1. Shadow Algorithms
Ikrima Elhassan

2. Outline Curved Shadows on curved surfaces (Williams paper)
Shadow volumes & implementation (Crow & Heidmann paper)
(A lot of) Extra stuff (flaws of shadow volumes and solutions)

3. Shadow Buffers Projecting shadows onto planes is trivial
Project the scene onto a plane using light as eye
For curved surfaces, we still use two views

4. Algorithm Compute z-buffer of the scene from the light’s view
Render the view from the eye perspective
For each point in the view, transform it into light space. If the point is not visible in light space, it’s in shadow, otherwise compute shading for the point.

5. Approximating the algorithm
Scene is computed from eye perspective, then a transform everything, point by point, to light space
Shadowing is taken as a post-process
Incorrectly shades the highlights; they are merely darkened
Suffers from aliasing and quantization problems

6. Algorithm (Cont) Transform only applied to visible points
Transform expense does not depend on complexity of scene
Depends on resolution, which increases with square of the resolution
Computation done in image space

7. Limitations Occluders must be within view of light source
For point lights, sphere of illumination should be sectored into multiple views
Cost increases because points must be transformed into multiple light views or transformed into the view that the point falls under
Causes an increase in memory

8. Limitations (Cont) Algorithm allows for self-shadowing surfaces
Problems with z-buffer precision when transforming points from surface in eye space onto surface in light space

9. Quantization Issues Imprecision problems arise
To alleviate problem, subtract z-bias to make transformed points lie on visible surface in light space
Treating these problems as quantization problems improves image further
Not as big of a problem b/c during shading, there’s a smooth lighting transition from light to dark
Also, low pass filtering is applied to create soft-shadows, reducing error

10. Conclusion Allows for self-shadowing
Cost is roughly twice cost of rendering plus cost of transforming points
With exact version, transformation cost is related to depth complexity
With modified version, cost is tied to screen resolution
Cost is roughly twice rendering b/c shading is not computed for light space
Memory is no longer an issue

11. Shadow Volumes

12. Straight to Shadow volumes
Combine both papers so we can have time for extra material
Papers provided the foundation for volume shadow algorithms
Other two techniques are outdated and will come back to them at the very end so we can focus on the current algorithm
Algorithm is to create “shadow volume” from occluders
Everything within the shadow volume is in shadow

13. Shadow Volume Concept Shadow volume is constructed from occluders
Although we can create volumes for every triangle in the occluders, we only need the silhouette
Different types of volume for different types of lights

14. Depth-Pass stencil testing
Render the Scene and keep the z-buffer.
Fragments with non-zero stencil values are considered to be in shadow. The generation of the values in the stencil buffer :
Render front face of shadow volume. If depth test passes, increment stencil value, else does nothing. Disable draw to frame and depth buffer.
Render back face of shadow volume. If depth test passes, decrement stencil value, else does nothing. Disable draw to frame and depth buffer.
Algorithm known as Depth-Pass b/c set the stencil values only when depth test passes

15. Depth-Pass stencil testing (Cont)
Assume objects have been rendered into framebuffer
Depth buffer would have been set with the correct values for depth testing
2 leftmost rays have 0 stencil values, meaning those fragments are not in shadow
For 3rd ray, when we render the front face of the shadow volume, fragment passes depth test and stencil value is incremented
When rendering back face of shadow volume, depth test fails; stencil value for the fragment is still 1 and fragment is in shadow
Does the shadow volume counting work for multiple shadow volumes? Yes, even for intersecting shadow volumes.

