Hi, I''m sure everyone is familiar with the shadow-projection matrix. It can be found in OpenGL game programming or at the following website: http://www.sgi.com/software/opengl/advanced96/node46.html However, I''m having difficulties in arriving this matrix equation. Can someone show me the mathematical proof to get the exact matrix formula? Thanks.

p=l-(d+n.l)/(n.(v-l))*(v-l) where p is the projected point, d is d for the plane you are projecting upon, n is the normal for that plane and v is the vertex being projected. It isn''t quite the same matrix in that I don''t see d in the matrix you referred to. This is for basically the same matrix except d is added to each entry on the diagonal. Don''t ask me to explaing it since I just copied it out of Real-Time Rendering.

Yes I''d also like to know a scheme with which I can transform a formula like the shadow projection into a matrix.

Gero

There isn't any magic to it. If you expand it out for one component, for example x, then you get ((d+n_y*l_y+n_z*l_z)*v_x-l_x*n_y*v_y-l_x*n_z*v_z-l_x*d as the numerator. That is pretty straight forward to factor into a dot product with (v_x,v_y,v_z,1). To normalize a homogeneous coordinate you divide through by w so the w component has to be the denominator after the matrix multiplication. The denominator is -n_x*v_x-n_y*v_y-n_z*v_z+n.l. That is similarly easy to factor into a dot product with (v_x,v_y,v_z,1).

[edited by - LilBudyWizer on June 14, 2002 12:59:47 PM]