/**
 * @brief			Description: Algorithm module of robotics, according to the
 *					book[modern robotics : mechanics, planning, and control].
 * @file:			RobotAlgorithmModule.c
 * @author:			Brian
 * @date:			2019/03/01 12:23
 * Copyright(c) 	2019 Brian. All rights reserved.
 *					  
 * Contact 			https://blog.csdn.net/Galaxy_Robot
 * @note:     
 *@warning:
*/

#include "RobotAlgorithmModule.h"
#include <math.h>
#include <string.h>
#include <stdlib.h>
#include <stdio.h>

/**
*@brief					Description:use GrublersFormula calculate The number of degrees of 
*						freedom of a mechanism with links and joints.
*@param[in]		N		the number of links( including the ground ).
*@param[in]		m		the number of degrees of freedom of a rigid body.
*						(m = 3 for planar mechanisms and m = 6 for spatial mechanisms).
*@param[in]		J		the number of joints.
*@param[in]		f		the number of freedoms provided by each joint..
*@return				The number of degrees of freedom of a mechanism
*@note:					This formula holds only if all joint constraints are independent.
*						If they are not independent then the formula provides a lower 
*						bound on the number of degrees of freedom.
*@warning:
*/
int GrublersFormula(int m, int N, int J, int *f)
{
	int i;
	int dof;
	int c = 0;
	for (i=1;i<=J;i++)
	{
		c = c + f[i-1];
	}
	dof = m*(N - 1 - J) + c;
	return dof;
}

/**
*@brief Description: Make  matrix b equal to  matrix a.
*@param[in]			a		a 3 x 3  matrix.
*@param[out]		b		result,b=a.
*@return		No return value.
*@note:
*@warning:
*/
void Matrix3Equal(double a[][3], double b[][3])
{
	int i;
	int j;
	for (i = 0; i < 3; i++)
	{
		for (j = 0; j < 3; j++)
		{
			b[i][j] = a[i][j];
		}
	}
	return;
}

/**
*@brief Description: Make  matrix b equal to  matrix a.
*@param[in]			a		a 4 x 4  matrix.
*@param[out]		b		result,b=a.
*@return		No return value.
*@note:
*@warning:
*/
void Matrix4Equal(double a[][4], double b[][4])
{
	int i;
	int j;
	for (i = 0; i < 4; i++)
	{
		for (j = 0; j < 4; j++)
		{
			b[i][j] = a[i][j];
		}
	}
	return;
}


/**
*@brief Description:Calculate a 3 x 3  matrix add a 3 x 3  matrix.
*@param[in]		a		a 3 x 3  matrix.
*@param[in]		b		a 3 x 3  matrix.
*@param[out]	c		result of a+b.
*@return		No return value.
*@note:
*@warning:
*/
void Matrix3Add(double a[][3], double b[][3], double c[][3])
{
	int i;
	int j;
	for (i = 0; i < 3; i++)
	{
		for (j = 0; j < 3; j++)
		{
			c[i][j] = a[i][j] + b[i][j];
		}
	}
	return;
}

/**
*@brief Description:Calculate a 4 x 4  matrix add a 4 x 4  matrix.
*@param[in]		a		a 4 x 4  matrix.
*@param[in]		b		a 4 x 4  matrix.
*@param[out]	c		result of a+b.
*@return		No return value.
*@note:
*@warning:
*/
void Matrix4Add(double a[][4], double b[][4], double c[][4])
{
	int i;
	int j;
	for (i = 0; i < 4; i++)
	{
		for (j = 0; j < 4; j++)
		{
			c[i][j] = a[i][j] + b[i][j];
		}
	}
	return;
}

/**
*@brief Description:Calculate a 3 x 3  matrix Subtract a 3 x 3  matrix.
*@param[in]		a		a 3 x 3  matrix.
*@param[in]		b		a 3 x 3  matrix.
*@param[out]	c		result of a-b.
*@return		No return value.
*@note:
*@warning:
*/
void Matrix3Sub(double a[][3], double b[][3], double c[][3])
{
	int i;
	int j;
	for (i = 0; i < 3; i++)
	{
		for (j = 0; j < 3; j++)
		{
			c[i][j] = a[i][j] - b[i][j];
		}
	}
	return;
}

/**
*@brief Description:Calculate a 4 x 4  matrix Subtract a 4 x 4  matrix.
*@param[in]		a		a 4 x 4  matrix.
*@param[in]		b		a 4 x 4  matrix.
*@param[out]	c		result of a-b.
*@return		No return value.
*@note:
*@warning:
*/
void Matrix4Sub(double a[][4], double b[][4], double c[][4])
{
	int i;
	int j;
	for (i = 0; i < 4; i++)
	{
		for (j = 0; j < 4; j++)
		{
			c[i][j] = a[i][j] - b[i][j];
		}
	}
	return;
}

/**
*@brief Description: Calculate two 3 x 3  matrix multiplication. 
*@param[in]		a		a 3 x 3  matrix.		
*@param[in]		b		a 3 x 3  matrix.	
*@param[out]	c		result of a*b.
*@return		No return value.
*@note:
*@warning:
*/
void Matrix3Mult(double a[][3],double b[][3],double c[][3])
{
	int i;
	int j;
	int k;
	for (i=0;i<3;i++)
	{		
		for (j=0;j<3;j++)
		{
			c[i][j] = 0.0;
			for (k=0;k<3;k++)
			{
				c[i][j] = c[i][j] + a[i][k] * b[k][j];
			}

		}
	}
	return;
}

/**
*@brief Description: Calculate two 4 x 4  matrix multiplication.
*@param[in]		a		a 4 x 4  matrix.
*@param[in]		b		a 4 x 4  matrix.
*@param[out]	c		result of a*b.
*@return		No return value.
*@note:
*@warning:
*/
void Matrix4Mult(double a[][4], double b[][4], double c[][4])
{
	int i;
	int j;
	int k;
	for (i = 0; i < 4; i++)
	{
		for (j = 0; j < 4; j++)
		{
			c[i][j] = 0.0;
			for (k = 0; k < 4; k++)
			{
				c[i][j] = c[i][j] + a[i][k] * b[k][j];
			}

		}
	}
	return;
}


/**
*@brief Description: Calculate  3 x 3  matrix multiply a value.
*@param[in]		a		a 3 x 3  matrix.
*@param[in]		Value	a scalar value.
*@param[out]	c		result of a*Value.
*@return		No return value.
*@note:
*@warning:
*/
void Matrix3MultValue(double a[][3], double Value, double c[][3])
{
	int i;
	int j;
	for (i=0;i<3;i++)
	{
		for (j=0;j<3;j++)
		{
			c[i][j] = a[i][j] * Value;
		}
	}
	return;
}

/**
*@brief Description: Calculate  4 x 4  matrix multiply a value.
*@param[in]		a		a 4 x 4  matrix.
*@param[in]		Value	a scalar value.
*@param[out]	c		result of a*Value.
*@return		No return value.
*@note:
*@warning:
*/
void Matrix4MultValue(double a[][4], double Value, double c[][4])
{
	int i;
	int j;
	for (i = 0; i < 4; i++)
	{
		for (j = 0; j < 4; j++)
		{
			c[i][j] = a[i][j] * Value;
		}
	}
	return;
}


/**
*@brief Description:Computes the result of a 3 x 3 Matrix multiply a 3-vector.
*@param[in]		R			a 3 x 3 Matrix.
*@param[in]		vec1		an input of 3-vector.
*@param[out]	vec2		the output result of 3-vector.
*@return		No return value.
*@note:
*@warning:
*/
void Matrix3MultVec(double R[3][3], double vec1[3], double vec2[3])
{
	int i;
	int j;
	for (i=0;i<3;i++)
	{
		vec2[i] = 0;
		for (j=0;j<3;j++)
		{
			vec2[i] = vec2[i] + R[i][j] * vec1[j];
		}
	}
	return;
}

/**
*@brief Description:Computes a 3-vector add a 3-vector.
*@param[in]		vec1		a 3-vector.
*@param[in]		vec2		a 3-vector.
*@param[out]	vec3		result of vec1 + vec2;
*@return		No return value.
*@note:
*@warning:
*/
void Vec3Add(double vec1[3], double vec2[3], double vec3[3])
{
	vec3[0] = vec1[0] + vec2[0];
	vec3[1] = vec1[1] + vec2[1];
	vec3[2] = vec1[2] + vec2[2];
	return;
}


/**
*@brief Description:Computes result of two 3-vector cross product.
*@param[in]		vec1		a first 3-vector.
*@param[in]		vec2		a first 3-vector.
*@param[out]	vec3		result of vec1 cross product vec2.
*@return		No return value.
*@note:
*@warning:
*/
void Vec3Cross(double vec1[3],double vec2[3],double vec3[3])
{
	vec3[0] = vec1[1] * vec2[2] - vec2[1] * vec1[2];
	vec3[1] = -(vec1[0] * vec2[2] - vec2[0] * vec1[2]);
	vec3[2] = vec1[0] * vec2[1] - vec2[0] * vec1[1];
	return;
}

/**
*@brief Description:Computes a 3-vector multiply a scalar value.
*@param[in]		vec1			a 3-vector.
*@param[in]		value			a scalar value.
*@param[out]	vec2			result of vec1 * value. 
*@return		No return value.
*@note:
*@warning:
*/
void Vec3MultValue(double vec1[3], double value, double vec2[3])
{
	vec2[0] = vec1[0] * value;
	vec2[1] = vec1[1] * value;
	vec2[2] = vec1[2] * value;
	return;
}

