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#define _GNU_SOURCE
#include <math.h>
#include <float.h>
#include "poseutils.h"
#include "strides.h"
// The implementation of mrcal_R_from_r is based on opencv.
// The sources have been heavily modified, but the opencv logic remains.
//
// from opencv-4.1.2+dfsg/modules/calib3d/src/calibration.cpp
//
// Copyright (C) 2000-2008, Intel Corporation, all rights reserved.
// Copyright (C) 2009, Willow Garage Inc., all rights reserved.
// Third party copyrights are property of their respective owners.
//
// Redistribution and use in source and binary forms, with or without modification,
// are permitted provided that the following conditions are met:
//
// * Redistribution's of source code must retain the above copyright notice,
// this list of conditions and the following disclaimer.
//
// * Redistribution's in binary form must reproduce the above copyright notice,
// this list of conditions and the following disclaimer in the documentation
// and/or other materials provided with the distribution.
//
// * The name of the copyright holders may not be used to endorse or promote products
// derived from this software without specific prior written permission.
//
// This software is provided by the copyright holders and contributors "as is" and
// any express or implied warranties, including, but not limited to, the implied
// warranties of merchantability and fitness for a particular purpose are disclaimed.
// In no event shall the Intel Corporation or contributors be liable for any direct,
// indirect, incidental, special, exemplary, or consequential damages
// (including, but not limited to, procurement of substitute goods or services;
// loss of use, data, or profits; or business interruption) however caused
// and on any theory of liability, whether in contract, strict liability,
// or tort (including negligence or otherwise) arising in any way out of
void mrcal_R_from_r_full( // outputs
double* R, // (3,3) array
int R_stride0, // in bytes. <= 0 means "contiguous"
int R_stride1, // 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,) vector
int r_stride0 // in bytes. <= 0 means "contiguous"
)
{
init_stride_2D(R, 3,3);
init_stride_3D(J, 3,3,3 );
init_stride_1D(r, 3 );
double norm2r = 0.0;
for(int i=0; i<3; i++)
norm2r += P1(r,i)*P1(r,i);
if( norm2r < DBL_EPSILON*DBL_EPSILON )
{
mrcal_identity_R_full(R, R_stride0, R_stride1);
if( J )
{
for(int i=0; i<3; i++)
for(int j=0; j<3; j++)
for(int k=0; k<3; k++)
P3(J,i,j,k) = 0.;
P3(J,1,2,0) = -1.;
P3(J,2,0,1) = -1.;
P3(J,0,1,2) = -1.;
P3(J,2,1,0) = 1.;
P3(J,0,2,1) = 1.;
P3(J,1,0,2) = 1.;
}
return;
}
double theta = sqrt(norm2r);
double c,s;
sincos(theta, &s, &c);