16. Infinite vs. Finite
In theory, shadow volume should extend to infinity but this is not a strict requirement
We extend to infinity to avoid the problem shown on left
We’ll discuss how to cap and extrude to infinity later

17. Summary of High Level algorithm
Render objects using only ambient lighting and other surface-shading attributes. Rendering cannot depend on lighting. Make sure depth buffer is written
Starting with a light source, clear stencil buffer and calculate the silhouette of all the occluders with respect to light
Extrude the silhouette away from the light source to a finite or infinite distance to form the shadow volumes (Infinite shadow volume extrusion is not a necessity)
Render shadow volumes using the depth-pass
Using the updated stencil buffer, do a lighting pass to shade (make it a tone darker) the fragments that corresponds to non-zero stencil values.
Repeat step 2 to 5 for all the lights in the scene.
Where do highlights fit in?
More lights means having more passes which can destroy frame rate

18. Extra Stuff Why do we need to find alternatives to shadow volumes?
Shadow volumes works great until camera is in a volume

19. Carmack’s solution (Depth-Fail)
Render back face of shadow volume. If depth test fails, increment stencil value, else does nothing. Disable draw to frame and depth buffer.
Render front face of shadow volume. If depth test fails, decrement stencil value, else does nothing. Disable draw to frame and depth buffer.
This works for when eye is outside volume, but it also fails in some cases
Robust solution requires a hybrid of both of these techniques

20. Depth Fail (Cont)
To put in non-zero values into the stencil buffer, depth-fail depends on the failure to render the shadow volume's back faces with respect to the eye position
Means the shadow volume must be a closed volume
Without capping, the depth-fail technique would produce erroneous results.
You can cap the shadow volume even at infinity.

21. Capping
We can build the front cap by reusing the front facing triangles with respect to the light source.
The geometries used in the front cap can then be extruded with reversed orderings to create the back cap.
Must reverse order to ensure back cap face outward
To create closed volume, all of the bounding primitives of the volume must face outward
Capped volumes are more expensive
Larger primitive count for the shadow volume
Additional computational resource needed to compute the front and back capping

22. Silhouette Determination
Many ways to calculate the silhouette edges and all are CPU cycles hungry
Broken lines indicate redundant internal edges
Only interested in the solid outline of the box
Silhouette determination is one of the two most expensive operations in stencil shadow volumes
Other is shadow volume rendering passes to update the stencil buffer

23. Silhouette Determination (Cont)
Loop through all the model's triangles
If triangle faces the light source (dot product > 0)
Insert the three edges (pair of vertices), into an edge stack
Check for previous occurrence of each edges or it's reverse in the stack
If an edge or its reverse is found in the stack, remove both edges
Start with new triangle

24. Generating Shadow Volume Capping
Capping should be done during silhouette determination because we need silhouette geometry
Front/Back caps are trivial, just use the silhouette (w/reverse order for the back)
For directional light sources, the light projects the silhouette to a single point (?)

25. Extruding to infinity
In vague terms, set the far clip plane at infinity
Changes the perspective matrix slightly
Use homogenous coordinates
For points, w is equal to 1.0.
For vectors, w is equal to 0.0.
For points at infinity, set w to be 0.0.

26. Problems with extruding to infinity
Ghost shadows occur
Shadow volume extends to both sides of an object
There’s really no solution

27. View Frustum Clipping The worst problem of stencil shadow volumes
Problem for both depth-pass and depth fail
To solve for depth fail, make the far clipping plane go to infinity so you have an infinite view frustum
Also have precision issues when extruding to infinity because far clip plane is so far away

28. Depth Pass vs. Depth Fail
Advantages
Does not require capping for shadow volumes
Less geometry to render
Faster of the two techniques
Easier to implement if we ignore the near plane clipping problem
Does not require an infinite perspective projection
Disadvantages
Not robust due to unsolvable near plane clipping problem
No self shadowing
Advantages
Robust solution since far plane clipping problem can be solved elegantly
Disadvantages
Requires capping to form closed shadow volumes
More geometry to render due to capping
Slower of the two techniques
Slightly more difficult to implement
Requires an infinite perspective projection
No self shadowing

29. Misc The math falls outside the scope of the presentation
A lot of areas to optimize and create a more efficient and robust algorithm
Stencil volumes can be perfectly implemented with vertex shaders
For more information,