/**
*@brief			Description: Computes the norm of a 3-vector.
*@param[in]		vec			an input 3-vector.
*@return		the norm of a an input 3-vector.
*@note:
*@warning:
*/
double Vec3Norm2(double vec[3])
{
	return sqrt(vec[0] * vec[0] + vec[1] * vec[1] + vec[2] * vec[2]);
}

/**
*@brief			Description: Computes the 2-norm of a n-vector.
*@param[in]		n			dimension of vector.
*@param[in]		vec			an input n-vector.
*@return		the norm of a an input 3-vector.
*@note:
*@warning:
*/
double VecNorm2(int n,double *vec)
{
	int i;
	double tmp=0.0;
	for (i=0;i<n;i++)
	{
		tmp = tmp + vec[i] * vec[i];
	}
	if (tmp<0.0)
	{
		tmp = 0;
	}
	return sqrt(tmp);
}


/**
*@brief			Copy  matrix from a to  b .
*@param[in]		a		First matrix.
*@param[in]		m		rows of matrix a.
*@param[in]		n		columns of matrix a.
*@param[in]		b		Second matrix.
*@return		No return value.
*@note:
*@warning:
*/
void MatrixCopy(const double *a, int m, int n, double *b)
{
	memcpy(b, a, m*n * sizeof(double));
	return;
}

/**
*@brief			Computes Matrix transpose.
*@param[in]		a			a matrix.
*@param[in]		m			rows of matrix a.
*@param[in]		n			columns of matrix a.
*@param[out]	b			transpose of matrix a.
*@return		No return value.
*@note:
*@waring:
*/
void MatrixT(double *a, int m, int n, double *b)
{
	int i, j;
	for (i = 0; i < m; i++)
	{
		for (j = 0; j < n; j++)
		{
			b[j*m + i] = a[i*n + j];
		}
	}
	return;
}



/**
*@brief			Computes matrix multiply.
*@param[in]		a		First matrix.
*@param[in]		m		rows of matrix a.
*@param[in]		n		columns of matrix b.
*@param[in]		b		Second matrix.
*@param[in]		l		columns of matrix b.
*@param[out]	c		result of a*b.
*@return		No return value.
*@note:
*@waring:
*/
void MatrixMult(const double *a, int m, int n, const double *b, int l, double *c)
{
	int i, j, k;
	for (i = 0; i < m; i++)
	{
		for (j = 0; j < l; j++)
		{
			c[i*l + j] = 0.0;
			for (k = 0; k < n; k++)
			{
				c[i*l + j] = c[i*l + j] + a[i*n + k] * b[k*l + j];
			}
		}
	}
	return;
}


/**
* @brief 			Description: Algorithm for Computing the roll-pitch-yaw angles(rotate around fix reference X,Y,Z axis).
* @param[in]		R				Rotation matrix.
* @param[out]		roll			Angles for rotate around fix reference X axis.
* @param[out]		pitch			Angles for rotate around fix reference Y axis.
* @param[out]		yaw				Angles for rotate around fix reference Z axis.
* @return			No return value.
* @note:
*@warning:
*/
void RotToRPY(double R[3][3],double *roll,double *pitch,double *yaw)
{
	if (fabs(1.0 + R[2][0]) < ZERO_ELEMENT)
	{
		*yaw = 0;
		*pitch = PI / 2.0;
		*roll = atan2(R[0][1], R[1][1]);

	}
	else if (fabs(1.0 - R[2][0]) < ZERO_ELEMENT)
	{
		*yaw = 0;
		*pitch = -PI / 2.0;
		*roll = atan2(R[0][1], R[1][1]);
	}
	else
	{

		*yaw = atan2(R[1][0], R[0][0]);
		*pitch = atan2(-R[2][0], sqrt(R[0][0] * R[0][0] + R[1][0] * R[1][0]));
		*roll = atan2(R[2][1], R[2][2]);
	}
	return;
}

/**
* @brief 			Description: Algorithm for Computing the rotation matrix of the roll-pitch-yaw angles.
* @param[in]		roll			Angles for rotate around fix reference X axis.
* @param[in]		pitch			Angles for rotate around fix reference Y axis.
* @param[in]		yaw				Angles for rotate around fix reference Z axis.
* @param[out]		R				Rotation matrix.
* @return			No return value.
* @note:
*@warning:
*/
void RPYToRot(double roll, double pitch, double yaw, double R[3][3])
{
	double alpha = yaw;
	double beta = pitch;
	double gamma = roll;
	R[0][0] = cos(alpha)*cos(beta);
	R[0][1] = cos(alpha)*sin(beta)*sin(gamma) - sin(alpha)*cos(gamma);
	R[0][2] = cos(alpha)*sin(beta)*cos(gamma) + sin(alpha)*sin(gamma);
	R[1][0] = sin(alpha)*cos(beta);
	R[1][1] = sin(alpha)*sin(beta)*sin(gamma) + cos(alpha)*cos(gamma);
	R[1][2] = sin(alpha)*sin(beta)*cos(gamma) - cos(alpha)*sin(gamma);
	R[2][0] = -sin(beta);
	R[2][1] = cos(beta)*sin(gamma);
	R[2][2] = cos(beta)*cos(gamma);
	return;
}

/**
*@brief			Computes the inverse of the rotation matrix R.
*@param[in]		R		rotation matrix .
*@param[out]	InvR	inverse matrix of R.
*@return		No return value.
*@note			Input R must be a 3 x 3 rotation matrix.
*/
void RotInv(double R[3][3], double InvR[3][3])
{
	int i;
	int j;
	for (i=0;i<3;i++)
	{
		for (j=0;j<3;j++)
		{
			InvR[i][j] = R[j][i];
		}
	}
	return;
}

/**
*@brief Description:Returns the 3 x 3 skew-symmetric matrix corresponding to omg.
*@param[in]		omg		a 3-vector.
*@param[out]	so3Mat	the 3 x 3 skew-symmetric matrix corresponding to omg.
*@return		No return value.
*@note:
*@warning:
*/
void VecToso3(double omg[3],double so3Mat[3][3])
{
	so3Mat[0][0] = 0.0;		so3Mat[0][1] = -omg[2]; so3Mat[0][2] = omg[1];
	so3Mat[1][0] = omg[2];	so3Mat[1][1] = 0;		so3Mat[1][2] = -omg[0];
	so3Mat[2][0] = -omg[1];	so3Mat[2][1] = omg[0];	so3Mat[2][2] = 0.0;
	return;
}


/**
*@brief			Description:Returns the 3-vector corresponding to the 3 x 3 skew-symmetric matrix so3mat.
*@param[in]		so3Mat		a 3 x 3 skew-symmetric matrix so3mat.
*@param[out]	omg			the 3-vector.
*@return		No return value.
*@note:
*@warning:
*/
void so3ToVec(double so3Mat[3][3], double omg[3])
{
	omg[0] = so3Mat[2][1]; omg[1] = so3Mat[0][2]; omg[2] = so3Mat[1][0];
	return;
}


/**
*@brief			Description:Extracts  the unit rotation axis omghat and the corresponding
*				rotation angle theta from exponential coordinates omghat*theta for rotation, expc3.
*@param[in]		expc3			
*@param[out]	omghat		the unit vector of rotation axis .
*@param[out]	theta		rotation angle.
*@return		No return value.
*@note:
*@warning:
*/
void AxisAng3(double expc3[3],double omghat[3],double *theta)
{
	int i;
	int ret = 0;
	*theta = sqrt(expc3[0] * expc3[0] + expc3[1] * expc3[1] + expc3[2] * expc3[2]);
	if (*theta<ZERO_ANGLE)
	{
		omghat[0] = 0.0;
		omghat[1] = 0.0;
		omghat[2] = 0.0;
		*theta = 0.0;
		return;
	}
	for (i=0;i<3;i++)
	{
		omghat[i]=expc3[i]/(*theta);
	}
	return ;
}

/**
*@brief			Description:Computes the rotation matrix R in SO(3) corresponding to
*				the matrix exponential of so3mat in so(3).
*@param[in]		so3Mat		[omghat]*theta,matrix exponential of so3mat in so(3).			
*@param[out]	R			rotation matrix R in SO(3).
*@return		No return value.
*@note:
*@warning:
*/
void MatrixExp3(double so3Mat[3][3],double R[3][3])
{
	double omgtheta[3];
	double omghat[3] = { 0 };
	double theta = 0;
	int ret = 0;
	int i;
	int j;
	double MatI3[3][3] =
	{
		1,0,0,
		0,1,0,
		0,0,1
	};
	so3ToVec(so3Mat, omgtheta);
	AxisAng3(omgtheta, omghat, &theta);
	if (theta<ZERO_ANGLE)
	{
		Matrix3Equal(MatI3, R);
		return ;
	}
	else
	{

		//calculate formula(3.51) in book [modern robotics : mechanics,planning,and control]
		double omgmat[3][3];
		double temp[3][3];
		Matrix3MultValue(so3Mat, 1.0 / theta, omgmat);
		Matrix3Mult(omgmat, omgmat, temp);
		for (i=0;i<3;i++)
		{
			for (j=0;j<3;j++)
			{
				R[i][j] = MatI3[i][j] + sin(theta)*so3Mat[i][j] / theta + (1 - cos(theta))*temp[i][j];
			}
		}
	}
	return;
}

