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poseutils.c
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poseutils.c
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// Copyright (c) 2017-2023 California Institute of Technology ("Caltech"). U.S.
// Government sponsorship acknowledged. All rights reserved.
//
// Licensed under the Apache License, Version 2.0 (the "License");
// You may obtain a copy of the License at
//
// http://www.apache.org/licenses/LICENSE-2.0
// Apparently I need this in MSVC to get constants
#define _USE_MATH_DEFINES
#include <stdio.h>
#include <string.h>
#include <math.h>
#include "poseutils.h"
#include "strides.h"
#include "minimath/minimath.h"
// All arrays stored in row-major order
//
// I have two different representations of pose transformations:
//
// - Rt is a concatenated (4,3) array: Rt = nps.glue(R,t, axis=-2). The
// transformation is R*x+t
//
// - rt is a concatenated (6) array: rt = nps.glue(r,t, axis=-1). The
// transformation is R*x+t where R = R_from_r(r)
// row vectors: vout = matmult(v,Mt)
// equivalent col vector expression: vout = matmult(M,v)
#define mul_vec3_gen33t_vout_scaled_full(vout, vout_stride0, \
v, v_stride0, \
Mt, Mt_stride0, Mt_stride1, \
scale) \
do { \
/* needed for in-place operations */ \
double outcopy[3] = { \
scale * \
(_P2(Mt,Mt_stride0,Mt_stride1,0,0)*_P1(v,v_stride0,0) + \
_P2(Mt,Mt_stride0,Mt_stride1,0,1)*_P1(v,v_stride0,1) + \
_P2(Mt,Mt_stride0,Mt_stride1,0,2)*_P1(v,v_stride0,2) ), \
scale * \
(_P2(Mt,Mt_stride0,Mt_stride1,1,0)*_P1(v,v_stride0,0) + \
_P2(Mt,Mt_stride0,Mt_stride1,1,1)*_P1(v,v_stride0,1) + \
_P2(Mt,Mt_stride0,Mt_stride1,1,2)*_P1(v,v_stride0,2) ), \
scale * \
(_P2(Mt,Mt_stride0,Mt_stride1,2,0)*_P1(v,v_stride0,0) + \
_P2(Mt,Mt_stride0,Mt_stride1,2,1)*_P1(v,v_stride0,1) + \
_P2(Mt,Mt_stride0,Mt_stride1,2,2)*_P1(v,v_stride0,2) ) }; \
_P1(vout,vout_stride0,0) = outcopy[0]; \
_P1(vout,vout_stride0,1) = outcopy[1]; \
_P1(vout,vout_stride0,2) = outcopy[2]; \
} while(0)
#define mul_vec3_gen33t_vout_full(vout, vout_stride0, \
v, v_stride0, \
Mt, Mt_stride0, Mt_stride1) \
mul_vec3_gen33t_vout_scaled_full(vout, vout_stride0, \
v, v_stride0, \
Mt, Mt_stride0, Mt_stride1, 1.0)
// row vectors: vout = scale*matmult(v,M)
#define mul_vec3_gen33_vout_scaled_full(vout, vout_stride0, \
v, v_stride0, \
M, M_stride0, M_stride1, \
scale) \
do { \
/* needed for in-place operations */ \
double outcopy[3] = { \
scale * \
(_P2(M,M_stride0,M_stride1,0,0)*_P1(v,v_stride0,0) + \
_P2(M,M_stride0,M_stride1,1,0)*_P1(v,v_stride0,1) + \
_P2(M,M_stride0,M_stride1,2,0)*_P1(v,v_stride0,2)), \
scale * \
(_P2(M,M_stride0,M_stride1,0,1)*_P1(v,v_stride0,0) + \
_P2(M,M_stride0,M_stride1,1,1)*_P1(v,v_stride0,1) + \
_P2(M,M_stride0,M_stride1,2,1)*_P1(v,v_stride0,2)), \
scale * \
(_P2(M,M_stride0,M_stride1,0,2)*_P1(v,v_stride0,0) + \
_P2(M,M_stride0,M_stride1,1,2)*_P1(v,v_stride0,1) + \
_P2(M,M_stride0,M_stride1,2,2)*_P1(v,v_stride0,2)) }; \
_P1(vout,vout_stride0,0) = outcopy[0]; \
_P1(vout,vout_stride0,1) = outcopy[1]; \
_P1(vout,vout_stride0,2) = outcopy[2]; \
} while(0)
#define mul_vec3_gen33_vout_full(vout, vout_stride0, \
v, v_stride0, \
Mt, Mt_stride0, Mt_stride1) \
mul_vec3_gen33_vout_scaled_full(vout, vout_stride0, \
v, v_stride0, \
Mt, Mt_stride0, Mt_stride1, 1.0)
// row vectors: vout = matmult(v,Mt)
// equivalent col vector expression: vout = matmult(M,v)
#define mul_vec3_gen33t_vaccum_full(vout, vout_stride0, \
v, v_stride0, \
Mt, Mt_stride0, Mt_stride1) \
do { \
