1. Soft Shadow Volumes for Ray Tracing
Samuli Laine
Helsinki University of Technology,
Hybrid Graphics Ltd.
Timo Aila
Helsinki University of Technology,
Hybrid Graphics Ltd.
Ulf Assarsson
ARTIS, GRAVIR /IMAG INRIA,
Chalmers University of Technology
Jaakko Lehtinen
Helsinki University of Technology,
Remedy Entertainment Ltd.
Tomas Akenine-Möller
Lund University

2. We present An algorithm for computing Soft Shadows
For planar area light sources
Exactly the same shadows as using shadow rays
Faster - up to 2 orders of magnitude
Can compute very high resolution soft shadows with low extra cost
E.g. allows for 1000 shadow samples per pixel
Requires computation of silhouettes
Trivial for polygon-based scenes

3. Soft Shadows – A Quick Recap
Area lights give soft shadows
Point light
Area light
Hard shadow
Soft shadow

4. Classic solution Multiple shadow rays Lots of shadow rays per pixel

5. Our solution - overview
Replace the shadow rays
With soft shadow volume computations
Plus one reference shadow ray
One shadow ray + soft shadow volume computations
Lots of shadow rays per pixel
pixel
pixel
Classic approach Our approach

6. What’s a Soft Shadow Volume?
Light source
Shadow caster
Soft Shadow Volume
Soft Shadow Volume =
A. Volume from which an edge projects onto the light source
B. Region of penumbra caused by an edge

7. Our solution - overview
Two parts:
from any receiving point p, we need to find silhouette edges affecting the visibility
A method for computing the visibility from silhouette information

8. Finding potential silhouettes
Fast method for determining silhouette edges that overlap light source from p
Arbitrary shadow caster
Arbitrary shadow receiving point p
HOW?

9. Hemicube Construction
Rasterize soft shadow volumes into a hemicube for each light source
hemicube
Bottom face of hemicube
Each cell contains list of edges
Each cell contains list of edges p
This cell contains potential silhouette edges from p

10. Hemicube Construction
Rasterize soft shadow volumes into a hemicube for each light source
Wedge marked to all cells it even partially overlaps → no artifacts
Bottom face of hemicube
Each cell contains list of edges

11. Hemicube Construction
Wedge marked to all cells it even partially overlaps → no artifacts
Bottom face of hemicube
Each cell contains list of edges

12. Hemicube Construction
Lots of edges does not need to be considered

13. Hemicube Construction
Lots of edges does not need to be considered
Because these edges cannot be silhouettes projected onto the light source from any point p p1 p2

14. Wedge Creation Criterions
Wedges are created for all edges that are silhouettes from any point on the light source
The wedge includes all positions from which the edge projects onto (occludes) the light source.

15. During Rendering Hemicube returns a conservative set of edges
All the necessary edges but also many more
We only want edges that are
Silhouettes from p
Project onto the light source.
Tested with Point-inside-wedge
Now we have the silhouette edges from p p p

16. Visibility Reconstruction
Which light samples si are visible from point p?
Brute force: cast a shadow ray for each si
Our recipe:
1. Find silhouette edges between p and light source
2. Project them onto light source  reduces to 2D
3. Compute relative depth complexity for every si
4. Solve visibility with a single shadow ray
5. Profit

17. Depth Complexity
Depth complexity of si = number of surfaces between p and si 1 2 
Light source as seen from p
Depth complexity function

18. From Silhouette Edges to Relative Depth Complexity
Projected silhouette edges define the first derivative of the depth complexity function
Hence, relative depth complexity can be solved by integrating the silhouette edges over the light source
Integration is linear  can be performed one edge at a time 1 2 

19.  Integration: Example
Left-to-right integration of a triangular silhouette +1 1 1 1 -1  -1
Light source as seen from p
Depth complexity function

20. Integration: Sampling Points
We don’t need the value of the depth complexity function except at the sampling points si
Sufficient to maintain a depth complexity counter for each si
Integration: find si that are inside update region and update their depth complexity counters +1

21. Integration: Rules
There’s a caveat - we only have the edges that overlap the light source
Loops are not necessarily closed, since parts outside the light source may be missing
We don’t have this edge!

22. Integration: Rules
Solution: apply special rules to edges that cross the left side of the light source
This accounts for potentially missing edges

23. Integration: Optimization
Place the light samples into uniformly sized buckets
During integration, only process affected buckets
Most edges span only one bucket
We use approx. sqrt(N) buckets for N light samples
We also process 4 samples in parallel using SSE vector instructions

24. From Relative Depth Complexity to Visibility
We are not done yet, since the constant of integration is not known  cannot solve visibility
Solution: cast a shadow ray ray to one si with lowest relative depth complexity
If blocked, all si are blocked
Otherwise, all si with lowest rel. depth complexity are visible

25. Experimental Results Comparisons done using a commercial ray tracer
Turtle by Illuminate Labs
Enabled heuristic shadow ray casting: stop if first 50% of rays agree
Our method was implemented into this ray tracer
We use the same ray caster for casting the reference ray

26. Columns: 580 triangles, adaptive AA, 960x540
Speedup factor
103
242

27. Formula: 60K triangles, adaptive AA, 960x540
Speedup factor 30 65

28. Sponza: 109K triangles, adaptive AA, 960x540
Speedup factor 11 33

29. Robots: 1.3M triangles, adaptive AA, 960x540
Speedup factor 21 58

30. Ring: 374K triangles, adaptive AA, 960x540
Speedup factor 13 32

31. Conclusions Fast shadow algorithm in wide range of scenes
Easy to plug into an existing ray tracer
Scalability considerations
Number of light samples: excellent (~ sqrt M)
Number of triangles: good (silhouettes: ~ N(something ≤ 1))
Output resolution: not so good (linear)
Spatial size of the light source: not so good (~ linear)

32. Future Work GPU implementation?
Improvement of the acceleration structure
To pump up the edge acceptance ratio (currently < 10%)

33. Thanks
Questions
Thanks for the cash: Bitboys, Hybrid Graphics, Remedy Entertainment, Nokia, National Technology Agency of Finland, ATI, Illuminate Labs, French Ministry of Research, Chalmers, Hans Werthén foundation, Carl Tryggers foundation, Ernhold Lundströms foundation, Swedish Foundation for Strategic Research

34. Semi-transparent shadow casters
Detect the light samples that are occluded only by semi-transparent occluders
Determine the color for these light samples by casting shadow rays
Blocked
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Blocked
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