/**
*@brief			Description:Computes the matrix logarithm so3mat in so(3) of the rotation matrix R in SO(3).
*@param[in]		R		the rotation matrix.
*@param[out]	so3Mat	matrix logarithm.
*@return		No return value.
*@note:
*@warning:
*/
void MatrixLog3(double R[3][3],double so3Mat[3][3])
{
	double omg[3] = { 0 };
	double acosinput = (R[0][0] + R[1][1] + R[2][2] - 1.0) / 2.0;
	if (fabs(acosinput - 1.0)<ZERO_VALUE)
	{
		memset(so3Mat, 0, 9 * sizeof(double));
	}
	else if (acosinput<=-1.0)
	{
		if ((1.0+R[2][2])>= ZERO_VALUE)
		{
			omg[0] = 1.0 / sqrt(2 * (1.0 + R[2][2]))*R[0][2];
			omg[1] = 1.0 / sqrt(2 * (1.0 + R[2][2]))*R[1][2];
			omg[2] = 1.0 / sqrt(2 * (1.0 + R[2][2]))*(1.0 + R[2][2]);
		}
		else if ((1.0+R[1][1]>= ZERO_VALUE))
		{
			omg[0] = 1.0 / sqrt(2 * (1.0 + R[1][1]))*R[0][1];
			omg[1] = 1.0 / sqrt(2 * (1.0 + R[1][1]))*(1.0 + R[1][1]);
			omg[2] = 1.0 / sqrt(2 * (1.0 + R[1][1]))*R[2][1];
		}
		else 
		{
			omg[0] = 1.0 / sqrt(2 * (1.0 + R[0][0]))*(1.0 + R[0][0]);
			omg[1] = 1.0 / sqrt(2 * (1.0 + R[0][0]))*R[1][0];
			omg[2] = 1.0 / sqrt(2 * (1.0 + R[0][0]))*R[2][0];
		}
		omg[0] = PI*omg[0];
		omg[1] = PI*omg[1];
		omg[2] = PI*omg[2];
		VecToso3(omg, so3Mat);
	}
	else
	{
		int i;
		int j;
		double theta = acos(acosinput);
		for (i=0;i<3;i++)
		{
			for (j=0;j<3;j++)
			{
				so3Mat[i][j] = 1.0 / (2.0*sin(theta))*(R[i][j] - R[j][i])*theta;
			}
		}
	}

	return;
}

/**
*@brief					Description:Builds the homogeneous transformation matrix T corresponding to a rotation 
*						matrix R in SO(3) and a position vector p in R3.
*@param[in]		R		a rotation matrix R in SO(3).
*@param[in]		p		a position vector p in R3.
*@param[out]	T		the homogeneous transformation matrix T.
*@return		No return value.
*@note:
*@warning:
*/
void RpToTrans(double R[3][3], double p[3], double T[4][4])
{
	int i;
	int j;
	for (i=0;i<3;i++)
	{
		for (j=0;j<3;j++)
		{
			T[i][j] = R[i][j];
		}
	}
	T[0][3] = p[0];
	T[1][3] = p[1];
	T[2][3] = p[2];
	T[3][0] = 0.0; 
	T[3][1] = 0.0; 
	T[3][2] = 0.0;
	T[3][3] = 1.0;
	return;
}

/**
*@brief Description: Extracts the rotation matrix R and position vector p 
from a homogeneous transformation matrix T.
*@param[in]		T		a homogeneous transformation matrix.
*@param[out]	R		the rotation matrix.
*@param[out]	p		position vector.
*@return		No return value.
*@note:
*@waring:
*/
void TransToRp(double T[4][4], double R[3][3], double p[3])
{
	int i;
	int j;
	for (i=0;i<3;i++)
	{
		for (j=0;j<3;j++)
		{
			R[i][j] = T[i][j];
		}
	}
	p[0] = T[0][3];
	p[1] = T[1][3];
	p[2] = T[2][3];
	return;
}

/**
*@brief Description:Computes the inverse of a homogeneous transformation matrix T.
*@param[in]		T		a homogeneous transformation matrix.
*@param[out]	InvT	the inverse of T.
*@return		No return value.
*@note:
*@warning:
*/
void TransInv(double T[4][4],double InvT[4][4])
{
	double R[3][3];
	double InvR[3][3];
	double p[3];
	double p2[3];
	TransToRp(T, R, p);
	RotInv(R, InvR);
	Matrix3MultValue(InvR, -1.0, R);
	Matrix3MultVec(R, p, p2);
	RpToTrans(InvR, p2, InvT);
	return;
}

/**
*@brief Description:Computes the se(3) matrix corresponding to a 6-vector twist V.
*@param[in]		V		a 6-vector twist V.
*@param[out]	se3Mat	the se(3) matrix.
*@return		No return value.
*@note:
*@warning:
*/
void VecTose3(double V[6], double se3Mat[4][4])
{
	double so3Mat[3][3];
	double omg[3];
	int i;
	int j;
	omg[0] = V[0];
	omg[1] = V[1];
	omg[2] = V[2];
	VecToso3(omg, so3Mat);
	for (i=0;i<3;i++)
	{
		for (j=0;j<3;j++)
		{
			se3Mat[i][j] = so3Mat[i][j];
		}

	}
	se3Mat[0][3] = V[3];
	se3Mat[1][3] = V[4];
	se3Mat[2][3] = V[5];
	se3Mat[3][0] = 0.0;
	se3Mat[3][1] = 0.0;
	se3Mat[3][2] = 0.0;
	se3Mat[3][3] = 0.0;
	return;
}

/**
*@brief Description:Computes the 6-vector twist corresponding to an se(3) matrix se3mat.
*@param[in]		se3Mat			an se(3) matrix.
*@param[out]	V				he 6-vector twist.
*@return		No return value.
*@note:
*@warning:
*/
void se3ToVec(double se3Mat[4][4],double V[6])
{
	V[0] = se3Mat[2][1];
	V[1] = se3Mat[0][2];
	V[2] = se3Mat[1][0];
	V[3] = se3Mat[0][3];
	V[4] = se3Mat[1][3];
	V[5] = se3Mat[2][3];
	return;
}

/**
*@brief Description:Computes the 6 x 6 adjoint representation [AdT ] 
of the homogeneous transformation matrix T.
*@param[in]		T		a homogeneous transformation matrix.
*@param[out]	AdT		the 6 x 6 adjoint representation [AdT ].
*@return		No return value.
*@note:
*@warning:
*/
void Adjoint(double T[4][4], double AdT[6][6])
{
	double R[3][3];
	double p[3];
	double so3Mat[3][3];
	int i;
	int j;
	TransToRp(T, R, p);
	VecToso3(p, so3Mat);
	
	for (i=0;i<3;i++)
	{
		for (j=0;j<3;j++)
		{
			AdT[i][j] = R[i][j];
		}
	}
	for (i = 0; i < 3; i++)
	{
		for (j = 3; j < 6; j++)
		{
			AdT[i][j] = 0.0;
		}
	}
	for (i=3;i<6;i++)
	{
		for (j = 3; j < 6; j++)
		{
			AdT[i][j] = R[i-3][j-3];
		}
	}
	double mat[3][3];
	Matrix3Mult(so3Mat, R, mat);
	for (i = 3; i < 6; i++)
	{
		for (j = 0; j < 3; j++)
		{
			AdT[i][j] = mat[i-3][j];
		}
	}

	return;
}

/**
*@brief			Description: Computes a normalized screw axis representation S of a screw described by 
*				a unit vector s in the direction of the screw axis, located at the point q, with pitch h.
*@param[in]		q		a point lying on the screw axis.
*@param[in]		s		a unit vector in the direction of the screw axis.
*@param[in]		h		the pitch of the screw axis.
*@param[in]		S		a normalized screw axis representation.
*@return		No return value.
*@note:
*@warning:
*/
void ScrewToAxis(double q[3], double s[3], double h,double S[6])
{
	double v[3];
	double temp[3];
	Vec3Cross(s, q, temp);
	Vec3MultValue(temp, -1.0, temp);
	Vec3MultValue(s, h, v);
	Vec3Add(v, temp, v);
	S[0] = s[0];
	S[1] = s[1];
	S[2] = s[2];
	S[3] = v[0];
	S[4] = v[1];
	S[5] = v[2];
	return;
}

/**
*@brief Description: Extracts the normalized screw axis S and the distance traveled along the screw
theta from the 6-vector of exponential coordinates S*theta.
*@param[in]		expc6		the 6-vector of exponential coordinates.
*@param[out]	S			the normalized screw axis.
*@param[out]	theta		the distance traveled along the screw.
*@return		No return value.
*@note:
*@warning:
*/
void AxisAng6(double expc6[6],double S[6],double *theta)
{
	*theta = Vec3Norm2(expc6);
	if (*theta<ZERO_ANGLE)
	{
		*theta = Vec3Norm2(&expc6[3]);
		if (*theta<ZERO_DISTANCE)
		{
			*theta=0.0;
			//S is undefine,no motion at all.
			S[0] = 0.0; S[1] = 0.0; S[2] = 0.0; S[3] = 0.0; S[4] = 0.0; S[5] = 0.0;
			return;
		}
	}
	Vec3MultValue(expc6, 1.0 / (*theta), S);
	Vec3MultValue(&expc6[3], 1.0 / (*theta), &S[3]);
	return ;
}