/* needed for in-place operations */ \
double outcopy[3] = { \
_P1(vout,vout_stride0,0) + \
_P2(Mt,Mt_stride0,Mt_stride1,0,0)*_P1(v,v_stride0,0) + \
_P2(Mt,Mt_stride0,Mt_stride1,0,1)*_P1(v,v_stride0,1) + \
_P2(Mt,Mt_stride0,Mt_stride1,0,2)*_P1(v,v_stride0,2), \
_P1(vout,vout_stride0,1) + \
_P2(Mt,Mt_stride0,Mt_stride1,1,0)*_P1(v,v_stride0,0) + \
_P2(Mt,Mt_stride0,Mt_stride1,1,1)*_P1(v,v_stride0,1) + \
_P2(Mt,Mt_stride0,Mt_stride1,1,2)*_P1(v,v_stride0,2), \
_P1(vout,vout_stride0,2) + \
_P2(Mt,Mt_stride0,Mt_stride1,2,0)*_P1(v,v_stride0,0) + \
_P2(Mt,Mt_stride0,Mt_stride1,2,1)*_P1(v,v_stride0,1) + \
_P2(Mt,Mt_stride0,Mt_stride1,2,2)*_P1(v,v_stride0,2) }; \
_P1(vout,vout_stride0,0) = outcopy[0]; \
_P1(vout,vout_stride0,1) = outcopy[1]; \
_P1(vout,vout_stride0,2) = outcopy[2]; \
} while(0)
// row vectors: vout = scale*matmult(v,M)
#define mul_vec3_gen33_vaccum_scaled_full(vout, vout_stride0, \
v, v_stride0, \
M, M_stride0, M_stride1, \
scale) \
do { \
/* needed for in-place operations */ \
double outcopy[3] = { \
_P1(vout,vout_stride0,0) + scale * \
(_P2(M,M_stride0,M_stride1,0,0)*_P1(v,v_stride0,0) + \
_P2(M,M_stride0,M_stride1,1,0)*_P1(v,v_stride0,1) + \
_P2(M,M_stride0,M_stride1,2,0)*_P1(v,v_stride0,2)), \
_P1(vout,vout_stride0,1) + scale * \
(_P2(M,M_stride0,M_stride1,0,1)*_P1(v,v_stride0,0) + \
_P2(M,M_stride0,M_stride1,1,1)*_P1(v,v_stride0,1) + \
_P2(M,M_stride0,M_stride1,2,1)*_P1(v,v_stride0,2)), \
_P1(vout,vout_stride0,2) + scale * \
(_P2(M,M_stride0,M_stride1,0,2)*_P1(v,v_stride0,0) + \
_P2(M,M_stride0,M_stride1,1,2)*_P1(v,v_stride0,1) + \
_P2(M,M_stride0,M_stride1,2,2)*_P1(v,v_stride0,2)) }; \
_P1(vout,vout_stride0,0) = outcopy[0]; \
_P1(vout,vout_stride0,1) = outcopy[1]; \
_P1(vout,vout_stride0,2) = outcopy[2]; \
} while(0)
// multiply two (3,3) matrices
static inline
void mul_gen33_gen33_vout_full(// output
double* m0m1,
int m0m1_stride0, int m0m1_stride1,
// input
const double* m0,
int m0_stride0, int m0_stride1,
const double* m1,
int m1_stride0, int m1_stride1)
{
/* needed for in-place operations */
double outcopy2[9];
for(int i=0; i<3; i++)
// one row at a time
mul_vec3_gen33_vout_scaled_full(&outcopy2[i*3], sizeof(outcopy2[0]),
&_P2(m0 , m0_stride0, m0_stride1, i,0), m0_stride1,
m1, m1_stride0, m1_stride1,
1.0);
for(int i=0; i<3; i++)
for(int j=0; j<3; j++)
P2(m0m1, i,j) = outcopy2[3*i+j];
}
static inline
double inner3(const double* restrict a,
const double* restrict b)
{
double s = 0.0;
for (int i=0; i<3; i++) s += a[i]*b[i];
return s;
}
// Make an identity rotation or transformation
void mrcal_identity_R_full(double* R, // (3,3) array
int R_stride0, // in bytes. <= 0 means "contiguous"
int R_stride1 // in bytes. <= 0 means "contiguous"
)
{
init_stride_2D(R, 3,3);
P2(R, 0,0) = 1.0; P2(R, 0,1) = 0.0; P2(R, 0,2) = 0.0;
P2(R, 1,0) = 0.0; P2(R, 1,1) = 1.0; P2(R, 1,2) = 0.0;
P2(R, 2,0) = 0.0; P2(R, 2,1) = 0.0; P2(R, 2,2) = 1.0;
}
void mrcal_identity_r_full(double* r, // (3,) array
int r_stride0 // in bytes. <= 0 means "contiguous"
)
{
init_stride_1D(r, 3);
P1(r, 0) = 0.0; P1(r, 1) = 0.0; P1(r, 2) = 0.0;
}
void mrcal_identity_Rt_full(double* Rt, // (4,3) array
int Rt_stride0, // in bytes. <= 0 means "contiguous"
int Rt_stride1 // in bytes. <= 0 means "contiguous"
)
{
init_stride_2D(Rt, 4,3);
mrcal_identity_R_full(Rt, Rt_stride0, Rt_stride1);
for(int i=0; i<3; i++) P2(Rt, 3, i) = 0.0;
}
void mrcal_identity_rt_full(double* rt, // (6,) array
int rt_stride0 // in bytes. <= 0 means "contiguous"
)
{
init_stride_1D(rt, 6);
mrcal_identity_r_full(rt, rt_stride0);
