How Do I Create Cheap Shadows In OpenGL?

Question

I have two models, A and B, and one light, L. I would like model A to cast a shadow on model B. I don't want to bother with shadow volumes or proper shadows for the moment, just a simple circle shadow will suffice. The effect is that model A is treated as a sphere for shadow casting purposes.

Here is how I envision the algorithm:

For each triangle in model B, draw the triangle. Project a circle onto the triangle along the line from L to A, increasing the size of the circle depending on how far away the triangle is. Ensure the circle is clipped to the triangle's boundaries (using the stencil buffer in some way, I imagine).

I'm working with OpenGL and plain C.

Any pointers on some reference documentation I can read? Or implmentation ideas?

Answer 1

This paper seems to cover your requirements, using OpenGL and hardware acceleration to create a detailed shadow map.

If I were trying to accomplish this, I would be tempted to use ray casting. For each triangle in B, create a vector from the triangle to the light. If it hits anything along the way, it is in shadow. This would be kind of slow unless you were using a decent acceleration structure and a fast triangle hit test. I like bounding volume hierarchies; many programs use them for collision detection as well.

Answer 2

I think it is actually easier to implement correct shadows because OpenGL can do the work for you.

I found a working shadow code with lots of documentation here: http://www.opengl.org/resources/code/samples/mjktips/TexShadowReflectLight.html

The code above renders the object twice: first normally then with a special matrix. It does a lot of unrelated things such as control with mouse and reflections. So here are the interesting parts.

This calculates the shadow matrix:

/* Create a matrix that will project the desired shadow. */
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];

}

I do not pretend to understand this completely. lightpos is the position of the light source. The first 3 coordinates of groundplane are the normal vector of the ground surface. The fourth is the offset (how far is it from 0,0,0).

And this part actually renders the shadow:

glPushMatrix();
/* Project the shadow. */
glMultMatrixf((GLfloat *) floorShadow);
drawDinosaur();
glPopMatrix();

There are some things you need to glEnable/glDisable first for this to work so look at the link.