/**
*@brief			Description: Computes the homogeneous transformation matrix T in SE(3) corresponding to
*				the matrix exponential of se3mat in se(3).
*@param[in]		se3mat			the matrix exponential of se3mat in se(3).
*@param[out]	T				the homogeneous transformation matrix T in SE(3).
*@return		No return value.
*@note:
*@warning:
*/
void MatrixExp6(double se3Mat[4][4], double T[4][4])
{
	int i;
	int j;
	double so3mat[3][3];
	double omgmat[3][3];
	double temp[3][3];
	double Gtheta[3][3];
	double p[3];
	double v[3];
	double omgtheta[3];
	double omghat[3];
	double theta;
	double MatI3[3][3] =
	{
		1.0,0.0,0.0,
		0.0,1.0,0.0,
		0.0,0.0,1.0
	};
	TransToRp(se3Mat, so3mat, p);//extracts so3mat from se3mat
	so3ToVec(so3mat, omgtheta);
	if (Vec3Norm2(omgtheta)<ZERO_ANGLE)
	{
		for (i=0;i<3;i++)
		{
			for (j=0;j<3;j++)
			{
				T[i][j] = MatI3[i][j];
			}
		}
		T[0][3] = se3Mat[0][3];
		T[1][3] = se3Mat[1][3];
		T[2][3] = se3Mat[2][3];
		T[3][0] = 0.0;
		T[3][1] = 0.0;
		T[3][2] = 0.0;
		T[3][3] = 1.0;
	}
	else
	{
		AxisAng3(omgtheta, omghat, &theta);
		MatrixExp3(so3mat, temp);
		for (i = 0; i < 3; i++)
		{
			for (j = 0; j < 3; j++)
			{
				T[i][j] = temp[i][j];
			}
		}
		Matrix3MultValue(so3mat, 1.0/theta,omgmat);
		Matrix3Mult(omgmat, omgmat, temp);
		for (i = 0; i < 3; i++)
		{
			for (j = 0; j < 3; j++)
			{
				Gtheta[i][j] = MatI3[i][j] * theta + (1.0 - cos(theta))*omgmat[i][j] + (theta - sin(theta))*temp[i][j];
			}
		}	
		v[0] = p[0] / theta; 
		v[1] = p[1] / theta;
		v[2] = p[2] / theta;
		Matrix3MultVec(Gtheta, v, p);
		T[0][3] = p[0]; T[1][3] = p[1]; T[2][3] = p[2];
		T[3][0] = 0.0;
		T[3][1] = 0.0;
		T[3][2] = 0.0;
		T[3][3] = 1.0;
	}
	return;
}


/**
*@brief Description: Computes the matrix logarithm se3mat in se(3) of 
the homogeneous transformation matrix T in SE(3)
*@param[in]		T			the homogeneous transformation matrix.			
*@param[out]	se3Mat		the matrix logarithm of T.
*@return		No return value.
*@note:
*@warning:
*/
void MatrixLog6(double T[4][4], double se3Mat[4][4])
{
	int i;
	int j;
	double R[3][3];
	double so3mat[3][3];
	double p[3];
	TransToRp(T, R, p);
	MatrixLog3(R, so3mat);
	int flag = 0;
	for (i=0;i<3;i++)
	{
		for (j=0;j<3;j++)
		{
			if (fabs(so3mat[i][j])<ZERO_ELEMENT)
			{
				continue;
			}
			else
			{
				flag = 1;
				break;
			}
		}
	}
	if (!flag)
	{
		for (i=0;i<3;i++)
		{
			for (j=0;j<3;j++)
			{
				se3Mat[i][j] = 0.0;
			}

		}
		se3Mat[0][3] = T[0][3];
		se3Mat[1][3] = T[1][3];
		se3Mat[2][3] = T[2][3];
		se3Mat[3][0] = 0.0;
		se3Mat[3][1] = 0.0;
		se3Mat[3][2] = 0.0;
		se3Mat[3][3] = 0.0;
	}
	else
	{
		double MatI3[3][3] =
		{
			1.0,0.0,0.0,
			0.0,1.0,0.0,
			0.0,0.0,1.0
		};
		double v[3];
		double temp[3][3];
		double InvGtheta[3][3];
		double theta = acos((R[0][0] + R[1][1] + R[2][2] - 1.0) / 2.0);
		for (i=0;i<3;i++)
		{
			for (j=0;j<3;j++)
			{
				se3Mat[i][j] = so3mat[i][j];
			}
		}

		Matrix3Mult(so3mat, so3mat, temp);
		for (i = 0; i < 3; i++)
		{
			for (j = 0; j < 3; j++)
			{
				InvGtheta[i][j] = MatI3[i][j] - 0.5*so3mat[i][j] + (1.0 / theta - 0.5*1.0 / tan(0.5*theta))*temp[i][j] / theta;
			}
		}
		Matrix3MultVec(InvGtheta, p, v);
		se3Mat[0][3] = v[0];
		se3Mat[1][3] = v[1];
		se3Mat[2][3] = v[2];
		se3Mat[3][0] = 0.0;
		se3Mat[3][1] = 0.0;
		se3Mat[3][2] = 0.0;
		se3Mat[3][3] = 0.0;
	}
	return ;
}

/**
*@brief			Description: Computes the end-effector frame given the zero position of the end-effector M,
*				the list of joint screws Slist expressed in the fixed-space frame, and the list of joint values thetalist.
*@param[in]		M			the zero position of the end-effector expressed in the fixed-space frame.
*@param[in]		Joint		Num	the number of joints.
*@param[in]		Slist		the list of joint screws Slist expressed in the fixed-space frame.
*							in the format of a matrix with the screw axes as the column.
*@param[in]		thetalist   the list of joint values.
*@param[out]	T			the end-effector frame expressed in the fixed-space frame.
*@return		No return value.
*@note:			when Slist is a matrix ,make sure that columns number of Slist is equal to JointNum,
*				rows number of Slist 6 .The function call should be written as
*				FKinBody(...,(double *)Slist,...).
*@warning:
*/
void FKinSpace(double M[4][4],int  JointNum,double *Slist, double *thetalist,double T[4][4])
{
	int i, j, k, l;
	double se3mat[4][4];
	double T2[4][4];
	double exp6[4][4];
	double V[6];
	Matrix4Equal(M, T);
	for (i= JointNum-1;i>=0;i--)
	{
		for (l=0;l<6;l++)
		{
			V[l] = Slist[l*JointNum+i];//get each column of Slist.
		}
		VecTose3(V, se3mat);
		for (j=0;j<4;j++)
		{
			for (k=0;k<4;k++)
			{
				se3mat[j][k] = se3mat[j][k] * thetalist[i];
			}
		}
		MatrixExp6(se3mat, exp6);
		Matrix4Mult(exp6, T, T2);
		Matrix4Equal(T2, T);
	}
	return ;
}

/**
*@brief			Description:Computes the end-effector frame given the zero position of the end-effector M,
*				the list of joint screws Blist expressed in the end-effector frame, and the list of joint values thetalist.
*@param[in]		M			the zero position of the end-effector expressed in the end-effector frame.
*@param[in]		JointNum	the number of joints.
*@param[in]		Blist		the list of joint screws Slist expressed in the end-effector frame.
*							in the format of a matrix with the screw axes as the column.
*@param[in]		thetalist   the list of joint values.
*@param[out]	T			the end-effector frame expressed in the end-effector frame.
*@return		No return value.
*@note:			when Blist is a matrix ,make sure that columns number of Slist is equal to JointNum,
*				rows number of Slist 6 .The function call should be written as
*				FKinBody(...,(double *)Blist,...).
*@warning:
*/
void FKinBody(double M[4][4], int  JointNum, double *Blist, double thetalist[], double T[4][4])
{
	int i, j, k, l;
	double se3mat[4][4];
	double T2[4][4];
	double exp6[4][4];
	double V[6];
	Matrix4Equal(M, T);
	for (i = 0; i < JointNum ; i++)
	{
		for (l = 0; l < 6; l++)
		{
			V[l] = Blist[l*JointNum + i];//get each column of Slist.
		}
		VecTose3(V, se3mat);
		for (j = 0; j < 4; j++)
		{
			for (k = 0; k < 4; k++)
			{
				se3mat[j][k] = se3mat[j][k] * thetalist[i];
			}
		}
		MatrixExp6(se3mat, exp6);
		Matrix4Mult(T, exp6, T2);
		Matrix4Equal(T2, T);
	}
	return ;
}


/**
*@brief Description: Computes the body Jacobian Jb(theta) in 6×n given a list of joint screws Bi 
expressed in the body frame and a list of joint angles.
*@param[in]		Blist		The joint screw axes in the end - effector frame when the manipulator is 
*							at the home position, in the format of a matrix with the screw axes as the row.
*@param[in]		thetalist	A list of joint coordinates.
*@param[out]	Jb			Body Jacobian matrix.
*@return        No return value.
*@note:			 when Blist and Jb are matrixes ,make sure that columns number of Slist or Jb is equal to JointNum,
*				 rows number of Slist or Jb is 6 .The function call should be written as
*				 JacobianSpace(JointNum,(double *)Slist,thetalist,(double *)Jb).
*@warning:
*/
void JacobianBody(int JointNum,double *Blist, double *thetalist,double *Jb)
{
	int i;
	int j;
	int k;
	double T1[4][4];
	double T2[4][4];
	double se3mat[4][4];
	double V[6];
	double AdT[6][6];
	double T[4][4] = {
		1,0,0,0,
		0,1,0,0,
		0,0,1,0,
		0,0,0,1
	};
	//Fist column of Jbn.
	for (i=0;i<6;i++)
	{
		Jb[i*JointNum+JointNum -1] = Blist[i*JointNum + JointNum-1];
	}
	//Jbi for i=n-1,n-2,...,1.
	for (i= JointNum -2;i>=0;i--)
	{
		for (j=0;j<6;j++)
		{
			V[j] = -1.0*Blist[j*JointNum+i+1];
		}
		VecTose3(V, se3mat);
		Matrix4MultValue(se3mat, thetalist[i + 1], se3mat);
		MatrixExp6(se3mat, T1);
		Matrix4Mult(T, T1,T2);
		Matrix4Equal(T2, T);
		Adjoint(T, AdT);
		for (j=0;j<6; j++)
		{
			Jb[j*JointNum + i] = 0;
			for (k=0;k<6;k++)
			{
				Jb[j*JointNum + i] = Jb[j*JointNum + i] + AdT[j][k] * Blist[k*JointNum + i];
			}
		}
	}
	return ;
}