for(int i=0; i<3; i++) P1(rt, i+3) = 0.0;
}
void mrcal_rotate_point_R_full( // output
double* x_out, // (3,) array
int x_out_stride0, // in bytes. <= 0 means "contiguous"
double* J_R, // (3,3,3) array. May be NULL
int J_R_stride0, // in bytes. <= 0 means "contiguous"
int J_R_stride1, // in bytes. <= 0 means "contiguous"
int J_R_stride2, // in bytes. <= 0 means "contiguous"
double* J_x, // (3,3) array. May be NULL
int J_x_stride0, // in bytes. <= 0 means "contiguous"
int J_x_stride1, // in bytes. <= 0 means "contiguous"
// input
const double* R, // (3,3) array. May be NULL
int R_stride0, // in bytes. <= 0 means "contiguous"
int R_stride1, // in bytes. <= 0 means "contiguous"
const double* x_in, // (3,) array. May be NULL
int x_in_stride0, // in bytes. <= 0 means "contiguous"
bool inverted // if true, I apply a
// rotation in the opposite
// direction. J_R corresponds
// to the input R
)
{
init_stride_1D(x_out, 3);
init_stride_3D(J_R, 3,3,3 );
init_stride_2D(J_x, 3,3 );
init_stride_2D(R, 3,3 );
init_stride_1D(x_in, 3 );
if(inverted)
{
// transpose R
int tmp;
tmp = R_stride0;
R_stride0 = R_stride1;
R_stride1 = tmp;
tmp = J_R_stride1;
J_R_stride1 = J_R_stride2;
J_R_stride2 = tmp;
}
if(J_R)
{
// out[i] = inner(R[i,:],in)
for(int i=0; i<3; i++)
{
int j=0;
for(; j<i; j++)
for(int k=0; k<3; k++)
P3(J_R, i,j,k) = 0.0;
for(int k=0; k<3; k++)
P3(J_R, i,j,k) = P1(x_in, k);
for(j++; j<3; j++)
for(int k=0; k<3; k++)
P3(J_R, i,j,k) = 0.0;
}
}
if(J_x)
for(int i=0; i<3; i++)
for(int j=0; j<3; j++)
P2(J_x, i,j) = P2(R, i,j);
// R*x
mul_vec3_gen33t_vout_full(x_out, x_out_stride0,
x_in, x_in_stride0,
R, R_stride0, R_stride1);
}
// mrcal_rotate_point_r() uses auto-differentiation, so it's implemented in C++
// in poseutils-uses-autodiff.cc
// Apply a transformation to a point
void mrcal_transform_point_Rt_full( // output
double* x_out, // (3,) array
int x_out_stride0, // in bytes. <= 0 means "contiguous"
double* J_Rt, // (3,4,3) array. May be NULL
int J_Rt_stride0, // in bytes. <= 0 means "contiguous"
int J_Rt_stride1, // in bytes. <= 0 means "contiguous"
int J_Rt_stride2, // in bytes. <= 0 means "contiguous"
double* J_x, // (3,3) array. May be NULL
int J_x_stride0, // in bytes. <= 0 means "contiguous"
int J_x_stride1, // in bytes. <= 0 means "contiguous"
// input
const double* Rt, // (4,3) array. May be NULL
int Rt_stride0, // in bytes. <= 0 means "contiguous"
int Rt_stride1, // in bytes. <= 0 means "contiguous"
const double* x_in, // (3,) array. May be NULL
int x_in_stride0, // in bytes. <= 0 means "contiguous"
bool inverted // if true, I apply a
// transformation in the opposite
// direction. J_Rt corresponds
// to the input Rt
)
{
init_stride_1D(x_out, 3);
init_stride_3D(J_Rt, 3,4,3 );
// init_stride_2D(J_x, 3,3 );
init_stride_2D(Rt, 4,3 );
// init_stride_1D(x_in, 3 );
if(!inverted)
{
// for in-place operation
double t[] = { P2(Rt,3,0), P2(Rt,3,1), P2(Rt,3,2) };
// I want R*x + t
// First R*x
mrcal_rotate_point_R_full(x_out, x_out_stride0,
J_Rt, J_Rt_stride0, J_Rt_stride1, J_Rt_stride2,
J_x, J_x_stride0, J_x_stride1,
Rt, Rt_stride0, Rt_stride1,
x_in, x_in_stride0,
false);
// And now +t. The J_R, J_x gradients are unaffected. J_t is identity
for(int i=0; i<3; i++)
P1(x_out,i) += t[i];
if(J_Rt)
mrcal_identity_R_full(&P3(J_Rt,0,3,0), J_Rt_stride0, J_Rt_stride2);
}
else
{
// inverted operation means
// y = transpose(R) (x - t)
double x_minus_t[] = { P1(x_in,0) - P2(Rt,3,0),
P1(x_in,1) - P2(Rt,3,1),
P1(x_in,2) - P2(Rt,3,2)};
// Compute. After this:
// x_out is done
