Matrix Inversion

Bobby-D · 2004-01-15T04:11:12

Can anyone tell me where I can find help on the maths behind a function for Inverting a 4x4 Matrix? I need to make a function to invert a matrix, but I don''t know how. Thanks. One by one, the peguins steal my sanity.

Math and Physics Programming

Started by Bobby-D January 14, 2004 02:05 AM

11 comments, last by Bobby-D 20 years, 3 months ago

circuit

134

January 14, 2004 12:46 PM

float determinant4f(const float m[16]){  return    m[12]*m[9]*m[6]*m[3]-    m[8]*m[13]*m[6]*m[3]-    m[12]*m[5]*m[10]*m[3]+    m[4]*m[13]*m[10]*m[3]+    m[8]*m[5]*m[14]*m[3]-    m[4]*m[9]*m[14]*m[3]-    m[12]*m[9]*m[2]*m[7]+    m[8]*m[13]*m[2]*m[7]+    m[12]*m[1]*m[10]*m[7]-    m[0]*m[13]*m[10]*m[7]-    m[8]*m[1]*m[14]*m[7]+    m[0]*m[9]*m[14]*m[7]+    m[12]*m[5]*m[2]*m[11]-    m[4]*m[13]*m[2]*m[11]-    m[12]*m[1]*m[6]*m[11]+    m[0]*m[13]*m[6]*m[11]+    m[4]*m[1]*m[14]*m[11]-    m[0]*m[5]*m[14]*m[11]-    m[8]*m[5]*m[2]*m[15]+    m[4]*m[9]*m[2]*m[15]+    m[8]*m[1]*m[6]*m[15]-    m[0]*m[9]*m[6]*m[15]-    m[4]*m[1]*m[10]*m[15]+    m[0]*m[5]*m[10]*m[15];}bool generateInverseMatrix4f(float i[16], const float m[16]){  float x=determinant4f(m);  if (x==0) return false;  i[0]= (-m[13]*m[10]*m[7] +m[9]*m[14]*m[7] +m[13]*m[6]*m[11]         -m[5]*m[14]*m[11] -m[9]*m[6]*m[15] +m[5]*m[10]*m[15])/x;  i[4]= ( m[12]*m[10]*m[7] -m[8]*m[14]*m[7] -m[12]*m[6]*m[11]         +m[4]*m[14]*m[11] +m[8]*m[6]*m[15] -m[4]*m[10]*m[15])/x;  i[8]= (-m[12]*m[9]* m[7] +m[8]*m[13]*m[7] +m[12]*m[5]*m[11]         -m[4]*m[13]*m[11] -m[8]*m[5]*m[15] +m[4]*m[9]* m[15])/x;  i[12]=( m[12]*m[9]* m[6] -m[8]*m[13]*m[6] -m[12]*m[5]*m[10]         +m[4]*m[13]*m[10] +m[8]*m[5]*m[14] -m[4]*m[9]* m[14])/x;  i[1]= ( m[13]*m[10]*m[3] -m[9]*m[14]*m[3] -m[13]*m[2]*m[11]         +m[1]*m[14]*m[11] +m[9]*m[2]*m[15] -m[1]*m[10]*m[15])/x;  i[5]= (-m[12]*m[10]*m[3] +m[8]*m[14]*m[3] +m[12]*m[2]*m[11]         -m[0]*m[14]*m[11] -m[8]*m[2]*m[15] +m[0]*m[10]*m[15])/x;  i[9]= ( m[12]*m[9]* m[3] -m[8]*m[13]*m[3] -m[12]*m[1]*m[11]         +m[0]*m[13]*m[11] +m[8]*m[1]*m[15] -m[0]*m[9]* m[15])/x;  i[13]=(-m[12]*m[9]* m[2] +m[8]*m[13]*m[2] +m[12]*m[1]*m[10]         -m[0]*m[13]*m[10] -m[8]*m[1]*m[14] +m[0]*m[9]* m[14])/x;  i[2]= (-m[13]*m[6]* m[3] +m[5]*m[14]*m[3] +m[13]*m[2]*m[7]         -m[1]*m[14]*m[7]  -m[5]*m[2]*m[15] +m[1]*m[6]* m[15])/x;  i[6]= ( m[12]*m[6]* m[3] -m[4]*m[14]*m[3] -m[12]*m[2]*m[7]         +m[0]*m[14]*m[7]  +m[4]*m[2]*m[15] -m[0]*m[6]* m[15])/x;  i[10]=(-m[12]*m[5]* m[3] +m[4]*m[13]*m[3] +m[12]*m[1]*m[7]         -m[0]*m[13]*m[7]  -m[4]*m[1]*m[15] +m[0]*m[5]* m[15])/x;  i[14]=( m[12]*m[5]* m[2] -m[4]*m[13]*m[2] -m[12]*m[1]*m[6]         +m[0]*m[13]*m[6]  +m[4]*m[1]*m[14] -m[0]*m[5]* m[14])/x;  i[3]= ( m[9]* m[6]* m[3] -m[5]*m[10]*m[3] -m[9]* m[2]*m[7]         +m[1]*m[10]*m[7]  +m[5]*m[2]*m[11] -m[1]*m[6]* m[11])/x;  i[7]= (-m[8]* m[6]* m[3] +m[4]*m[10]*m[3] +m[8]* m[2]*m[7]         -m[0]*m[10]*m[7]  -m[4]*m[2]*m[11] +m[0]*m[6]* m[11])/x;  i[11]=( m[8]* m[5]* m[3] -m[4]*m[9]* m[3] -m[8]* m[1]*m[7]         +m[0]*m[9]* m[7]  +m[4]*m[1]*m[11] -m[0]*m[5]* m[11])/x;  i[15]=(-m[8]* m[5]* m[2] +m[4]*m[9]* m[2] +m[8]* m[1]*m[6]         -m[0]*m[9]* m[6]  -m[4]*m[1]*m[10] +m[0]*m[5]* m[10])/x;  return true;}

[edited by - circuit on January 14, 2004 1:49:47 PM]

FReY

424

January 15, 2004 02:09 AM

Okay, in order to do it by Gauss reduction (I assume you know how to do Gauss reduction?!?):

Assume you want to invert matrix A, set matrix B to the identity matrix.

Reduce A to the identity matrix (using Gauss reduction) but use exactly the same operations on matrix B that you used on matrix A.

When eventually matrix A becomes the identity matrix, matrix B will be your original matrix A''s inverse.

Simple no?

do unto others... and then run like hell.

Bobby-D

122

Author

January 15, 2004 04:11 AM

Wow, thanks guys for all the replies. It''s all been very helpful. My knowledge of matricies is fairly limited, but I think i''m starting to understand. At least now I know what to look for. Much Appreciated.

One by one, the peguins steal my sanity.

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