/**
*@brief			Description:Computes the space Jacobian Js(theta) in R6 x n given a list of joint screws Si 
*				expressed in the fixed space frame and a list of joint angles.
*@param[in]		JointNum	joints number.
*@param[in]		Slist		The joint screw axes expressed in the fixed space frame when the manipulator is
*							at the home position, in the format of a matrix with the screw axes as the column.
*@param[in]		thetalist	A list of joint coordinates.
*@param[out]	Js			Space Jacobian matrix.
*@return		 No return value.
*@note:			 when Slist and Js are matrices ,make sure that columns number of Slist or Js is equal to JointNum,
*				 rows number of Slist or Js is 6 .The function call should be written as 
*				 JacobianSpace(JointNum,(double *)Slist,thetalist,(double *)Js).
*@warning:
*/
void JacobianSpace(int JointNum, double *Slist, double *thetalist, double *Js)
{
	int i;
	int j;
	int k;
	double T1[4][4];
	double T2[4][4];
	double se3mat[4][4];
	double V[6];
	double AdT[6][6];
	double T[4][4] = {
		1,0,0,0,
		0,1,0,0,
		0,0,1,0,
		0,0,0,1
	};
	//Fist column of Js.
	for (i = 0; i < 6; i++)
	{
		Js[i*JointNum + 0] = Slist[i*JointNum + 0];
	}
	//Jsi for i=2,3,...,n.
	for (i = 1; i <JointNum; i++)
	{
		for (j = 0; j < 6; j++)
		{
			V[j] = Slist[j*JointNum + i - 1];
		}
		VecTose3(V, se3mat);
		Matrix4MultValue(se3mat, thetalist[i - 1], se3mat);
		MatrixExp6(se3mat, T1);
		Matrix4Mult(T, T1, T2);
		Matrix4Equal(T2, T);
		Adjoint(T, AdT);
		for (j = 0; j < 6; j++)
		{
			Js[j*JointNum + i] = 0;
			for (k = 0; k < 6; k++)
			{
				Js[j*JointNum + i] = Js[j*JointNum + i] + AdT[j][k] * Slist[k*JointNum + i];
			}
		}
	}
	return;
}

#define SIGN(a,b) ((b) >= 0.0 ? fabs(a) : -fabs(a))
#define MAX(a,b) (a>b?a:b)
#define MIN(a,b) (a<b?a:b)

/**
*@brief			Computes (a^2+b^2)^(1/2),
*@param[in]		a
*@param[in]		b
*@note:
*@warning:
*/
double pythag(const double a, const double b)
{
	double absa, absb;
	absa = fabs(a);
	absb = fabs(b);
	if (absa > absb) return absa*sqrt(1.0 + (absb / absa)*(absb / absa));
	else return (absb == 0.0 ? 0.0 : absb*sqrt(1.0 + (absa / absb)*(absa / absb)));

}

void reorder(double *u,int m,int n,double *w,double *v) 
{
	/*Given the output of decompose, this routine sorts the singular values, and corresponding columns
		of u and v, by decreasing magnitude.Also, signs of corresponding columns are flipped so as to
		maximize the number of positive elements.*/
	int i, j, k, s, inc = 1;
	double sw;
	double *su = (double *)malloc(m * sizeof(double));
	if (su==NULL)
	{
		return;
	}
	double *sv = (double *)malloc(n * sizeof(double));
	if (sv==NULL)
	{
		free(su);
		return;
	}
	do { inc *= 3; inc++; } while (inc <= n);// Sort.The method is Shell’s sort.(The work is negligible as compared to that already done in decompose.)
		do {
			inc /= 3;
			for (i = inc; i < n; i++) {
				sw = w[i];
				for (k = 0; k < m; k++) su[k] = u[k*n + i];
				for (k = 0; k < n; k++) sv[k] = v[k*n + i];
				j = i;
				while (w[j - inc] < sw) {
					w[j] = w[j - inc];
					for (k = 0; k < m; k++) u[k*n + j] = u[k*n + j - inc];
					for (k = 0; k < n; k++) v[k*n + j] = v[k*n + j - inc];
					j -= inc;
					if (j < inc) break;
				}
				w[j] = sw;
				for (k = 0; k < m; k++) u[k*n + j] = su[k];
				for (k = 0; k < n; k++) v[k*n + j] = sv[k];
			}
		} while (inc > 1);
		for (k = 0; k < n; k++) {
			//Flip signs.
				s = 0;
				for (i = 0; i < m; i++) if (u[i*n + k] < 0.0) s++;
				for (j = 0; j < n; j++) if (v[j*n + k] < 0.0) s++;
			if (s > (m + n) / 2) {
				for (i = 0; i < m; i++) u[i*n + k] = -u[i*n + k];
				for (j = 0; j < n; j++) v[j*n + k] = -v[j*n + k];
			}
		}
		free(su);
		free(sv);
		return;
}



/**
*@brief			Given the matrix a,this routine computes its singular value decomposition.
*@param[in/out]	a		input matrix a or output matrix u.
*@param[in]		m		number of rows of matrix a.
*@param[in]		n		number of columns of matrix a.
*@param[in]		tol		any	singular values less than a tolerance are treated as zero.
*@param[out]	w		output vector w.
*@param[out]	v		output matrix v.	
*@return        No return value.
*@note:			input a must be a  m rows and n columns matrix,w is n-vector,v is a n rows and n columns matrix.
*@warning:
*/
int svdcmp(double *a, int m, int n, double tol, double *w, double *v)
{

	int flag, i, its, j, jj, k, l, nm;
	double anorm, c, f, g, h, s, scale, x, y, z;
	double *rv1 = (double *)malloc(n * sizeof(double));
	if (rv1==NULL)
	{
		return 1;
	}
	g = scale = anorm = 0.0;
	for (i=0;i<n;i++)//Householder reduction to bidiagonal form.
	{
		l = i + 2;
		rv1[i] = scale*g;
		g = s = scale = 0.0;
		if (i<m)
		{
			for (k = i; k < m; k++)scale += fabs(a[k*n + i]);
			if (scale!=0.0)
			{
				for (k = i; k < m;k++)
				{
					a[k*n + i] /= scale;
					s += a[k*n + i] * a[k*n + i];
				}
				f = a[i*n + i];
				g = -SIGN(sqrt(s), f);
				h = f*g - s;
				a[i*n + i] = f - g;
				for (j=l-1;j<n;j++)
				{
					for (s = 0.0, k = i; k < m;k++)
					{
						s += a[k*n + i] * a[k*n + j];
					}
					f = s / h;
					for (k = i; k < m;k++)
					{
						a[k*n + j] += f*a[k*n + i];
					}
				}
				for (k = i; k < m;k++)
				{
					a[k*n + i] *= scale;
				}
			}
		}
		w[i] = scale*g;
		g = s = scale = 0.0;
		if (i+1 <= m && (i+1)!=n)
		{
			for (k=l-1;k<n;k++)
			{
				scale += fabs(a[i*n + k]);
			}
			if (scale!=0.0)
			{
				for (k=l-1;k<n;k++)
				{
					a[i*n + k] /= scale;
					s += a[i*n + k] * a[i*n + k];
				}
				f = a[i*n + l - 1];
				g = -SIGN(sqrt(s), f);
				h = f*g - s;
				a[i*n + l - 1] = f - g;
				for (k=l-1;k<n;k++)
				{
					rv1[k] = a[i*n + k] / h;
				}
				for (j = l - 1; j < m; j++)
				{
					for (s = 0.0, k = l - 1; k < n; k++)
					{
						s += a[j*n + k] * a[i*n + k];
					}
					for (k = l - 1; k < n; k++)
					{
						a[j*n + k] += s*rv1[k];
					}
				}
				for (k=l-1;k<n;k++)
				{
					a[i*n + k] *= scale;
				}
			}
		}
		anorm = MAX(anorm, (fabs(w[i]) + fabs(rv1[i])));
	}

	for (i=n-1;i>=0;i--)//Accumulation of right-hand transformations.
	{
		if (i<n-1)
		{
			if (g!=0.0)
			{
				for (j = l;j<n;j++)//Double division to avoid possible underflow.
				{
					v[j*n + i] = (a[i*n + j] / a[i*n + l]) / g;
				}
				for (j = l;j<n;j++)
				{
					for (s = 0.0, k = l;k<n;k++)
					{
						s += a[i*n + k] * v[k*n + j];
					}
					for (k = l;k<n;k++)
					{
						v[k*n + j] += s*v[k*n + i];
					}
				}
			}
			for (j = l;j<n;j++)
			{
				v[i*n + j] = v[j*n + i] = 0.0;
			}
		}
		v[i*n + i] = 1.0;
		g = rv1[i];
		l = i;
	}

	for (i=MIN(m,n)-1;i>=0;i--)//Accumulation of left-hand transformations.
	{
		l = i + 1;
		g = w[i];
		for (j = l;j<n;j++)
		{
			a[i*n + j] = 0.0;
		}
		if (g!=0.0)
		{
			g = 1.0 / g;
			for (j = l;j<n;j++)
			{
				for (s = 0.0, k = l; k < m;k++)
				{
					s += a[k*n + i] * a[k*n + j];
				}
				f = (s / a[i*n + i])*g;
				for (k = i; k < m;k++)
				{
					a[k*n + j] += f*a[k*n + i];
				}
			}
			for (j = i; j < m;j++)
			{
				a[j*n + i] *= g;
			}
		}
		else
		{
			for (j = i; j < m;j++)
			{
				a[j*n + i] = 0.0;
			}
		}
		++a[i*n + i];
	}

	for (k=n-1;k>=0;k--)
	{
		/* Diagonalization of the bidiagonal form: Loop over
		singular values, and over allowed iterations. */
		for (its=0;its<30;its++)
		{
			flag = 1;
			for (l = k;l>=0;l--)//Test for splitting.
			{
				nm = l - 1;		
				if (l==0 || fabs(rv1[l])<= tol*anorm)
				{
					flag = 0;
					break;
				}
				if (fabs(w[nm]) <=tol*anorm)break;

