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

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

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

Classic solution
•
Multiple shadow rays
Lots of shadow rays per pixel pixel

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
Classic approach pixel
Our approach

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

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

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

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

Hemicube Construction
Bottom face of hemicube
Each cell contains list of edges

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

Hemicube Construction
Lots of edges does not need to be considered

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 p
1 p
2

Wedge Creation Criterions
1.
Wedges are created for all edges that are silhouettes from any point on the light source
2.
The wedge includes all positions from which the edge projects onto
(occludes) the light source.

During Rendering
•
Hemicube returns a conservative set of edges
–
All the necessary edges but also many more
•
We only want edges that are
1.
Silhouettes from p
2.
Project onto the light source.
•
Tested with Point-inside-wedge
•
Now we have the silhouette edges from p p p

Visibility Reconstruction
•
Which light samples s i are visible from point p ?
•
Brute force: cast a shadow ray for each s i
•
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 s i
4. Solve visibility with a single shadow ray
5. Profit

Depth Complexity
•
Depth complexity of s i between p and s i
= number of surfaces

0
1
2 0
1
1
1
0
Light source as seen from p Depth complexity function

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

0
1
2
1
1 1
0

Integration: Example
•
Left-to-right integration of a triangular silhouette

0 -1
1
0
1 -1
Light source as seen from p Depth complexity function

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

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!

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

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

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 s i with lowest relative depth complexity
•
If blocked, all s i are blocked
•
Otherwise, all s i with lowest rel.
depth complexity are visible

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

Columns: 580 triangles, adaptive AA, 960x540
Speedup factor
L = 256
103
L = 1024
242

Formula: 60K triangles, adaptive AA, 960x540
Speedup factor
L = 200
30
L = 800
65

Sponza: 109K triangles, adaptive AA, 960x540
Speedup factor
L = 150
11
L = 600
33

Robots: 1.3M triangles, adaptive AA, 960x540
Speedup factor
L = 200
21
L = 800
58

Ring: 374K triangles, adaptive AA, 960x540
Speedup factor
L = 150
13
L = 600
32

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)

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

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

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
Visible
Blocked