Book Excerpt: Shadow Techniques for Relief Texture Mapped Objects

The following is an excerpt from Advanced Game Development with Programmable Graphics Hardware (ISBN 1-56881-240-X) published by A K Peters, Ltd.

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Integrating shadows to the relief map objects is an important feature in fully integrating the effect into a game scenario. The corrected depth option (see Chapter 5), which ensures that the depth values stored in Z-buffer include the displaced depth from the relief map, makes it possible to implement correct shadow effects for such objects. We consider the use of stencil shadows and shadow maps in this context. We can implement three types of shadows: shadows from relief object to the world, from the world to relief object and from relief object to itself (self-shadows).

Let us first consider what can be achieved using stencil volume shadows. When generating the shadow volumes, we can only use the polygons from the original mesh to generate the volume. This means that the shadows from relief objects to the world will not show the displaced geometry of the relief texture, but will reflect the shape of the original triangle mesh without the displaced pixels (Figure 1).

However, as we have the corrected depth stored in Z-buffer when rendering the lighting pass we can have shadows volumes from the world projected onto the relief objects correctly, and they will follow the displaced geometry properly. Self-shadows (relief object to itself) are not possible with stencil shadows.

Thus, using relief maps in conjunction with shadow volumes, we have the following:

Relief mapped objects integrate much better into shadow map algorithms. Using a shadow map, we can resolve all three cases; as for any other object, we render the relief mapped object into the shadow map. As the shadow map only needs depth values, the shader, used when rendering the object to the shadow map, does not need to calculate lighting. Also if no self-shadows are desired, we could simplify the ray intersect function to invoke only the linear search (as in this case we only need to know if a pixel has an intersection and we do not need the exact intersection point). The shader used when rendering relief objects to a shadow map is given in Listing 4.4, and an example is shown in Figure 2.

To project shadows from the world to the relief map objects, we need to pass the shadow map texture and light matrix (light frustum view/projection/bias multiplied by inverse camera view matrix). Then, just before calculating the final colour in the shader we project the displaced pixel position into the light space and compare the depth map at that position to the pixel depth in light space.

#ifdef RM_SHADOWS
  // transform pixel position to shadow map space
  sm= mul (viewinverse_lightviewprojbias,position);   
  sm/=sm.w;
  if (sm.z> f1tex2D (shadowmap,sm.xy))
    att=0; // set attenuation to 0
#endif

An example of this approach is shown in Figure 3. This is compared with a conventional render using a normal map in conjunction with a shadow map. Thus, using relief maps in conjunction with shadow maps, we can implement the following:

Listing 4.4
Using relief mapped objects in conjunction with shadow maps.

float ray_intersect_rm_shadow(
    in sampler2D reliefmap,
    in float2 tx,
    in float3 v,
    in float f,
    in float tmax)
{
  const int linear_search_steps=10;

  float t=0.0;
  float best_t=tmax+0.001;
  float size=best_t/linear_search_steps;

  // search for first point inside object
  for ( int i=0;i<linear_search_steps-1;i++ )
  {
    t+=size;
    float3 p=ray_position(t,tx,v,f);
    float4 tex= tex2D (reliefmap,p.xy);
    if (best_t>tmax)
    if (p.z>tex.w)
         best_t=t;
  }

  return best_t;
}

f2s main_frag_relief_shadow(
    v2f IN,
    uniform sampler2D rmtex: TEXUNIT0 , // rm texture map
    uniform float4 planes,     // near and far plane info
    uniform float tile,                  // tile factor
    uniform float depth)       // depth factor
{
    f2s OUT;

    // view vector in eye space
    float3 view= normalize (IN.vpos);

    // view vector in tangent space
    float3 v= normalize ( float3 ( dot (view,IN.tangent.xyz),
        dot (view,IN.binormal.xyz), dot (-view,IN.normal)));

    // mapping scale from object to texture space
    float2 mapping= float2 (IN.tangent.w,IN.binormal.w)/tile;

    // quadric coefficients transformed to texture space
    float2 quadric=IN.curvature.xy*mapping.xy*mapping.xy/depth;

    // view vector in texture space
    v.xy/=mapping;
    v.z/=depth;

    // quadric applied to view vector coodinates
    float f=quadric.x*v.x*v.x+quadric.y*v.y*v.y;

    // compute max distance for search min(t(z=0),t(z=1))
    float d=v.z*v.z-4*f;
    float tmax=100;
    if (d>0)     // t when z=1
        tmax=(-v.z+ sqrt (d))/(-2*f);
    d=v.z/f;     // t when z=0
    if (d>0)
        tmax= min (tmax,d);

#ifndef RM_DEPTHCORRECT
  // no depth correct, use simple ray_intersect
  float t=ray_intersect_rm_shadow(rmtex,IN. texcoord*tile,v,f,tmax);
  if (t>tmax)
      discard ; // no intesection, discard fragment
#else
    // with depth correct, use full ray_intersect
    float t=ray_intersect_rm(rmtex,IN.texcoord*tile,v,f,tmax);
    if (t>tmax)
        discard ; // no intesection, discard fragment

    // compute displaced pixel position in view space
    float3 p=IN.vpos.xyz+view*t;

    // a=-far/(far-near)
    // b=-far*near/(far-near)
    // Z=(a*z+b)/-z
    OUT.depth=((planes.x*p.z+planes.y)/-p.z);
#endif

    return OUT;
}