v3v3_v3(float min[3], float max[3], const float vec[3])
{
if (min[0] > vec[0]) {
min[0] = vec[0];
}
if (min[1] > vec[1]) {
min[1] = vec[1];
}
if (min[2] > vec[2]) {
min[2] = vec[2];
}
if (max[0] < vec[0]) {
max[0] = vec[0];
}
if (max[1] < vec[1]) {
max[1] = vec[1];
}
if (max[2] < vec[2]) {
max[2] = vec[2];
}
}
void minmax_v2v2_v2(float min[2], float max[2], const float vec[2])
{
if (min[0] > vec[0]) {
min[0] = vec[0];
}
if (min[1] > vec[1]) {
min[1] = vec[1];
}
if (max[0] < vec[0]) {
max[0] = vec[0];
}
if (max[1] < vec[1]) {
max[1] = vec[1];
}
}
void minmax_v3v3_v3_array(float r_min[3], float r_max[3], const float (*vec_arr)[3], int nbr)
{
while (nbr--) {
minmax_v3v3_v3(r_min, r_max, *vec_arr++);
}
}
/** ensure \a v1 is \a dist from \a v2 */
void dist_ensure_v3_v3fl(float v1[3], const float v2[3], const float dist)
{
if (!equals_v3v3(v2, v1)) {
float nor[3];
sub_v3_v3v3(nor, v1, v2);
normalize_v3(nor);
madd_v3_v3v3fl(v1, v2, nor, dist);
}
}
void dist_ensure_v2_v2fl(float v1[2], const float v2[2], const float dist)
{
if (!equals_v2v2(v2, v1)) {
float nor[2];
sub_v2_v2v2(nor, v1, v2);
normalize_v2(nor);
madd_v2_v2v2fl(v1, v2, nor, dist);
}
}
void axis_sort_v3(const float axis_values[3], int r_axis_order[3])
{
float v[3];
copy_v3_v3(v, axis_values);
#define SWAP_AXIS(a, b) \
{ \
SWAP(float, v[a], v[b]); \
SWAP(int, r_axis_order[a], r_axis_order[b]); \
} \
(void)0
if (v[0] < v[1]) {
if (v[2] < v[0]) {
SWAP_AXIS(0, 2);
}
}
else {
if (v[1] < v[2]) {
SWAP_AXIS(0, 1);
}
else {
SWAP_AXIS(0, 2);
}
}
if (v[2] < v[1]) {
SWAP_AXIS(1, 2);
}
#undef SWAP_AXIS
}
/***************************** Array Functions *******************************/
MINLINE double sqr_db(double f)
{
return f * f;
}
double dot_vn_vn(const float *array_src_a, const float *array_src_b, const int size)
{
double d = 0.0f;
const float *array_pt_a = array_src_a + (size - 1);
const float *array_pt_b = array_src_b + (size - 1);
int i = size;
while (i--) {
d += (double)(*(array_pt_a--) * *(array_pt_b--));
}
return d;
}
double len_squared_vn(const float *array, const int size)
{
double d = 0.0f;
const float *array_pt = array + (size - 1);
int i = size;
while (i--) {
d += sqr_db((double)(*(array_pt--)));
}
return d;
}
float normalize_vn_vn(float *array_tar, const float *array_src, const int size)
{
const double d = len_squared_vn(array_src, size);
float d_sqrt;
if (d > 1.0e-35) {
d_sqrt = (float)sqrt(d);
mul_vn_vn_fl(array_tar, array_src, size, 1.0f / d_sqrt);
}
else {
copy_vn_fl(array_tar, size, 0.0f);
d_sqrt = 0.0f;
}
return d_sqrt;
}
float normalize_vn(float *array_tar, const int size)
{
return normalize_vn_vn(array_tar, array_tar, size);
}
void range_vn_i(int *array_tar, const int size, const int start)
{
int *array_pt = array_tar + (size - 1);
int j = start + (size - 1);
int i = size;
while (i--) {
*(array_pt--) = j--;
}
}
void range_vn_u(uint *array_tar, const int size, const uint start)
{
uint *array_pt = array_tar + (size - 1);
uint j = start + (uint)(size - 1);
int i = size;
while (i--) {
*(array_pt--) = j--;
}
}
void range_vn_fl(float *array_tar, const int size, const float start, const float step)
{
float *array_pt = array_tar + (size - 1);
int i = size;
while (i--) {
*(array_pt--) = start + step * (float)(i);
}
}
void negate_vn(float *array_tar, const int size)
{
float *array_pt = array_tar + (size - 1);
int i = size;
while (i--) {
*(array_pt--) *= -1.0f;
}
}
void negate_vn_vn(float *array_tar, const float *array_src, const int size)
{
float *tar = array_tar + (size - 1);
const float *src = array_src + (size - 1);
int i = size;
while (i--) {
*(tar--) = -*(src--);
}
}
void mul_vn_vn(float *array_tar, const float *array_src, const int size)
{
float *tar = array_tar + (size - 1);
const float *src = array_src + (size - 1);
int i = size;
while (i--) {
*(tar--) *= *(src--);
}
}
void mul_vn_vnvn(float *array_tar,
const float *array_src_a,
const float *array_src_b,
const int size)
{
float *tar = array_tar + (size - 1);
const float *src_a = array_src_a + (size - 1);
const float *src_b = array_src_b + (size - 1);
int i = size;
while (i--) {
*(tar--) = *(src_a--) * *(src_b--);
}
}
void mul_vn_fl(float *array_tar, const int size, const float f)
{
float *array_pt = array_tar + (size - 1);
int i = size;
while (i--) {
*(array_pt--) *= f;
}
}
void mul_vn_vn_fl(float *array_tar, const float *array_src, const int size, const float f)
{
float *tar = array_tar + (size - 1);
const float *src = array_src + (size - 1);
int i = size;