			}
			if (flag)//Cancellation of rv1[l], if l > 0.
			{
				c = 0.0;
				s = 1.0;
				for (i=l;i<k+1;i++)
				{
					f = s*rv1[i];
					rv1[i] = c*rv1[i];
					if (fabs(f) <= tol*anorm)break;
					g = w[i];
					h = pythag(f, g);
					w[i] = h;
					h = 1.0 / h;
					c = g*h;
					s = -f*h;
					for (j = 0; j < m;j++)
					{
						y = a[j*n + nm];
						z = a[j*n + i];
						a[j*n + nm] = y*c + z*s;
						a[j*n + i] = z*c - y*s;
					}
				}
			}
			z = w[k];
			if (l==k)//Convergence
			{
				if (z<0.0)//Singular value is made nonnegative..
				{
					w[k] = -z;
					for (j=0;j<n;j++)
					{
						v[j*n + k] = -v[j*n + k];
					}
				}
				break;
			}
			//if (its==29)
			//{
			//	printf("no convergence in 30 svdcmp iterations\n");
			//}
			x = w[l]; //Shift from bottom 2-by-2 minor.
			nm = k - 1;
			y = w[nm];
			g = rv1[nm];
			h = rv1[k];
			f = ((y - z)*(y + z) + (g - h)*(g + h)) / (2.0*h*y);
			g = pythag(f, 1.0);
			f = ((x - z)*(x + z) + h*((y / (f + SIGN(g, f))) - h)) / x;
			c = s = 1.0;
			for (j = l;j<=nm;j++)//Next QR transformation:
			{
				i = j + 1;
				g = rv1[i];
				y = w[i];
				h = s*g;
				g = c*g;
				z = pythag(f, h);
				rv1[j] = z;
				c = f / z;
				s = h / z;
				f = x*c + g*s;
				g = g*c - x*s;
				h = y*s;
				y *= c;
				for (jj=0;jj<n;jj++)
				{
					x = v[jj*n + j];
					z = v[jj*n + i];
					v[jj*n + j] = x*c + z*s;
					v[jj*n + i] = z*c - x*s;
				}
				z = pythag(f, h);
				w[j] = z;
				if (z)//Rotation can be arbitrary if z = 0.
				{
					z = 1.0 / z;
					c = f*z;
					s = h*z;
				}
				f = c*g + s*y;
				x = c*y - s*g;
				for (jj = 0; jj < m;jj++)
				{
					y = a[jj*n + j];
					z = a[jj*n + i];
					a[jj*n + j] = y*c + z*s;
					a[jj*n + i] = z*c - y*s;
				}
			}
			rv1[l] = 0.0;
			rv1[k] = f;
			w[k] = x;
		}
	}
	free(rv1);
	reorder(a, m, n, w, v);//对特征值按降序排列，且调整对应矩阵
	return 0;
}

double u[PINV_MAX * PINV_MAX] = { 0 };
double w[PINV_MAX] = { 0 };
double vw[PINV_MAX * PINV_MAX] = { 0 };
double v[PINV_MAX * PINV_MAX] = { 0 };
double uT[PINV_MAX * PINV_MAX] = { 0 };
/**
*@brief			Computes Moore-Penrose pseudoinverse by  Singular Value Decomposition (SVD) algorithm.
*@param[in]		a			an arbitrary order matrix.
*@param[in]		m			rows.
*@param[in]		n			columns.
*@param[in]		tol			any	singular values less than a tolerance are treated as zero.
*@param[out]	b			Moore-Penrose pseudoinverse of matrix a.
*@return        0:success,Nonzero:failure.
*@retval		0			success.
*@retval		1			failure when use malloc to allocate memory.
*@note:		
*@warning:
*/
int MatrixPinv(const double *a, int m, int n, double tol, double *b)
{
	int i, j;
	int ret;
	memcpy(u, a, m*n * sizeof(double));
	ret=svdcmp(u, m, n, tol,w, v);
	for (i = 0; i < n; i++)
	{
		if (w[i] <= tol)
		{
			w[i] = 0;
		}
		else
		{
			w[i] = 1.0 / w[i];
		}
	}
	for (i = 0; i < n; i++)
	{
		for (j = 0; j < n; j++)
		{
			vw[i*n + j] = v[i*n + j] * w[j];
		}
	}
	MatrixT(u, m, n, uT);
	MatrixMult(vw, n, n, uT, m, b);
	return 0;
}

/**
*@brief 		Description:use an iterative Newton-Raphson root-finding method.
*@param[in]		JointNum		Number of joints.
*@param[in]		Blist			The joint screw axes in the Body frame when the manipulator
*								is at the home position, in the format of a matrix with the
*								screw axes as the columns.
*@param[in]		M				The home configuration of the end-effector.
*@param[in]		T				The desired end-effector configuration Tsd.
*@param[in]		thetalist0		An initial guess of joint angles that are close to satisfying Tsd.
*@param[in]		eomg			A small positive tolerance on the end-effector orientation error.
*								The returned joint angles must give an end-effector orientation error less than eomg.
*@param[in]		ev				A small positive tolerance on the end-effector linear position error. The returned
*								joint angles must give an end-effector position error less than ev.
*@param[in]		maxiter			The maximum number of iterations before the algorithm is terminated.
*@param[out]	thetalist		Joint angles that achieve T within the specified tolerances.
*@return		0:success,Nonzero:failure
*@retval		0				success.
*@retval		1				The maximum number of iterations reach before the algorithm is terminated.
*@retval		2				failure to allocate memory for Jacobian matrix.
*@note:
*@warning:
*/
int IKinBodyNR(int JointNum, double *Blist, double M[4][4], double T[4][4], double *thetalist0, double eomg, double ev, int maxiter, double *thetalist)
{
	int i, j;
	double Tsb[4][4];
	double iTsb[4][4];
	double Tbd[4][4];
	double se3Mat[4][4];

	double Vb[6];
	int ErrFlag;
	double *Jb = (double *)malloc(JointNum * 6 * sizeof(double));
	if (Jb == NULL)
	{
		return 2;
	}
	double *pJb = (double *)malloc(JointNum * 6 * sizeof(double));
	if (pJb == NULL)
	{
		free(Jb);
		return 2;
	}
	double *dtheta = (double *)malloc(JointNum * sizeof(double));
	if (dtheta == NULL)
	{
		free(Jb);
		free(pJb);
		return 2;
	}
	MatrixCopy(thetalist0, JointNum, 1, thetalist);
	FKinBody(M, JointNum, Blist, thetalist, Tsb);
	TransInv(Tsb, iTsb);
	Matrix4Mult(iTsb,T,Tbd);
	MatrixLog6(Tbd, se3Mat);
	se3ToVec(se3Mat, Vb);
	ErrFlag = VecNorm2(3, &Vb[0]) > eomg || VecNorm2(3, &Vb[3]) > ev;
	i = 0;

#if(DEBUGMODE)
	///////////////////Debug///////////
	printf("iteration:%4d  thetalist:  ", i);
	int k;
	for (k = 0; k < JointNum; k++)
	{
		printf("%4.6lf\t", thetalist[k]);
	}
	printf("\n");
	////////////////////////////////////
#endif

	while (ErrFlag && i<maxiter)
	{
		JacobianBody(JointNum, Blist, thetalist, Jb);
		MatrixPinv(Jb, 6, JointNum, 2.2E-15, pJb);
		MatrixMult(pJb, JointNum,6 , Vb, 1, dtheta);
		for (j=0;j<JointNum;j++)
		{
			thetalist[j] = thetalist[j] + dtheta[j];
		}
		i++;
		FKinBody(M, JointNum, Blist, thetalist, Tsb);
		TransInv(Tsb, iTsb);
		Matrix4Mult(iTsb, T, Tbd);
		MatrixLog6(Tbd, se3Mat);
		se3ToVec(se3Mat, Vb);
		ErrFlag = VecNorm2(3, &Vb[0]) > eomg || VecNorm2(3, &Vb[3]) > ev;
#if (DEBUGMODE)
		///////////////////////DEBUG///////////
		printf("iteration:%4d  thetalist:  ", i);
		for (k = 0; k < JointNum; k++)
		{
			printf("%4.6lf\t", thetalist[k]);
		}
		printf("\n");
		//////////////////////////////////////
#endif

