# linear algebra

What topics of linear algebra are important
for game development and Opengl?

Thanks.

I would actually say: all algebra

Good luck

Like goater, I’d say all linear algebra is useful. The more you understand this branch of mathematics the better. However, you can get by with a basic knowledge of vectors, matrices, an understanding of R1, R2, R3 & R4 space, linear transformations, inverse matrices, transposing matrices and that’s about it. You probably don’t need stuff like eigenvectors, orthogonality of subspaces, etc.

Hope that helps.

How good do you want the game engine to be?

To understand topics like Opengl matrix trasformation, what topics of linear algebra is fundamental?
For examples I don’t known why I need to combine modelview and projection matrix to get frustum clipping plane.
I have a tutorial in Opengl that explain like to perform frustum clipping planes,
but I have many problem to understand the function ExtractFrustum.

Any can explain this function?

float frustum[6][4];
ExtractFrustum()
{
float proj[16];
float modl[16];
float clip[16];
float t;

/* Get the current PROJECTION matrix from OpenGL */
glGetFloatv( GL_PROJECTION_MATRIX, proj );

/* Get the current MODELVIEW matrix from OpenGL */
glGetFloatv( GL_MODELVIEW_MATRIX, modl );

/* Combine the two matrices (multiply projection by modelview) */
clip[ 0] = modl[ 0] * proj[ 0] + modl[ 1] * proj[ 4] + modl[ 2] * proj[ 8] + modl[ 3] * proj[12];
clip[ 1] = modl[ 0] * proj[ 1] + modl[ 1] * proj[ 5] + modl[ 2] * proj[ 9] + modl[ 3] * proj[13];
clip[ 2] = modl[ 0] * proj[ 2] + modl[ 1] * proj[ 6] + modl[ 2] * proj[10] + modl[ 3] * proj[14];
clip[ 3] = modl[ 0] * proj[ 3] + modl[ 1] * proj[ 7] + modl[ 2] * proj[11] + modl[ 3] * proj[15];

clip[ 4] = modl[ 4] * proj[ 0] + modl[ 5] * proj[ 4] + modl[ 6] * proj[ 8] + modl[ 7] * proj[12];
clip[ 5] = modl[ 4] * proj[ 1] + modl[ 5] * proj[ 5] + modl[ 6] * proj[ 9] + modl[ 7] * proj[13];
clip[ 6] = modl[ 4] * proj[ 2] + modl[ 5] * proj[ 6] + modl[ 6] * proj[10] + modl[ 7] * proj[14];
clip[ 7] = modl[ 4] * proj[ 3] + modl[ 5] * proj[ 7] + modl[ 6] * proj[11] + modl[ 7] * proj[15];

clip[ 8] = modl[ 8] * proj[ 0] + modl[ 9] * proj[ 4] + modl[10] * proj[ 8] + modl[11] * proj[12];
clip[ 9] = modl[ 8] * proj[ 1] + modl[ 9] * proj[ 5] + modl[10] * proj[ 9] + modl[11] * proj[13];
clip[10] = modl[ 8] * proj[ 2] + modl[ 9] * proj[ 6] + modl[10] * proj[10] + modl[11] * proj[14];
clip[11] = modl[ 8] * proj[ 3] + modl[ 9] * proj[ 7] + modl[10] * proj[11] + modl[11] * proj[15];

clip[12] = modl[12] * proj[ 0] + modl[13] * proj[ 4] + modl[14] * proj[ 8] + modl[15] * proj[12];
clip[13] = modl[12] * proj[ 1] + modl[13] * proj[ 5] + modl[14] * proj[ 9] + modl[15] * proj[13];
clip[14] = modl[12] * proj[ 2] + modl[13] * proj[ 6] + modl[14] * proj[10] + modl[15] * proj[14];
clip[15] = modl[12] * proj[ 3] + modl[13] * proj[ 7] + modl[14] * proj[11] + modl[15] * proj[15];

/* Extract the numbers for the RIGHT plane */
frustum[0][0] = clip[ 3] - clip[ 0];
frustum[0][1] = clip[ 7] - clip[ 4];
frustum[0][2] = clip[11] - clip[ 8];
frustum[0][3] = clip[15] - clip[12];

/* Normalize the result */
t = sqrt( frustum[0][0] * frustum[0][0] + frustum[0][1] * frustum[0][1] + frustum[0][2] * frustum[0][2] );
frustum[0][0] /= t;
frustum[0][1] /= t;
frustum[0][2] /= t;
frustum[0][3] /= t;

/* Extract the numbers for the LEFT plane */
frustum[1][0] = clip[ 3] + clip[ 0];
frustum[1][1] = clip[ 7] + clip[ 4];
frustum[1][2] = clip[11] + clip[ 8];
frustum[1][3] = clip[15] + clip[12];

/* Normalize the result */
t = sqrt( frustum[1][0] * frustum[1][0] + frustum[1][1] * frustum[1][1] + frustum[1][2] * frustum[1][2] );
frustum[1][0] /= t;
frustum[1][1] /= t;
frustum[1][2] /= t;
frustum[1][3] /= t;

/* Extract the BOTTOM plane */
frustum[2][0] = clip[ 3] + clip[ 1];
frustum[2][1] = clip[ 7] + clip[ 5];
frustum[2][2] = clip[11] + clip[ 9];
frustum[2][3] = clip[15] + clip[13];

/* Normalize the result */
t = sqrt( frustum[2][0] * frustum[2][0] + frustum[2][1] * frustum[2][1] + frustum[2][2] * frustum[2][2] );
frustum[2][0] /= t;
frustum[2][1] /= t;
frustum[2][2] /= t;
frustum[2][3] /= t;

/* Extract the TOP plane */
frustum[3][0] = clip[ 3] - clip[ 1];
frustum[3][1] = clip[ 7] - clip[ 5];
frustum[3][2] = clip[11] - clip[ 9];
frustum[3][3] = clip[15] - clip[13];

/* Normalize the result */
t = sqrt( frustum[3][0] * frustum[3][0] + frustum[3][1] * frustum[3][1] + frustum[3][2] * frustum[3][2] );
frustum[3][0] /= t;
frustum[3][1] /= t;
frustum[3][2] /= t;
frustum[3][3] /= t;

/* Extract the FAR plane */
frustum[4][0] = clip[ 3] - clip[ 2];
frustum[4][1] = clip[ 7] - clip[ 6];
frustum[4][2] = clip[11] - clip[10];
frustum[4][3] = clip[15] - clip[14];

/* Normalize the result */
t = sqrt( frustum[4][0] * frustum[4][0] + frustum[4][1] * frustum[4][1] + frustum[4][2] * frustum[4][2] );
frustum[4][0] /= t;
frustum[4][1] /= t;
frustum[4][2] /= t;
frustum[4][3] /= t;

/* Extract the NEAR plane */
frustum[5][0] = clip[ 3] + clip[ 2];
frustum[5][1] = clip[ 7] + clip[ 6];
frustum[5][2] = clip[11] + clip[10];
frustum[5][3] = clip[15] + clip[14];

/* Normalize the result */
t = sqrt( frustum[5][0] * frustum[5][0] + frustum[5][1] * frustum[5][1] + frustum[5][2] * frustum[5][2] );
frustum[5][0] /= t;
frustum[5][1] /= t;
frustum[5][2] /= t;
frustum[5][3] /= t;
}