Data Structures | Functions
get_trans_matrix.cpp File Reference

Functions to find transfomations matrix for motion of >=3 points. More...

#include <stdio.h>
#include <stdlib.h>
#include <unistd.h>
#include <sys/ioctl.h>
#include <fcntl.h>
#include <signal.h>
#include <curses.h>
#include <string>
#include <time.h>
#include <vector>
#include <gsl/gsl_matrix.h>
#include <gsl/gsl_vector.h>
#include <gsl/gsl_blas.h>
#include <gsl/gsl_linalg.h>
#include <gsl/gsl_rng.h>
#include <gsl/gsl_randist.h>
#include <gsl/gsl_multifit_nlin.h>
#include <gsl/gsl_deriv.h>
#include <math.h>
#include "dataprocess.h"
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Data Structures

struct  g_vals
 Structure containing parameters necessary to calculate rotation matrix. More...

Functions

int get_trans_matrix (vector< double > &datapoints_base, vector< double > &datapoints_new, vector< vector< double > > &rotmat, vector< double > &p_vec)
 Takes in 3-d position data of a set of points in 2 poses and calculates the rotation matrix and translation vector.
void getavgvec (vector< double > &datavec, vector< double > &avgvec, int np)
 Get mean position vector.
void get_distri_matrices (gsl_matrix *G, gsl_matrix *P, vector< double > &datapoints_new, double *pav_ar, vector< double > &datapoints_base, double *a_ar)
 Get matrices that describe point distribution.
void get_matrix_adjoin (gsl_matrix *M, gsl_matrix *M_adj)
 Get matrix adjoint of given matrix (using gsl)
int sol_betas_fdf (gsl_vector *betas, void *g_vals, gsl_vector *err, gsl_matrix *J)
 Equation (and its Jacobian) to be solved using least squares.
int sol_betas_f (gsl_vector *betas, void *g_vals, gsl_vector *err)
 Equations to be solved using least squares.
int sol_betas_df (gsl_vector *betas, void *g_vals, gsl_matrix *J)
 Jacobian of set of equations to be solved using least squares.
int get_betas (double &b1, double &b2, double g1sq, double g2sq, double g3)
void getRot (gsl_matrix *R, gsl_matrix *G, gsl_matrix *GtG, double b1, double b2)

Detailed Description

Functions to find transfomations matrix for motion of >=3 points.

This file defines functions that will implement the method of Veldpaus, Woltring & Dortmans (1988) to calculate the best transformation matrix relating thigh marker set to the tibial marker set.

Function Documentation

int get_betas ( double &  b1,
double &  b2,
double  g1sq,
double  g2sq,
double  g3 
)

References g_vals::g1sq, g_vals::g2sq, print_results_lm(), sol_betas_df(), sol_betas_f(), sol_betas_fdf(), and solve_gsl_lm().

Referenced by get_trans_matrix().

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void get_distri_matrices ( gsl_matrix *  G,
gsl_matrix *  P,
vector< double > &  datapoints_new,
double *  pav_ar,
vector< double > &  datapoints_base,
double *  a_ar 
)

Get matrices that describe point distribution.

The function returns two matrices G and P given by the equations:

\[ G = \frac{1}{m} \times \sum_{i=1}^m ((p_i-p)(a_i-a)') \]

\[ P = \frac{1}{m} \times \sum_{i=1}^m ((p_i-p)(p_i-p)') \]

where $p_i$ = datapoints in the new pose, $p$ = average position vector for the points in new pose, $ a_i$ = datapoints in the old pose, $ a$ = average position vector for the points in old pose.

Parameters:
[out]GThe matrix relating point orientation in old pose to new pose
[out]PThe matrix describing point distribution, in new pose
[in]datapoints_newVector containing position data of all points in new pose
[in]pav_ar= array containing average position vector for the points in new pose
[in]datapoints_baseVector containing position data of all points in base pose
[in]a_ar= array containing average position vector for the points in base pose

References vect2double().

Referenced by get_trans_matrix().

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void get_matrix_adjoin ( gsl_matrix *  M,
gsl_matrix *  M_adj 
)

Get matrix adjoint of given matrix (using gsl)

References colcat(), and gsl_vector_cross_product3D().

Referenced by get_trans_matrix(), and getRot().

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int get_trans_matrix ( vector< double > &  datapoints_base,
vector< double > &  datapoints_new,
vector< vector< double > > &  rotmat,
vector< double > &  p_vec 
)

Takes in 3-d position data of a set of points in 2 poses and calculates the rotation matrix and translation vector.

Parameters:
[in]datapoints_baseThe co-ordinates of the points in the base frame
[in]datapoints_newThe co-ordinates of the points in the new frame
[out]rotmatThe 2-dimensional C++ Vector representing the Rotation matrix
[out]p_vecThe 1-dimensional C++ Vector representing the translation vector

This function is recommended over calc_trans_mat() in case we have position data for more than 3 points, and errors in position data are significant. It uses method of Veldpaus, Woltring & Dortmans (1988) to calculate the best transformation matrix relating thigh marker set to the tibial marker set.

References get_betas(), get_distri_matrices(), get_matrix_adjoin(), getavgvec(), getRot(), gsl_det(), and vect2double().

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void getavgvec ( vector< double > &  datavec,
vector< double > &  avgvec,
int  np 
)

Get mean position vector.

Referenced by get_trans_matrix().

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void getRot ( gsl_matrix *  R,
gsl_matrix *  G,
gsl_matrix *  GtG,
double  b1,
double  b2 
)

References get_matrix_adjoin(), and gsl_inverse().

Referenced by get_trans_matrix().

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int sol_betas_df ( gsl_vector *  betas,
void *  g_vals,
gsl_matrix *  J 
)

Jacobian of set of equations to be solved using least squares.

Jacobian is obtained as the matrix:

\[ J = \left[\begin{array}{cc} 2\beta_1 & -2 \\ -2g_3 & 2\beta_2 \end{array}\right] \]

Referenced by get_betas().

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int sol_betas_f ( gsl_vector *  betas,
void *  g_vals,
gsl_vector *  err 
)

Equations to be solved using least squares.

Equations are :

\[ \beta_1^2 - 2\beta_2 = g_1^2 \]

\[ \beta_2^2 -2\beta_1 g_3 = g_2^2 \]

Referenced by get_betas().

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int sol_betas_fdf ( gsl_vector *  betas,
void *  g_vals,
gsl_vector *  err,
gsl_matrix *  J 
)

Equation (and its Jacobian) to be solved using least squares.

Referenced by get_betas().

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