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#include "geometry.h"
namespace PTools{
/** \brief Matrix multiplication
* This function is a simple matrix multiplication routine for 4x4 matrix
*/
void mat44xmat44( const dbl mat1[ 4 ][ 4 ], const dbl mat2[ 4 ][ 4 ], dbl result[ 4 ][ 4 ] )
{
// gives mat1*mat2 (mat2 left multiplied by mat1)
// this works even if result == mat1 (ie pointing the to same memory)
dbl temp[4][4];
//std::cout << mat1 << " " << mat2 << " " << result;
//printmat44(mat1);
//printmat44(mat2);
for ( int rl = 0; rl < 4; rl++ )
for ( int rc = 0; rc < 4; rc++ )
{
// compute the element result[rl][rc]:
dbl sum = 0.0 ;
for ( int p = 0; p < 4; p++ )
sum += mat1[ rl ][ p ] * mat2[ p ][ rc ] ;
temp[ rl ][ rc ] = sum ;
}
//printmat44(result);
memcpy(result, temp, 16*sizeof(dbl));
}
void MakeRotationMatrix( Coord3D A, Coord3D B, dbl theta, dbl out[ 4 ][ 4 ] )
{
// compute AB vector (dx; dy; dz):
dbl dx = B.x - A.x ;
dbl dy = B.y - A.y ;
dbl dz = B.z - A.z ;
dbl mat1[ 4 ][ 4 ] ;
// translation of vector BA
for ( int i = 0; i < 4; i++ )
for ( int j = 0; j < 4; j++ )
if ( i != j )
{
mat1[ i ][ j ] = 0 ;
}
else
mat1[ i ][ j ] = 1 ;
mat1[ 0 ][ 3 ] = -A.x;
mat1[ 1 ][ 3 ] = -A.y;
mat1[ 2 ][ 3 ] = -A.z;
// rotation to get back to plan Oxz: rotation 1 around X, angle -gamma (-g).
dbl d = sqrt( dy*dy + dz*dz ) ; // projection of AB on the Oxy plan
if ( real(d) == 0 ) // AB belongs to (Ox)
{
dbl cost = cos( theta );
dbl sint = sin( theta );
out[ 0 ][ 0 ] = 1 ;
out[ 0 ][ 1 ] = 0 ;
out[ 0 ][ 2 ] = 0 ;
out[ 0 ][ 3 ] = 0 ;
out[ 1 ][ 0 ] = 0 ;
out[ 1 ][ 1 ] = cost ;
out[ 1 ][ 2 ] = sint ;
out[ 1 ][ 3 ] = 0 ;
out[ 2 ][ 0 ] = 0 ;
out[ 2 ][ 1 ] = -sint;
out[ 2 ][ 2 ] = cost ;
out[ 2 ][ 3 ] = 0 ;
out[ 3 ][ 0 ] = 0 ;
out[ 3 ][ 1 ] = 0 ;
out[ 3 ][ 2 ] = 0 ;
out[ 3 ][ 3 ] = 1 ;
//printmat44(out);
return ;
}
dbl cosg = dz / d ;
dbl sing = dy / d ;
dbl mat2[ 4 ][ 4 ] ;
mat2[ 0 ][ 0 ] = 1 ;
mat2[ 0 ][ 1 ] = 0 ;
mat2[ 0 ][ 2 ] = 0 ;
mat2[ 0 ][ 3 ] = 0 ;
mat2[ 1 ][ 0 ] = 0 ;
mat2[ 1 ][ 1 ] = cosg ;
mat2[ 1 ][ 2 ] = -sing ;
mat2[ 1 ][ 3 ] = 0 ;
mat2[ 2 ][ 0 ] = 0;
mat2[ 2 ][ 1 ] = sing;
mat2[ 2 ][ 2 ] = cosg ;
mat2[ 2 ][ 3 ] = 0 ;
mat2[ 3 ][ 0 ] = 0 ;
mat2[ 3 ][ 1 ] = 0 ;
mat2[ 3 ][ 2 ] = 0;
mat2[ 3 ][ 3 ] = 1 ;
//printmat44(mat2);
dbl mat3[ 4 ][ 4 ];
mat44xmat44( mat2, mat1, mat3 ); // mat3 == mat2*mat1 (!= mat1*mat2 )
// rotation to get back to the Oz axis: rotation 2. Axis (Oy), angle p.