// J_R is done
// J_x is done
mrcal_rotate_point_R_full(x_out, x_out_stride0,
J_Rt, J_Rt_stride0, J_Rt_stride1, J_Rt_stride2,
J_x, J_x_stride0, J_x_stride1,
Rt, Rt_stride0, Rt_stride1,
x_minus_t, sizeof(double),
true);
// I want J_t = -transpose(R)
if(J_Rt)
for(int i=0; i<3; i++)
for(int j=0; j<3; j++)
P3(J_Rt, i, 3, j) = -P2(Rt, j, i);
}
}
// Invert a rotation matrix. This is a transpose
//
// The input is given in R_in in a (3,3) array
//
// The result is returned in a (3,3) array R_out. In-place operation is
// supported
void mrcal_invert_R_full( // output
double* R_out, // (3,3) array
int R_out_stride0, // in bytes. <= 0 means "contiguous"
int R_out_stride1, // in bytes. <= 0 means "contiguous"
// input
const double* R_in, // (3,3) array
int R_in_stride0, // in bytes. <= 0 means "contiguous"
int R_in_stride1 // in bytes. <= 0 means "contiguous"
)
{
init_stride_2D(R_out, 3,3);
init_stride_2D(R_in, 3,3);
// transpose(R). Extra stuff to make in-place operations work
for(int i=0; i<3; i++)
P2(R_out,i,i) = P2(R_in,i,i);
for(int i=0; i<3; i++)
for(int j=i+1; j<3; j++)
{
double tmp = P2(R_in,i,j);
P2(R_out,i,j) = P2(R_in,j,i);
P2(R_out,j,i) = tmp;
}
}
// Convert a transformation representation from Rt to rt. This is mostly a
// convenience functions since 99% of the work is done by mrcal_r_from_R().
void mrcal_rt_from_Rt_full(// output
double* rt, // (6,) vector
int rt_stride0, // in bytes. <= 0 means "contiguous"
double* J_R, // (3,3,3) array. Gradient. May be NULL
// No J_t. It's always the identity
int J_R_stride0, // in bytes. <= 0 means "contiguous"
int J_R_stride1, // in bytes. <= 0 means "contiguous"
int J_R_stride2, // in bytes. <= 0 means "contiguous"
// input
const double* Rt, // (4,3) array
int Rt_stride0, // in bytes. <= 0 means "contiguous"
int Rt_stride1 // in bytes. <= 0 means "contiguous"
)
{
mrcal_r_from_R_full(rt, rt_stride0,
J_R, J_R_stride0, J_R_stride1, J_R_stride2,
Rt, Rt_stride0, Rt_stride1);
init_stride_1D(rt, 6);
// init_stride_3D(J_R, 3,3,3);
init_stride_2D(Rt, 4,3);
for(int i=0; i<3; i++)
P1(rt, i+3) = P2(Rt,3,i);
}
// Convert a transformation representation from Rt to rt. This is mostly a
// convenience functions since 99% of the work is done by mrcal_R_from_r().
void mrcal_Rt_from_rt_full(// output
double* Rt, // (4,3) array
int Rt_stride0, // in bytes. <= 0 means "contiguous"
int Rt_stride1, // in bytes. <= 0 means "contiguous"
double* J_r, // (3,3,3) array. Gradient. May be NULL
// No J_t. It's just the identity
int J_r_stride0, // in bytes. <= 0 means "contiguous"
int J_r_stride1, // in bytes. <= 0 means "contiguous"
int J_r_stride2, // in bytes. <= 0 means "contiguous"
// input
const double* rt, // (6,) vector
int rt_stride0 // in bytes. <= 0 means "contiguous"
)
{
mrcal_R_from_r_full(Rt, Rt_stride0, Rt_stride1,
J_r, J_r_stride0, J_r_stride1, J_r_stride2,
rt, rt_stride0);
init_stride_1D(rt, 6);
// init_stride_3D(J_r, 3,3,3);
init_stride_2D(Rt, 4,3);
for(int i=0; i<3; i++)
P2(Rt,3,i) = P1(rt,i+3);
}
// Invert an Rt transformation
//
// b = Ra + t -> a = R'b - R't
void mrcal_invert_Rt_full( // output
double* Rt_out, // (4,3) array
int Rt_out_stride0, // in bytes. <= 0 means "contiguous"
int Rt_out_stride1, // in bytes. <= 0 means "contiguous"
// input
const double* Rt_in, // (4,3) array
int Rt_in_stride0, // in bytes. <= 0 means "contiguous"
int Rt_in_stride1 // in bytes. <= 0 means "contiguous"
)
{
init_stride_2D(Rt_out, 4,3);
init_stride_2D(Rt_in, 4,3);
// transpose(R). Extra stuff to make in-place operations work
