Shadow Algorithms

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. 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 Depth Pass vs. Depth Fail

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, http://developer.nvidia.com/docs/IO/2585/ATT/RobustShadowVolumes.pdf