View Full Version : about shadow

03-12-2003, 12:32 PM
Hi, buddy:

I have a problem about shadow. For example, if I have point light L(x,y,z), some point object V(v1,v2,v3), and any plane Ax+By+Cz+D=0, how can I find the shadow matrix, I mean the point V's shadow in the plane Ax+By+Cz+D=0.

Appreciate here.

03-12-2003, 01:34 PM
I dont remember off the top of my head, but if you goodle for "Shadow Projection Matrix" or just "Shadow Matrix", then you should get something.

03-13-2003, 05:18 AM
man, use projective shadow mapping! ist way kewler!

03-13-2003, 01:33 PM
The question has nothing to do with shadows, so looking for shadow mapping (projective or otherwise) won't be useful.

If you know the plane P, vertex v and light position l, then the point the question is talking about is the intersection of the line lv with the plane P.

if l and v are given in homogeneous coordinates then the line equation lv is (l-v)*lambda+l (where lambda is the scalar parameter).

The intersection of lv with P is given by

lv*p' = 0

and you have to solve for lambda.

However: what is probably more useful is to construct a matrix with l as the optical centre and P as the image plane. THis is.. er... more complicated to describe. The easiest way (I think) would be to compute n = the orthogonal vector from l to p and then transform the plane so n points down the negative z axis and then work out the range of your light source and construct the left/right/top/bottom planes by backprojecting the fov onto the transformed plane and using the LRTB parametrs to construct an opengl matrix.

I hope this helps

03-13-2003, 05:56 PM
void shadowMatrix(GLfloat shadowMat[4][4], GLfloat groundplane[4], GLfloat lightpos[4])
GLfloat dot;
/* Find dot product between light position vector and ground plane normal. */
dot = groundplane[X] * lightpos[X] +
groundplane[Y] * lightpos[Y] +
groundplane[Z] * lightpos[Z] +
groundplane[W] * lightpos[W];
shadowMat[0][0] = dot - lightpos[X] * groundplane[X];
shadowMat[1][0] = 0.f - lightpos[X] * groundplane[Y];
shadowMat[2][0] = 0.f - lightpos[X] * groundplane[Z];
shadowMat[3][0] = 0.f - lightpos[X] * groundplane[W];
shadowMat[X][1] = 0.f - lightpos[Y] * groundplane[X];
shadowMat[1][1] = dot - lightpos[Y] * groundplane[Y];
shadowMat[2][1] = 0.f - lightpos[Y] * groundplane[Z];
shadowMat[3][1] = 0.f - lightpos[Y] * groundplane[W];
shadowMat[X][2] = 0.f - lightpos[Z] * groundplane[X];
shadowMat[1][2] = 0.f - lightpos[Z] * groundplane[Y];
shadowMat[2][2] = dot - lightpos[Z] * groundplane[Z];
shadowMat[3][2] = 0.f - lightpos[Z] * groundplane[W];
shadowMat[X][3] = 0.f - lightpos[W] * groundplane[X];
shadowMat[1][3] = 0.f - lightpos[W] * groundplane[Y];
shadowMat[2][3] = 0.f - lightpos[W] * groundplane[Z];
shadowMat[3][3] = dot - lightpos[W] * groundplane[W];

2 secs google search on "Shadow Matrix" http://www.opengl.org/discussion_boards/ubb/biggrin.gif

03-13-2003, 05:58 PM
looks like it works for both directional lights and point lights. I think http://www.opengl.org/discussion_boards/ubb/biggrin.gif Gonna try that myself

03-13-2003, 06:06 PM
yep, working. Brings my radeon 9700 to a crawl. http://www.opengl.org/discussion_boards/ubb/biggrin.gif Need to optimise my code....

X = 0, Y = 1, Z = 2, W = 3 BTW.

also, enable polygon offset or you'll get aliasing

[This message has been edited by oliii (edited 03-13-2003).]