for(int i=0; i<3; i++)
P2(Rt_out,i,i) = P2(Rt_in,i,i);
for(int i=0; i<3; i++)
for(int j=i+1; j<3; j++)
{
double tmp = P2(Rt_in,i,j);
P2(Rt_out,i,j) = P2(Rt_in,j,i);
P2(Rt_out,j,i) = tmp;
}
// -transpose(R)*t
mul_vec3_gen33t_vout_scaled_full(&P2(Rt_out,3,0), Rt_out_stride1,
&P2(Rt_in, 3,0), Rt_in_stride1,
Rt_out, Rt_out_stride0, Rt_out_stride1,
-1.0);
}
// Invert an rt transformation
//
// b = rotate(a) + t -> a = invrotate(b) - invrotate(t)
//
// drout_drin is not returned: it is always -I
// drout_dtin is not returned: it is always 0
void mrcal_invert_rt_full( // output
double* rt_out, // (6,) array
int rt_out_stride0, // in bytes. <= 0 means "contiguous"
double* dtout_drin, // (3,3) array
int dtout_drin_stride0, // in bytes. <= 0 means "contiguous"
int dtout_drin_stride1, // in bytes. <= 0 means "contiguous"
double* dtout_dtin, // (3,3) array
int dtout_dtin_stride0, // in bytes. <= 0 means "contiguous"
int dtout_dtin_stride1, // in bytes. <= 0 means "contiguous"
// input
const double* rt_in, // (6,) array
int rt_in_stride0 // in bytes. <= 0 means "contiguous"
)
{
init_stride_1D(rt_out, 6);
// init_stride_2D(dtout_drin, 3,3);
init_stride_2D(dtout_dtin, 3,3);
init_stride_1D(rt_in, 6);
// r uses an angle-axis representation, so to undo a rotation r, I can apply
// a rotation -r (same axis, equal and opposite angle)
for(int i=0; i<3; i++)
P1(rt_out,i) = -P1(rt_in,i);
mrcal_rotate_point_r_full( &P1(rt_out,3), rt_out_stride0,
dtout_drin, dtout_drin_stride0, dtout_drin_stride1,
dtout_dtin, dtout_dtin_stride0, dtout_dtin_stride1,
// input
rt_out, rt_out_stride0,
&P1(rt_in,3), rt_in_stride0,
false);
for(int i=0; i<3; i++)
P1(rt_out,3+i) *= -1.;
if(dtout_dtin)
for(int i=0; i<3; i++)
for(int j=0; j<3; j++)
P2(dtout_dtin,i,j) *= -1.;
}
// Compose two Rt transformations
// R0*(R1*x + t1) + t0 =
// (R0*R1)*x + R0*t1+t0
void mrcal_compose_Rt_full( // output
double* Rt_out, // (4,3) array
int Rt_out_stride0, // in bytes. <= 0 means "contiguous"
int Rt_out_stride1, // in bytes. <= 0 means "contiguous"
// input
const double* Rt_0, // (4,3) array
int Rt_0_stride0, // in bytes. <= 0 means "contiguous"
int Rt_0_stride1, // in bytes. <= 0 means "contiguous"
const double* Rt_1, // (4,3) array
int Rt_1_stride0, // in bytes. <= 0 means "contiguous"
int Rt_1_stride1 // in bytes. <= 0 means "contiguous"
)
{
init_stride_2D(Rt_out, 4,3);
init_stride_2D(Rt_0, 4,3);
init_stride_2D(Rt_1, 4,3);
// for in-place operation
double t0[] = { P2(Rt_0,3,0),
P2(Rt_0,3,1),
P2(Rt_0,3,2) };
// t <- R0*t1
mul_vec3_gen33t_vout_full(&P2(Rt_out,3,0), Rt_out_stride1,
&P2(Rt_1, 3,0), Rt_1_stride1,
Rt_0, Rt_0_stride0, Rt_0_stride1);
// R <- R0*R1
mul_gen33_gen33_vout_full( Rt_out, Rt_out_stride0, Rt_out_stride1,
Rt_0, Rt_0_stride0, Rt_0_stride1,
Rt_1, Rt_1_stride0, Rt_1_stride1 );
// t <- R0*t1+t0
for(int i=0; i<3; i++)
P2(Rt_out,3,i) += t0[i];
}
// Compose two rt transformations. It is assumed that we're getting no gradients
// at all or we're getting ALL the gradients: only dr_r0 is checked for NULL
//
// dr_dt0 is not returned: it is always 0
// dr_dt1 is not returned: it is always 0
// dt_dr1 is not returned: it is always 0
// dt_dt0 is not returned: it is always the identity matrix
void mrcal_compose_rt_full( // output
double* rt_out, // (6,) array
int rt_out_stride0, // in bytes. <= 0 means "contiguous"
double* dr_r0, // (3,3) array; may be NULL
int dr_r0_stride0, // in bytes. <= 0 means "contiguous"
int dr_r0_stride1, // in bytes. <= 0 means "contiguous"
