1. ## linear algebra

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

Thanks.

2. ## Re: linear algebra

I would actually say: all algebra

Good luck

3. ## Re: linear algebra

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.

4. ## Re: linear algebra

How good do you want the game engine to be?

5. ## Re: linear algebra

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;
}

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