while (i--) {
*(tar--) = *(src--) * f;
}
}
void add_vn_vn(float *array_tar, const float *array_src, const int size)
{
float *tar = array_tar + (size - 1);
const float *src = array_src + (size - 1);
int i = size;
while (i--) {
*(tar--) += *(src--);
}
}
void add_vn_vnvn(float *array_tar,
const float *array_src_a,
const float *array_src_b,
const int size)
{
float *tar = array_tar + (size - 1);
const float *src_a = array_src_a + (size - 1);
const float *src_b = array_src_b + (size - 1);
int i = size;
while (i--) {
*(tar--) = *(src_a--) + *(src_b--);
}
}
void madd_vn_vn(float *array_tar, const float *array_src, const float f, const int size)
{
float *tar = array_tar + (size - 1);
const float *src = array_src + (size - 1);
int i = size;
while (i--) {
*(tar--) += *(src--) * f;
}
}
void madd_vn_vnvn(float *array_tar,
const float *array_src_a,
const float *array_src_b,
const float f,
const int size)
{
float *tar = array_tar + (size - 1);
const float *src_a = array_src_a + (size - 1);
const float *src_b = array_src_b + (size - 1);
int i = size;
while (i--) {
*(tar--) = *(src_a--) + (*(src_b--) * f);
}
}
void sub_vn_vn(float *array_tar, const float *array_src, const int size)
{
float *tar = array_tar + (size - 1);
const float *src = array_src + (size - 1);
int i = size;
while (i--) {
*(tar--) -= *(src--);
}
}
void sub_vn_vnvn(float *array_tar,
const float *array_src_a,
const float *array_src_b,
const int size)
{
float *tar = array_tar + (size - 1);
const float *src_a = array_src_a + (size - 1);
const float *src_b = array_src_b + (size - 1);
int i = size;
while (i--) {
*(tar--) = *(src_a--) - *(src_b--);
}
}
void msub_vn_vn(float *array_tar, const float *array_src, const float f, const int size)
{
float *tar = array_tar + (size - 1);
const float *src = array_src + (size - 1);
int i = size;
while (i--) {
*(tar--) -= *(src--) * f;
}
}
void msub_vn_vnvn(float *array_tar,
const float *array_src_a,
const float *array_src_b,
const float f,
const int size)
{
float *tar = array_tar + (size - 1);
const float *src_a = array_src_a + (size - 1);
const float *src_b = array_src_b + (size - 1);
int i = size;
while (i--) {
*(tar--) = *(src_a--) - (*(src_b--) * f);
}
}
void interp_vn_vn(float *array_tar, const float *array_src, const float t, const int size)
{
const float s = 1.0f - t;
float *tar = array_tar + (size - 1);
const float *src = array_src + (size - 1);
int i = size;
while (i--) {
*(tar) = (s * *(tar)) + (t * *(src));
tar--;
src--;
}
}
void copy_vn_i(int *array_tar, const int size, const int val)
{
int *tar = array_tar + (size - 1);
int i = size;
while (i--) {
*(tar--) = val;
}
}
void copy_vn_short(short *array_tar, const int size, const short val)
{
short *tar = array_tar + (size - 1);
int i = size;
while (i--) {
*(tar--) = val;
}
}
void copy_vn_ushort(ushort *array_tar, const int size, const ushort val)
{
ushort *tar = array_tar + (size - 1);
int i = size;
while (i--) {
*(tar--) = val;
}
}
void copy_vn_uchar(uchar *array_tar, const int size, const uchar val)
{
uchar *tar = array_tar + (size - 1);
int i = size;
while (i--) {
*(tar--) = val;
}
}
void copy_vn_fl(float *array_tar, const int size, const float val)
{
float *tar = array_tar + (size - 1);
int i = size;
while (i--) {
*(tar--) = val;
}
}
/** \name Double precision versions 'db'.
* \{ */
void add_vn_vn_d(double *array_tar, const double *array_src, const int size)
{
double *tar = array_tar + (size - 1);
const double *src = array_src + (size - 1);
int i = size;
while (i--) {
*(tar--) += *(src--);
}
}
void add_vn_vnvn_d(double *array_tar,
const double *array_src_a,
const double *array_src_b,
const int size)
{
double *tar = array_tar + (size - 1);
const double *src_a = array_src_a + (size - 1);
const double *src_b = array_src_b + (size - 1);
int i = size;
while (i--) {
*(tar--) = *(src_a--) + *(src_b--);
}
}
void mul_vn_db(double *array_tar, const int size, const double f)
{
double *array_pt = array_tar + (size - 1);
int i = size;
while (i--) {
*(array_pt--) *= f;
}
}
void interp_v3_v3v3_db(double target[3], const double a[3], const double b[3], const double t)
{
const double s = 1.0f - t;
target[0] = s * a[0] + t * b[0];
target[1] = s * a[1] + t * b[1];
target[2] = s * a[2] + t * b[2];
}
void interp_v2_v2v2_db(double target[2], const double a[2], const double b[2], const double t)
{
const double s = 1.0f - t;
target[0] = s * a[0] + t * b[0];
target[1] = s * a[1] + t * b[1];
}
/** \} */
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