double* dr_r1, // (3,3) array; may be NULL
int dr_r1_stride0, // in bytes. <= 0 means "contiguous"
int dr_r1_stride1, // in bytes. <= 0 means "contiguous"
double* dt_r0, // (3,3) array; may be NULL
int dt_r0_stride0, // in bytes. <= 0 means "contiguous"
int dt_r0_stride1, // in bytes. <= 0 means "contiguous"
double* dt_t1, // (3,3) array; may be NULL
int dt_t1_stride0, // in bytes. <= 0 means "contiguous"
int dt_t1_stride1, // in bytes. <= 0 means "contiguous"
// input
const double* rt_0, // (6,) array
int rt_0_stride0, // in bytes. <= 0 means "contiguous"
const double* rt_1, // (6,) array
int rt_1_stride0 // in bytes. <= 0 means "contiguous"
)
{
init_stride_1D(rt_out, 6);
init_stride_2D(dr_r0, 3,3);
init_stride_2D(dr_r1, 3,3);
init_stride_2D(dt_r0, 3,3);
init_stride_2D(dt_t1, 3,3);
init_stride_1D(rt_0, 6);
init_stride_1D(rt_1, 6);
// r0 (r1 x + t1) + t0 = r0 r1 x + r0 t1 + t0
// -> I want (r0 r1, r0 t1 + t0)
// to make in-place operation work
double rt0[6];
for(int i=0; i<6; i++)
rt0[i] = P1(rt_0, i);
// Compute r01
mrcal_compose_r_full( rt_out, rt_out_stride0,
dr_r0, dr_r0_stride0, dr_r0_stride1,
dr_r1, dr_r1_stride0, dr_r1_stride1,
rt_0, rt_0_stride0,
rt_1, rt_1_stride0);
// t01 <- r0 t1
mrcal_rotate_point_r_full( &P1(rt_out,3), rt_out_stride0,
dt_r0, dt_r0_stride0, dt_r0_stride1,
dt_t1, dt_t1_stride0, dt_t1_stride1,
rt0, -1,
&P1(rt_1,3), rt_1_stride0,
false );
// t01 <- r0 t1 + t0
for(int i=0; i<3; i++)
P1(rt_out,3+i) += rt0[3+i];
}
void mrcal_compose_r_tinyr0_gradientr0_full( // output
double* dr_dr0, // (3,3) array; may be NULL
int dr_dr0_stride0, // in bytes. <= 0 means "contiguous"
int dr_dr0_stride1, // in bytes. <= 0 means "contiguous"
// input
const double* r_1, // (3,) array
int r_1_stride0 // in bytes. <= 0 means "contiguous"
)
{
init_stride_2D(dr_dr0, 3, 3);
init_stride_1D(r_1, 3);
// All the comments and logic appear in compose_r_core() in
// poseutils-uses-autodiff.cc. This is a special-case function with
// manually-computed gradients (because I want to make sure they're fast)
double norm2_r1 = 0.0;
for(int i=0; i<3; i++)
norm2_r1 += P1(r_1,i)*P1(r_1,i);
if(norm2_r1 < 2e-8*2e-8)
{
// Both vectors are tiny, so I have r01 = r0 + r1, and the gradient is
// an identity matrix
for(int i=0; i<3; i++)
for(int j=0; j<3; j++)
P2(dr_dr0,i,j) = i==j ? 1.0 : 0.0;
return;
}
// I'm computing
// R(angle=gamma, axis=n) =
// compose( R(angle=alpha, axis=l), R(angle=beta, axis=m) )
// where
// A = alpha/2
// B = beta /2
// I have
// r01 = r1
// - inner(r0,r1) (B/tanB - 1) / 4B^2 r1
// + B/tanB r0
// + cross(r0,r1) / 2
//
// I differentiate:
//
// dr01/dr0 =
// - outer(r1,r1) (B/tanB - 1) / 4B^2
// + B/tanB I
// - skew_symmetric(r1) / 2
double B = sqrt(norm2_r1) / 2.;
double B_over_tanB = B / tan(B);
for(int i=0; i<3; i++)
for(int j=0; j<3; j++)
P2(dr_dr0,i,j) =
- P1(r_1,i)*P1(r_1,j) * (B_over_tanB - 1.) / (4.*B*B);
for(int i=0; i<3; i++)
P2(dr_dr0,i,i) +=
B_over_tanB;
P2(dr_dr0,0,1) -= -P1(r_1,2)/2.;
P2(dr_dr0,0,2) -= P1(r_1,1)/2.;
P2(dr_dr0,1,0) -= P1(r_1,2)/2.;
P2(dr_dr0,1,2) -= -P1(r_1,0)/2.;
P2(dr_dr0,2,0) -= -P1(r_1,1)/2.;
P2(dr_dr0,2,1) -= P1(r_1,0)/2.;
}
void mrcal_compose_r_tinyr1_gradientr1_full( // output
double* dr_dr1, // (3,3) array; may be NULL
int dr_dr1_stride0, // in bytes. <= 0 means "contiguous"
int dr_dr1_stride1, // in bytes. <= 0 means "contiguous"
// input
const double* r_0, // (3,) array
int r_0_stride0 // in bytes. <= 0 means "contiguous"
)
{
init_stride_2D(dr_dr1, 3, 3);
init_stride_1D(r_0, 3);
// All the comments and logic appear in compose_r_core() in