	}
	free(Jb);
	free(pJb);
	free(dtheta);
	return ErrFlag;
}



/**
*@brief 		Description:use an iterative Newton-Raphson root-finding method.
*@param[in]		JointNum		Number of joints.
*@param[in]		Slist			The joint screw axes in the space frame when the manipulator
*								is at the home position, in the format of a matrix with the
*								screw axes as the columns.
*@param[in]		M				The home configuration of the end-effector.
*@param[in]		T				The desired end-effector configuration Tsd.
*@param[in]		thetalist0		An initial guess of joint angles that are close to satisfying Tsd.
*@param[in]		eomg			A small positive tolerance on the end-effector orientation error. 
*								The returned joint angles must give an end-effector orientation error less than eomg.
*@param[in]		ev				A small positive tolerance on the end-effector linear position error. The returned 
*								joint angles must give an end-effector position error less than ev.
*@param[in]		maxiter			The maximum number of iterations before the algorithm is terminated.
*@param[out]	thetalist		Joint angles that achieve T within the specified tolerances.
*@return		0:success,Nonzero:failure
*@retval		0
*@note :
*@warning:
*/
int IKinSpaceNR(int JointNum, double *Slist, double M[4][4], double T[4][4], double *thetalist0, double eomg, double ev, int maxiter,double *thetalist)
{
	int i, j;
	double Tsb[4][4];
	double iTsb[4][4];
	double Tbd[4][4];
	double AdT[6][6];
	double se3Mat[4][4];
	double Vb[6];
	double Vs[6];
	int ErrFlag;
	double *Js = (double *)malloc(JointNum * 6 * sizeof(double));
	if (Js == NULL)
	{
		return 2;
	}
	double *pJs = (double *)malloc(JointNum * 6 * sizeof(double));
	if (pJs == NULL)
	{
		free(Js);
		return 2;
	}
	double *dtheta = (double *)malloc(JointNum * sizeof(double));
	if (dtheta == NULL)
	{
		free(Js);
		free(pJs);
		return 2;
	}
	MatrixCopy(thetalist0, JointNum, 1, thetalist);
	FKinSpace(M, JointNum, Slist, thetalist, Tsb);
	TransInv(Tsb, iTsb);
	Matrix4Mult(iTsb, T, Tbd);
	MatrixLog6(Tbd, se3Mat);
	se3ToVec(se3Mat, Vb);
	Adjoint(Tsb, AdT);
	MatrixMult((double *)AdT, 6, 6, Vb, 1, Vs);
	ErrFlag = VecNorm2(3, &Vs[0]) > eomg || VecNorm2(3, &Vs[3]) > ev;
	i = 0;

#if(DEBUGMODE)
	///////////////////Debug///////////
	printf("iteration:%4d  thetalist:  ", i);
	int k;
	for (k = 0; k < JointNum; k++)
	{
		printf("%4.4lf, ", thetalist[k]);
	}
	printf("\n");
	////////////////////////////////////
#endif

	while (ErrFlag && i < maxiter)
	{
		JacobianSpace(JointNum, Slist, thetalist, Js);
		MatrixPinv(Js, 6, JointNum, 2.2E-15, pJs);
		MatrixMult(pJs, JointNum, 6, Vs, 1, dtheta);
		for (j = 0; j < JointNum; j++)
		{
			thetalist[j] = thetalist[j] + dtheta[j];
		}
		i++;
		FKinSpace(M, JointNum, Slist, thetalist, Tsb);
		TransInv(Tsb, iTsb);
		Matrix4Mult(iTsb, T, Tbd);
		MatrixLog6(Tbd, se3Mat);
		se3ToVec(se3Mat, Vb);
		Adjoint(Tsb, AdT);
		MatrixMult((double *)AdT, 6, 6, Vb, 1, Vs);
		ErrFlag = VecNorm2(3, &Vs[0]) > eomg || VecNorm2(3, &Vs[3]) > ev;
#if (DEBUGMODE)
		///////////////////////DEBUG///////////
		printf("iteration:%4d  thetalist:  ", i);
		for (k = 0; k < JointNum; k++)
		{
			printf("%4.4lf, ", thetalist[k]);
		}
		printf("\n");
		//////////////////////////////////////
#endif

	}
	free(Js);
	free(pJs);
	free(dtheta);
	return ErrFlag;
}



/**
* @brief 			Description: Algorithm for Computing the ZYX Euler Angles according to rotation matrix.
* @param[in]		R				Rotation matrix.
* @param[out]		alpha			Angles for rotation around Z axis.
* @param[out]		beta			Angles for rotation around Y axis.
* @param[out]		gamma			Angles for rotation around X axis.
* @return			No return value.
* @note:
*@warning:
*/
void RotToZYXEulerAngle(double R[3][3], double *alpha, double *beta, double *gamma)
{

	if (fabs(1.0 + R[2][0])<ZERO_ELEMENT)
	{
		*alpha = 0;
		*beta = PI / 2.0;
		*gamma = atan2(R[0][1], R[1][1]);

	}
	else if (fabs(1.0 - R[2][0])<ZERO_ELEMENT)
	{
		*alpha = 0;
		*beta = -PI / 2.0;
		*gamma = atan2(R[0][1], R[1][1]);
	}
	else
	{

		*alpha = atan2(R[1][0], R[0][0]);
		*beta = atan2(-R[2][0], sqrt(R[0][0] * R[0][0] + R[1][0] * R[1][0]));
		*gamma = atan2(R[2][1], R[2][2]);
	}
	return;

}

/**
* @brief 			Description: Algorithm for Computing the rotation matrix of ZYX Euler Angles.
* @param[in]		alpha			Angles for rotation around Z axis.
* @param[in]		beta			Angles for rotation around Y axis.
* @param[in]		gamma			Angles for rotation around X axis.
* @param[out]		R				Rotation matrix.
* @return			No return value.
* @note:
* @waring:
*/
void ZYXEulerAngleToRot(double alpha, double beta, double gamma, double R[3][3])
{
	R[0][0] = cos(alpha)*cos(beta);
	R[0][1] = cos(alpha)*sin(beta)*sin(gamma) - sin(alpha)*cos(gamma);
	R[0][2] = cos(alpha)*sin(beta)*cos(gamma) + sin(alpha)*sin(gamma);
	R[1][0] = sin(alpha)*cos(beta);
	R[1][1] = sin(alpha)*sin(beta)*sin(gamma) + cos(alpha)*cos(gamma);
	R[1][2] = sin(alpha)*sin(beta)*cos(gamma) - cos(alpha)*sin(gamma);
	R[2][0] = -sin(beta);
	R[2][1] = cos(beta)*sin(gamma);
	R[2][2] = cos(beta)*cos(gamma);
	return;
}


/**
 * @brief 			Description: Computes the unit vector of Euler axis and rotation angle corresponding to rotation matrix.
 * @param[in]		R				A rotation matrix.
 * @param[out]		omghat			the unit vector of Euler axis .
 * @param[out]		theta			the rotation angle.
 * @return			No return value.
 * @retval			0
 * @note:			if  theta is zero ,the unit axis is undefined and set it as a zero vector [0;0;0].
 *@warning:
*/
void RotToAxisAng(double R[3][3],double omghat[3],double *theta)
{
	double tmp;
	double omg[3] = { 0 };
	double acosinput = (R[0][0] + R[1][1] + R[2][2] - 1.0) / 2.0;
	if (fabs(acosinput-1.0)<ZERO_VALUE)
	{
		memset(omghat, 0, 3 * sizeof(double));
		*theta = 0.0;
	}
	else if (acosinput <= -1.0)
	{
		if ((1.0 + R[2][2]) >= ZERO_VALUE)
		{
			omg[0] = 1.0 / sqrt(2 * (1.0 + R[2][2]))*R[0][2];
			omg[1] = 1.0 / sqrt(2 * (1.0 + R[2][2]))*R[1][2];
			omg[2] = 1.0 / sqrt(2 * (1.0 + R[2][2]))*(1.0 + R[2][2]);
		}
		else if ((1.0 + R[1][1] >= ZERO_VALUE))
		{
			omg[0] = 1.0 / sqrt(2 * (1.0 + R[1][1]))*R[0][1];
			omg[1] = 1.0 / sqrt(2 * (1.0 + R[1][1]))*(1.0 + R[1][1]);
			omg[2] = 1.0 / sqrt(2 * (1.0 + R[1][1]))*R[2][1];
		}
		else
		{
			omg[0] = 1.0 / sqrt(2 * (1.0 + R[0][0]))*(1.0 + R[0][0]);
			omg[1] = 1.0 / sqrt(2 * (1.0 + R[0][0]))*R[1][0];
			omg[2] = 1.0 / sqrt(2 * (1.0 + R[0][0]))*R[2][0];
		}
		omghat[0] = omg[0];
		omghat[1] = omg[1];
		omghat[2] = omg[2];
		*theta=PI;
	}
	else
	{
		*theta = acos(acosinput);
		tmp = 2.0*sin(*theta);
		omghat[0] = (R[2][1] - R[1][2]) / tmp;
		omghat[1] = (R[0][2] - R[2][0]) / tmp;
		omghat[2] = (R[1][0] - R[0][1]) / tmp;

	}

	return;
}


/**
 * @brief 			Description: Computes the unit quaternion corresponding to the Euler axis and rotation angle.
 * @param[in]		omg				Unit vector of Euler axis.
 * @param[in]		theta			Rotation angle.
 * @param[in]		q				The unit quaternion
 * @return			No return value.
 * @note:
 *@warning:
*/
void AxisAngToQuaternion(double omg[3],double theta, double q[4])
{
	q[0] = cos(theta / 2.0);
	q[1] = omg[0] * sin(theta / 2.0);
	q[2] = omg[1] * sin(theta / 2.0);
	q[3] = omg[2] * sin(theta / 2.0);
	return;
}