dbl f = sqrt( dx*dx + dy*dy + dz*dz ); // norm
dbl cosp, sinp ;
cosp = d / f;
sinp = dx / f;
mat1[ 0 ][ 0 ] = cosp ;
mat1[ 0 ][ 1 ] = 0 ;
mat1[ 0 ][ 2 ] = -sinp ;
mat1[ 0 ][ 3 ] = 0 ;
mat1[ 1 ][ 0 ] = 0 ;
mat1[ 1 ][ 1 ] = 1 ;
mat1[ 1 ][ 2 ] = 0 ;
mat1[ 1 ][ 3 ] = 0 ;
mat1[ 2 ][ 0 ] = sinp ;
mat1[ 2 ][ 1 ] = 0 ;
mat1[ 2 ][ 2 ] = cosp ;
mat1[ 2 ][ 3 ] = 0 ;
mat1[ 3 ][ 0 ] = 0 ;
mat1[ 3 ][ 1 ] = 0 ;
mat1[ 3 ][ 2 ] = 0 ;
mat1[ 3 ][ 3 ] = 1 ;
mat44xmat44( mat1, mat3, mat2 ); // result stored in mat2
// effective rotation (around 0z axis, angle theta)
dbl rotmatrix[ 4 ][ 4 ] ;
dbl cost = cos( theta );
dbl sint = sin( theta );
rotmatrix[ 0 ][ 0 ] = cost ;
rotmatrix[ 0 ][ 1 ] = sint;
rotmatrix[ 0 ][ 2 ] = 0;
rotmatrix[ 0 ][ 3 ] = 0;
rotmatrix[ 1 ][ 0 ] = -sint;
rotmatrix[ 1 ][ 1 ] = cost;
rotmatrix[ 1 ][ 2 ] = 0;
rotmatrix[ 1 ][ 3 ] = 0;
rotmatrix[ 2 ][ 0 ] = 0 ;
rotmatrix[ 2 ][ 1 ] = 0 ;
rotmatrix[ 2 ][ 2 ] = 1;
rotmatrix[ 2 ][ 3 ] = 0;
rotmatrix[ 3 ][ 0 ] = 0 ;
rotmatrix[ 3 ][ 1 ] = 0 ;
rotmatrix[ 3 ][ 2 ] = 0;
rotmatrix[ 3 ][ 3 ] = 1;
mat44xmat44( rotmatrix, mat2, mat3 ); // result stored in mat3
//rotation -2:
mat1[ 0 ][ 0 ] = cosp ;
mat1[ 0 ][ 1 ] = 0 ;
mat1[ 0 ][ 2 ] = sinp ;
mat1[ 0 ][ 3 ] = 0 ;
mat1[ 1 ][ 0 ] = 0 ;
mat1[ 1 ][ 1 ] = 1 ;
mat1[ 1 ][ 2 ] = 0 ;
mat1[ 1 ][ 3 ] = 0 ;
mat1[ 2 ][ 0 ] = -sinp ;
mat1[ 2 ][ 1 ] = 0 ;
mat1[ 2 ][ 2 ] = cosp ;
mat1[ 2 ][ 3 ] = 0 ;
mat1[ 3 ][ 0 ] = 0 ;
mat1[ 3 ][ 1 ] = 0 ;
mat1[ 3 ][ 2 ] = 0 ;
mat1[ 3 ][ 3 ] = 1 ;
mat44xmat44( mat1, mat3, rotmatrix ); // result in rotmatrix
//rotation -1:
mat2[ 0 ][ 0 ] = 1 ;
mat2[ 0 ][ 1 ] = 0 ;
mat2[ 0 ][ 2 ] = 0 ;
mat2[ 0 ][ 3 ] = 0 ;
mat2[ 1 ][ 0 ] = 0 ;
mat2[ 1 ][ 1 ] = cosg ;
mat2[ 1 ][ 2 ] = sing ;
mat2[ 1 ][ 3 ] = 0 ;
mat2[ 2 ][ 0 ] = 0 ;
mat2[ 2 ][ 1 ] = -sing ;
mat2[ 2 ][ 2 ] = cosg ;
mat2[ 2 ][ 3 ] = 0 ;
mat2[ 3 ][ 0 ] = 0 ;
mat2[ 3 ][ 1 ] = 0 ;
mat2[ 3 ][ 2 ] = 0 ;
mat2[ 3 ][ 3 ] = 1 ;
mat44xmat44( mat2, rotmatrix, mat3 );
//translation-1:
for ( int i = 0; i < 4; i++ )
for ( int j = 0; j < 4; j++ )
if ( i != j )
{