// poseutils-uses-autodiff.cc. This is a special-case function with
// manually-computed gradients (because I want to make sure they're fast)
double norm2_r0 = 0.0;
for(int i=0; i<3; i++)
norm2_r0 += P1(r_0,i)*P1(r_0,i);
if(norm2_r0 < 2e-8*2e-8)
{
// Both vectors are tiny, so I have r01 = r0 + r1, and the gradient is
// an identity matrix
for(int i=0; i<3; i++)
for(int j=0; j<3; j++)
P2(dr_dr1,i,j) = i==j ? 1.0 : 0.0;
return;
}
// I'm computing
// R(angle=gamma, axis=n) =
// compose( R(angle=alpha, axis=l), R(angle=beta, axis=m) )
// where
// A = alpha/2
// B = beta /2
// I have
// r01 = r0
// - inner(r0,r1) (A/tanA - 1) / 4A^2 r0
// + A/tanA r1
// + cross(r0,r1) / 2
//
// I differentiate:
//
// dr01/dr1 =
// - outer(r0,r0) (A/tanA - 1) / 4A^2
// + A/tanA I
// + skew_symmetric(r0) / 2
double A = sqrt(norm2_r0) / 2.;
double A_over_tanA = A / tan(A);
for(int i=0; i<3; i++)
for(int j=0; j<3; j++)
P2(dr_dr1,i,j) =
- P1(r_0,i)*P1(r_0,j) * (A_over_tanA - 1.) / (4.*A*A);
for(int i=0; i<3; i++)
P2(dr_dr1,i,i) +=
A_over_tanA;
P2(dr_dr1,0,1) += -P1(r_0,2)/2.;
P2(dr_dr1,0,2) += P1(r_0,1)/2.;
P2(dr_dr1,1,0) += P1(r_0,2)/2.;
P2(dr_dr1,1,2) += -P1(r_0,0)/2.;
P2(dr_dr1,2,0) += -P1(r_0,1)/2.;
P2(dr_dr1,2,1) += P1(r_0,0)/2.;
}
void mrcal_r_from_R_full( // output
double* r, // (3,) vector
int r_stride0, // in bytes. <= 0 means "contiguous"
double* J, // (3,3,3) array. Gradient. May be NULL
int J_stride0, // in bytes. <= 0 means "contiguous"
int J_stride1, // in bytes. <= 0 means "contiguous"
int J_stride2, // in bytes. <= 0 means "contiguous"
// input
const double* R, // (3,3) array
int R_stride0, // in bytes. <= 0 means "contiguous"
int R_stride1 // in bytes. <= 0 means "contiguous"
)
{
init_stride_1D(r, 3);
init_stride_3D(J, 3,3,3);
init_stride_2D(R, 3,3);
// Looking at https://en.wikipedia.org/wiki/Rodrigues%27_rotation_formula the
// Rodrigues rotation formula for th rad rotation around unit axis v is
//
// R = I + sin(th) V + (1 - cos(th)) V^2
//
// where V = skew_symmetric(v):
//
// [ 0 -v2 v1]
// V(v) = [ v2 0 -v0]
// [-v1 v0 0]
//
// and
//
// v(V) = [-V12, V02, -V01]
//
// I, V^2 are symmetric; V is anti-symmetric. So R - Rt = 2 sin(th) V
//
// Let's define
//
// [ R21 - R12 ]
// u = [ -R20 + R02 ] = v(R) - v(Rt)
// [ R10 - R01 ]
//
// From the above equations we see that u = 2 sin(th) v. So I compute the
// axis v = u/mag(u). I want th in [0,pi] so I can't compute th from u since
// there's an ambiguity: sin(th) = sin(pi-th). So instead, I compute th from
// trace(R) = 1 + 2*cos(th)
//
// There's an extra wrinkle here. Computing the axis from mag(u) only works
// if sin(th) != 0. So there are two special cases that must be handled: th
// ~ 0 and th ~ 180. If th ~ 0, then the axis doesn't matter and r ~ 0. If
// th ~ 180 then the axis DOES matter, and we need special logic.
const double tr = P2(R,0,0) + P2(R,1,1) + P2(R,2,2);
const double u[3] =
{
P2(R,2,1) - P2(R,1,2),
P2(R,0,2) - P2(R,2,0),
P2(R,1,0) - P2(R,0,1)
};
const double costh = (tr - 1.) / 2.;
// In radians. If my angle is this close to 0, I use the special-case paths
const double eps = 1e-8;
// near 0 we have norm2u ~ 4 th^2
const double norm2u =
u[0]*u[0] +
u[1]*u[1] +
u[2]*u[2];
if(// both conditions to handle roundoff error
norm2u > 4. * eps*eps &&
1. - fabs(costh) > eps*eps/2. )
{
// normal path
const double th = acos(costh);
for(int i=0; i<3; i++)
P1(r,i) = u[i]/sqrt(norm2u) * th;
}
else if(costh > 0)
{
// small th. Can't divide by it. But I can look at the limit.
