1. Reflections from Bumpy Surfaces
GPU Graphics

2. What are we trying to achieve?
Most surfaces are not flat like glass
Some of these surfaces still give off reflections, we would like to model this effect

3. Methods for Reflection
Ray Tracing (expensive)
Environment Mapping (cube maps)
Is an option in the shader 4 model
In shader model 3 we can not update the cube map in real time easily
Spherical Environment Mapping (with cube map)

4. Cube Map Example Can not be updated in real-time easily
Cube Map pictures taken from
Can not be updated in real-time easily
Only currently works well for static scenes
Shader 4 will allow arrays of textures, will make real-time cube maps easy to implement

5. Simple Cube Map Lookup Reflect incoming View vector around Normal T
Intersect Vr with environment map and perform texture lookup
What is the issue here? T N Vr
Two points with identical mirror
directions will look up the
same direction in the environment map V O
Works well on the tea pot, works really badly on flat surfaces like floors
2D view of an environment map

6. Spherical Environment MappingEM
V = view vector,
reflected about the point normal at x r V V r
P = point on sphere interior
using regular cube map r EM V
mod
reflector O
P = intersection between line x + V t
and sphere using V = P – O to index
cube map based at O x r
mod
Pg 212 of Advanced Renderman
r < infinity
V = modified view vector
mod
Assume the environment map exists on the interior of a sphere with a finite radius and center
Define a ray using the position and mirror direction of the point, calculate the ray intersection with environment sphere
Use intersection as the environment lookup direction

7. An even simpler case: The planar reflection
Two Pass algorithm
Reflected image is rendered to a texture
Reflected surface is shaded with reflected texture from first pass
Only useful for something like floors

8. Rendering Reflection to Texture
Camera Pos: Er = reflecta(E)
Front: Fr = reflecta(F)
Right: Rr = reflecta(R)
Up: Ur = - reflecta(U) E F R
Reflector Plane (A)
If we reflect the whole viewpoint reference frame it will cause culling issues
If we flip the up vector we do not get the culling issue.
Use a culling plane to make sure only objects on the same side as the viewpoint are reflected
Essentially altering the view matrix,
Model view and projection matrices stay the same Ur Rr Fr
1. Reflect the current viewpoint about the reflector plane.
2. Render the relevant parts of the scene from the new viewpoint. Er

9. Reflection Texture Lookup
For the Perfect Reflector:
for_each fragment {
Fpos = fragment world position
Vr = reflected view matrix
Epos = eye space position = Fpos * Vr
Ppos = post projective space = Epos * P
S = scale translate matrix
texture_lookup = (S*P*Vr*Fpos).xy
color = tex2d(texture_lookup) }
Vr is same from the first pass
Post projective space = homogenous clipping space
P = projection matrix
S moves all coordinates into [-1,1] to [0,1] range
(Same techniques as is used with shadow maps)
S, P, and Vr are computed on CPU and passed as constants

10. Reflection Texture Lookup
For the Bumpy Reflector
N = normal
E = viewpoint
Er = reflected viewpoint
N1 = fragment’s normal
V = view vector
VN1 = view vector reflected about N1
P = perfect reflector’s reflection
P1 = non-perfect reflector’s reflection P1 P h
N1 is taken from a texture lookup for the normal map
fPos1 is what we want, that is the texture lookup for the reflection
VN1 is V reflected around N1
Er is E reflected around the surface N1 N E
viewpoint VN V 1
fPos
fPos1
Solve for fPos1 Er
reflected viewpoint