mat1[ i ][ j ] = 0 ;
}
else
mat1[ i ][ j ] = 1 ;
mat1[ 0 ][ 3 ] = A.x;
mat1[ 1 ][ 3 ] = A.y;
mat1[ 2 ][ 3 ] = A.z;
mat44xmat44( mat1, mat3, out );
}
void ABrotate( Coord3D A, Coord3D B, Rigidbody& target, dbl theta )
{
dbl matrix[ 4 ][ 4 ];
MakeRotationMatrix( A, B, theta, matrix );
target.MatrixMultiply(matrix);
// mat44xrigid( source, result, matrix );
}
void VectProd( const Coord3D& u, const Coord3D& v, Coord3D& UvectV )
{
UvectV.x = u.y * v.z - u.z * v.y ;
UvectV.y = u.z * v.x - u.x * v.z ;
UvectV.z = u.x * v.y - u.y * v.x ;
}
void printmat44( const dbl mat[ 4 ][ 4 ] )
{
for (uint i=0; i<4; i++)
{
for (uint j=0; j<4; j++)
{
printf("%12.7f", real(mat[i][j])) ;
}
std::cout << std::endl;
}
std::cout << "\n\n";
}
void MakeVect( const Coord3D& a, const Coord3D& b, Coord3D& result )
{
result.x = b.x - a.x;
result.y = b.y - a.y;
result.z = b.z - a.z;
}
dbl Dihedral( const Coord3D& a, const Coord3D& b, const Coord3D& c, const Coord3D& d )
{
// calculate the dihedral angle defined by a, b, c and d.
// The method is described in: J.K Rainey, Ph.D. Thesis,
// University of Toronto, 2003.
// Collagen structure and preferential assembly explored
// by parallel microscopy and bioinformatics.
// also described here:
// http://structbio.biochem.dal.ca/jrainey/dihedralcalc.html
Coord3D b1 = b-a;
Coord3D b2 = c-b;
Coord3D b3 = d-c;
Coord3D n1;
VectProd (b2, b3, n1);
Coord3D n2;
VectProd(b1, b2, n2);
Coord3D n3;
VectProd(b2,b3,n3);
dbl phi = atan2( Norm(b2) * ScalProd(b1, n1), ScalProd(n2 , n3) ) ;
return phi;
}
dbl Angle(const Coord3D& vector1, const Coord3D& vector2)
{
dbl pdtscal=ScalProd(vector1,vector2);
dbl A = sqrt(ScalProd(vector1,vector1)) ;
dbl B = sqrt(ScalProd(vector2,vector2));
dbl costheta = pdtscal / (A*B) ;
return acos(costheta);
}
dbl MakeTranslationMat44(Coord3D t, dbl out[4][4] )
{
for (int i=0; i<4; i++)
for(int j=0; j<4; j++)
if (i==j) out[i][i]=1.0;
else out[i][j]=0.0;
out[0][3]=t.x;
out[1][3]=t.y;
out[2][3]=t.z;
}
} //namespace PTools
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