/**
 * @brief 			Description:Computes the unit quaternion corresponding to a rotation matrix.
 * @param[in]		q				Unit quaternion.
 * @param[out]		R				Rotation matrix.
 * @return			No return value.
 * @note:
 * @warning:
*/
void QuaternionToRot(double q[4], double R[3][3])
{
	R[0][0] = q[0] * q[0] + q[1] * q[1] - q[2] * q[2] - q[3] * q[3];
	R[0][1] = 2.0*(q[1] * q[2] - q[0] * q[3]);
	R[0][2] = 2.0*(q[0] * q[2] + q[1] * q[3]);
	R[1][0] = 2.0*(q[0] * q[3] + q[1] * q[2]);
	R[1][1] = q[0] * q[0] - q[1] * q[1] + q[2] * q[2] - q[3] * q[3];
	R[1][2] = 2.0*(q[2] * q[3] - q[0] * q[1]);
	R[2][0] = 2.0*(q[1] * q[3] - q[0] * q[2]);
	R[2][1] = 2.0*(q[0] * q[1] + q[2] * q[3]);
	R[2][2] = q[0] * q[0] - q[1] * q[1] - q[2] * q[2] + q[3] * q[3];
	return;
}

/**
 * @brief 			Description: Computes the unit quaternion corresponding to the rotation matrix.
 * @param[in]		R				The rotation matrix.
 * @param[out]		q				The unit quaternion.
 * @return			No return value.
 * @note:
 * @warning:
*/
void RotToQuaternion(double R[3][3], double q[4])
{
	double omghat[3];
	double theta;
	RotToAxisAng(R, omghat, &theta);
	AxisAngToQuaternion(omghat, theta, q);
	return;
}


/**
* @brief 			单位四元数转换为旋转矩阵。
* @param[in]		q				单位四元数[ox,oy,oz,ow].
* @param[out]		R				旋转矩阵.
* @return			无返回值.
* @note:
* @warning:         (1)此函数不对输入参数做检查，需保证输入为单位四元数。
					(2)四元数顺序为[ox,oy,oz,w]。
*/
void q2rot(double q[4], double R[3][3])
{
	double q1[4] = { 0 };

	q1[0] = q[3];
	q1[1] = q[0];
	q1[2] = q[1];
	q1[3] = q[2];
	QuaternionToRot(q1, R);
	return;
}

/**
* @brief 			旋转矩阵转单位四元数。
* @param[in]		R				旋转矩阵
* @param[out]		q				单位四元数.[ox,oy,oz,ow].
* @return			无返回值.
* @note:
* @warning:         (1)此函数不对输入参数做检查，需保证输入为旋转矩阵。
					(2)四元数顺序为[ox,oy,oz,w]。
*/
void rot2q(double R[3][3], double q[4])
{
	double q1[4] = { 0 };
	RotToQuaternion(R, q1);
	q[0] = q1[1];
	q[1] = q1[2];
	q[2] = q1[3];
	q[3] = q1[0];
	return;
}


/**
 * @brief 			Description: Computes the parameters of  orientation interpolation between two orientations.
 * @param[in]		Rs				Start orientation.
 * @param[in]		Re				End orientation. 
 * @param[in]		Param			structure of orientation interpolation parameters..
 * @return			No return value.
 * @note:
 * @warning:
*/
void InitialOrientInpParam(double Rs[3][3],double Re[3][3], OrientInpParam *Param)
{
	double InvR[3][3];
	MatrixCopy((double *)Rs, 3, 3, (double *)Param->Rs);
	MatrixCopy((double *)Re, 3, 3, (double *)Param->Re);
	RotInv(Rs, InvR);
	MatrixMult((double *)InvR, 3, 3, (double *)Re, 3, (double *)Param->R);
	RotToAxisAng(Param->R, Param->omg, &Param->theta);
	MatrixCopy((double *)Param->R, 3, 3, (double *)Param->Ri);
	Param->thetai = 0.0;
	Param->InpFlag = 1;
	return;
}


/**
 * @brief 			Description: Computes orientations in each interpolation cycle.
 * @param[in]		Param			Interpolation parameter structure.
 * @param[out]		dtheta			angle  need to rotate from previous orientation to next orientation in next time step.
 * @return			Ri1				orientations in next interpolation cycle.
 * @retval			0
 * @note:
 * @warning:
*/
void QuaternionOrientInp(OrientInpParam *Param, double dtheta, double Ri1[3][3])
{
	double q[4];
	double R[3][3];
	Param->InpFlag = 2;
	Param->thetai = Param->thetai + dtheta;
	if (Param->thetai >= Param->theta)
	{
		Param->thetai = Param->theta;
		Param->InpFlag = 3;
	}
	AxisAngToQuaternion(Param->omg, Param->thetai, q);
	QuaternionToRot(q, R);
	MatrixMult((double *)Param->Rs, 3, 3, (double *)R, 3, (double *)Ri1);
	MatrixCopy((double *)Ri1, 3, 3, (double *)Param->Ri);
	return;
}

/**
 * @brief 			Description:Computes the parameters of line path for interpolation.
 * @param[in]		p1				Coordinates of start point.
 * @param[in]		p2				Coordinates of end point.
 * @param[out]		p				Line path parameters structure.
 * @return			No return value.
 * @note:
 * @warning:
*/
void InitialLinePathParam(double p1[3],double p2[3], LineInpParam *p)
{
	int i;
	for (i=0;i<3;i++)
	{
		p->p1[i] = p1[i];
		p->p2[i] = p2[i];
		p->pi[i] = p1[i];
	}
	p->L = sqrt((p2[0] - p1[0])*(p2[0] - p1[0]) + (p2[1] - p1[1])*(p2[1] - p1[1]) + (p2[2] - p1[2])*(p2[2] - p1[2]));

	if (p->L<ZERO_DISTANCE)
	{
		p->t[0] = 0.0;
		p->t[1] = 0.0;
		p->t[2] = 0.0;
	}
	else
	{ 
		p->t[0] = (p2[0] - p1[0]) / p->L;
		p->t[1] = (p2[1] - p1[1]) / p->L;
		p->t[2] = (p2[2] - p1[2]) / p->L;
	}
	p->InpFlag = 1;
	p->Li = 0;
	return;
}

/**
 * @brief 			Description:Computes the line path interpolation coordinates in each interpolation cycle.
 * @param[in]		p				Line path parameters structure.
 * @param[in]		dL				step length in next interpolation cycle. 
 * @param[in]		pi1				coordinates in next interpolation cycle.
 * @return			No return value.
 * @note:
 * @warning:
*/
void LinePathInp(LineInpParam *p, double dL, double pi1[3])
{
	p->InpFlag = 2;
	if (p->Li + dL>=p->L)
	{
		pi1[0] = p->p2[0];
		pi1[1] = p->p2[1];
		pi1[2] = p->p2[2];
		p->Li = p->L;
		p->InpFlag = 3;
	}
	else if ( p->L- p->Li < 2.0*dL)
	{
		//avoid distance of  final step  is too small.
		dL = 0.5*dL;
		pi1[0] = p->pi[0] + p->t[0] * dL;
		pi1[1] = p->pi[1] + p->t[1] * dL;
		pi1[2] = p->pi[2] + p->t[2] * dL;
		p->Li = p->Li+dL;
	}
	else
	{
		pi1[0] = p->pi[0] + p->t[0] * dL;
		pi1[1] = p->pi[1] + p->t[1] * dL;
		pi1[2] = p->pi[2] + p->t[2] * dL;
		p->Li = p->Li + dL;
	}

	p->pi[0] = pi1[0];
	p->pi[1] = pi1[1];
	p->pi[2] = pi1[2];
	return;
}

/**
 * @brief 			Description: Computes the parameters of both line path and orientation for interpolation.
 * @param[in]		p1				Start coordinates,including x,y,z coordinates and orientation angles roll-pitch-yaw angles.
 * @param[in]		p2				End coordinates,including x,y,z coordinates and orientation angles roll-pitch-yaw angles.
 * @param[out]		LPO				Parameters of both line path and orientation for interpolation.
 * @return			No return value.
 * @note:
 * @warning:
*/
void InitialLinePOInpParam( double p1[6], double p2[6], LinePOParam *LPO)
{
	double Rs[3][3];
	double Re[3][3];
	RPYToRot(p1[3], p1[4], p1[5], Rs);
	RPYToRot(p2[3], p2[4], p2[5], Re);
	InitialLinePathParam( p1, p2, &(LPO->Line));
	InitialOrientInpParam(Rs, Re, &(LPO->Orient));
	RpToTrans(Rs, p1, LPO->Ts);
	RpToTrans(Rs, p1, LPO->Ti);
	RpToTrans(Re, p2, LPO->Te);
	LPO->InpFlag = 1;
	return;
}

/**
 * @brief 			Description:Computes the line path interpolation coordinates and orientation in each interpolation cycle.
 * @param[out]		LPO				Line path and orientation parameters structure.
 * @param[in]		dL				Line path interpolation step length.
 * @param[out]		dtheta			angle interpolation step length for Orientation interpolation.
 * @return			No return value.
 * @note:
 * @warning:
*/
void LinePOInp(LinePOParam *LPO,double dL,double dtheta,double Ti[4][4])
{
	double pi[3];
	double Ri[3][3];
	LPO->InpFlag = 2;
	LinePathInp(&LPO->Line, dL, pi);
	QuaternionOrientInp(&LPO->Orient, dtheta, Ri);
	if (LPO->Line.InpFlag==3 && LPO->Orient.InpFlag==3)
	{
		LPO->InpFlag = 3;
	}
	RpToTrans(Ri, pi, Ti);
	MatrixCopy((double *)Ti, 4, 4, (double *)LPO->Ti);
	return;
}