double c1 = 1. - c;
double itheta = 1./theta;
double r_unit[3];
for(int i=0; i<3; i++)
r_unit[i] = P1(r,i) * itheta;
// R = cos(theta)*I + (1 - cos(theta))*r*rT + sin(theta)*[r_x]
P2(R, 0,0) = c + c1*r_unit[0]*r_unit[0];
P2(R, 0,1) = c1*r_unit[0]*r_unit[1] - s*r_unit[2];
P2(R, 0,2) = c1*r_unit[0]*r_unit[2] + s*r_unit[1];
P2(R, 1,0) = c1*r_unit[0]*r_unit[1] + s*r_unit[2];
P2(R, 1,1) = c + c1*r_unit[1]*r_unit[1];
P2(R, 1,2) = c1*r_unit[1]*r_unit[2] - s*r_unit[0];
P2(R, 2,0) = c1*r_unit[0]*r_unit[2] - s*r_unit[1];
P2(R, 2,1) = c1*r_unit[1]*r_unit[2] + s*r_unit[0];
P2(R, 2,2) = c + c1*r_unit[2]*r_unit[2];
if( J )
{
// opencv had some logic with lots of 0s. I unrolled all of the
// loops, and removed all the resulting 0 terms
double a0, a1, a3;
double a2 = itheta * c1;
double a4 = itheta * s;
a0 = -s *r_unit[0];
a1 = (s - 2*a2)*r_unit[0];
a3 = (c - a4)*r_unit[0];
P3(J,0,0,0) = a0 + a1*r_unit[0]*r_unit[0] + a2*(r_unit[0]+r_unit[0]);
P3(J,0,1,0) = a1*r_unit[0]*r_unit[1] + a2*r_unit[1] - a3*r_unit[2];
P3(J,0,2,0) = a1*r_unit[0]*r_unit[2] + a2*r_unit[2] + a3*r_unit[1];
P3(J,1,0,0) = a1*r_unit[0]*r_unit[1] + a2*r_unit[1] + a3*r_unit[2];
P3(J,1,1,0) = a0 + a1*r_unit[1]*r_unit[1];
P3(J,1,2,0) = a1*r_unit[1]*r_unit[2] - a3*r_unit[0] - a4;
P3(J,2,0,0) = a1*r_unit[0]*r_unit[2] + a2*r_unit[2] - a3*r_unit[1];
P3(J,2,1,0) = a1*r_unit[1]*r_unit[2] + a3*r_unit[0] + a4;
P3(J,2,2,0) = a0 + a1*r_unit[2]*r_unit[2];
a0 = -s *r_unit[1];
a1 = (s - 2*a2)*r_unit[1];
a3 = (c - a4)*r_unit[1];
P3(J,0,0,1) = a0 + a1*r_unit[0]*r_unit[0];
P3(J,0,1,1) = a1*r_unit[0]*r_unit[1] + a2*r_unit[0] - a3*r_unit[2];
P3(J,0,2,1) = a1*r_unit[0]*r_unit[2] + a3*r_unit[1] + a4;
P3(J,1,0,1) = a1*r_unit[0]*r_unit[1] + a2*r_unit[0] + a3*r_unit[2];
P3(J,1,1,1) = a0 + a1*r_unit[1]*r_unit[1] + a2*(r_unit[1]+r_unit[1]);
P3(J,1,2,1) = a1*r_unit[1]*r_unit[2] + a2*r_unit[2] - a3*r_unit[0];
P3(J,2,0,1) = a1*r_unit[0]*r_unit[2] - a3*r_unit[1] - a4;
P3(J,2,1,1) = a1*r_unit[1]*r_unit[2] + a2*r_unit[2] + a3*r_unit[0];
P3(J,2,2,1) = a0 + a1*r_unit[2]*r_unit[2];
a0 = -s *r_unit[2];
a1 = (s - 2*a2)*r_unit[2];
a3 = (c - a4)*r_unit[2];
P3(J,0,0,2) = a0 + a1*r_unit[0]*r_unit[0];
P3(J,0,1,2) = a1*r_unit[0]*r_unit[1] - a3*r_unit[2] - a4;
P3(J,0,2,2) = a1*r_unit[0]*r_unit[2] + a2*r_unit[0] + a3*r_unit[1];
P3(J,1,0,2) = a1*r_unit[0]*r_unit[1] + a3*r_unit[2] + a4;
P3(J,1,1,2) = a0 + a1*r_unit[1]*r_unit[1];
P3(J,1,2,2) = a1*r_unit[1]*r_unit[2] + a2*r_unit[1] - a3*r_unit[0];
P3(J,2,0,2) = a1*r_unit[0]*r_unit[2] + a2*r_unit[0] - a3*r_unit[1];
P3(J,2,1,2) = a1*r_unit[1]*r_unit[2] + a2*r_unit[1] + a3*r_unit[0];
P3(J,2,2,2) = a0 + a1*r_unit[2]*r_unit[2] + a2*(r_unit[2]+r_unit[2]);
}
}
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