//
// u / (2 sinth)*th = u/2 *th/sinth ~ u/2
for(int i=0; i<3; i++)
P1(r,i) = u[i] / 2.;
}
else
{
// cos(th) < 0. So th ~ +-180 = +-180 + dth where dth ~ 0. And I have
//
// R = I + sin(th) V + (1 - cos(th) ) V^2
// = I + sin(+-180 + dth) V + (1 - cos(+-180 + dth)) V^2
// = I - sin(dth) V + (1 + cos(dth)) V^2
// ~ I - dth V + 2 V^2
//
// Once again, I, V^2 are symmetric; V is anti-symmetric. So
//
// R - Rt = 2 sin(th) V
// = -2 sin(dth) V
// = -2 dth V
// I want
//
// r = th v
// = dth v +- 180deg v
//
// r = v((R - Rt) / -2.) +- 180deg v
// = u/-2 +- 180deg v
//
// Now we need v; let's look at the symmetric parts:
//
// R + Rt = 2 I + 4 V^2
//-> V^2 = (R + Rt)/4 - I/2
//
// [ 0 -v2 v1]
// V(v) = [ v2 0 -v0]
// [-v1 v0 0]
//
// [ -(v1^2+v2^2) v0 v1 v0 v2 ]
// V^2(v) = [ v0 v1 -(v0^2+v2^2) v1 v2 ]
// [ v0 v2 v1 v2 -(v0^2+v1^2) ]
//
// I want v be a unit vector. Can I assume that? From above:
//
// tr(V^2) = -2 norm2(v)
//
// So I want to assume that tr(V^2) = -2. The earlier expression had
//
// R + Rt = 2 I + 4 V^2
//
// -> tr(R + Rt) = tr(2 I + 4 V^2)
// -> tr(V^2) = (tr(R + Rt) - 6)/4
// = (2 tr(R) - 6)/4
// = (1 + 2*cos(th) - 3)/2
// = -1 + cos(th)
//
// Near th ~ 180deg, this is -2 as required. So we can assume that
// mag(v)=1:
//
// [ v0^2 - 1 v0 v1 v0 v2 ]
// V^2(v) = [ v0 v1 v1^2 - 1 v1 v2 ]
// [ v0 v2 v1 v2 v2^2 - 1 ]
//
// So
//
// v^2 = 1 + diag(V^2)
// = 1 + 2 diag(R)/4 - I/2
// = 1 + diag(R)/2 - 1/2
// = (1 + diag(R))/2
for(int i=0; i<3; i++)
P1(r,i) = u[i] / -2.;
// Now r += pi v
const double vsq[3] =
{
(P2(R,0,0) + 1.) /2.,
(P2(R,1,1) + 1.) /2.,
(P2(R,2,2) + 1.) /2.
};
// This is abs(v) initially
double v[3] = {};
for(int i=0; i<3; i++)
if(vsq[i] > 0.0)
v[i] = sqrt(vsq[i]);
else
{
// round-off sets this at 0; it's already there. Leave it
}
// Now I need to get the sign of each individual value. Overall, the
// sign of the vector v doesn't matter. I set the sign of a notably
// non-zero abs(v[i]) to >0, and go from there.
// threshold can be anything notably > 0. I'd like to encourage the same
// branch to always be taken, so I set the thresholds relatively low
if( v[0] > 0.1)
{
// I leave v[0]>0.
// V^2[0,1] must have the same sign as v1
// V^2[0,2] must have the same sign as v2
if( (P2(R,0,1) + P2(R,1,0)) < 0 ) v[1] *= -1.;
if( (P2(R,0,2) + P2(R,2,0)) < 0 ) v[2] *= -1.;
}
else if(v[1] > 0.1)
{
// I leave v[1]>0.
// V^2[1,0] must have the same sign as v0
// V^2[1,2] must have the same sign as v2
if( (P2(R,1,0) + P2(R,0,1)) < 0 ) v[0] *= -1.;
if( (P2(R,1,2) + P2(R,2,1)) < 0 ) v[2] *= -1.;
}
else
{
// I leave v[2]>0.
// V^2[2,0] must have the same sign as v0
// V^2[2,1] must have the same sign as v1
if( (P2(R,2,0) + P2(R,0,2)) < 0 ) v[0] *= -1.;
if( (P2(R,2,1) + P2(R,1,2)) < 0 ) v[1] *= -1.;
}
for(int i=0; i<3; i++)
P1(r,i) += v[i] * M_PI;
}
if(J != NULL)
{
// Not all (3,3) matrices R are valid rotations, and I make sure to evaluate