1. ATO Project: Year 3 Main Tasks
Dynamic terrains
Multi-agent planning and crowd simulation
Physical modeling and collision response

2. ATO Project: Year 3 Related technologies
Interactive shadow generation
Interactive ray tracing
Sound rendering

3. ATO Project: Year 3 Related technologies
Interactive shadow generation
Interactive ray tracing
Sound rendering

4. Logarithmic perspective shadow maps (LogPSMs)
Brandon Lloyd
Dinesh Manocha

5. Collaborators Naga Govindaraju (Microsoft) Steve Molnar (NVIDIA)
Cory Quammen (UNC)

6. Why are shadows important?
Improved spatial understanding
shape
location
Improved realism
Aesethics
Shadows help us understand the spatial relationships between objects including their relative size and location. Without shadows the right half of the image appears to be floating.
Shadows are also an important lighting effect that enhance realism
In addition they can contribute to the overall ambience of an environment.

7. Why are shadows important?
Without shadows, the character floats at some unknown distance above what appears to be a striped plane. The presence of shadows indicates how high the character is and reveals the curved nature of the plane
images from Hasenfratz et al. 2003

8. Shadows important in games
Doom3 reportedly spends up to 50% of the frame time computing shadows
Shadows are a very important component of computer games where spatial understanding, realism, and aesthetics all come into play. They are so important that a popular computer game reportedly spends over 50% of the frame time computing shadows

9. What is a shadow?
Light
Shadows occur on surfaces seen by the eye, but not seen by the light.
Eye
Object
Shadow

10. Approaches for real-time shadows
Heuristic
Just put a dark spot under objects
Not accurate
Shadow volumes
High-accuracy
Slow for complex scenes

11. Shadow maps
Use the depth map in the light view to determine if something is between a point and the light
Eye
Light
Point in shadow
visible to the eye but not visible to the light

12. Why shadow maps? Simple two pass algorithm
Supports wide range of geometric representations
Cheap to render
Disadvantage: Prone to errors – especially at shadow edges

13. Videos standard shadow map LogPSM
In the first video we see the jagged aliasing artifacts along shadow edges produced by a standard shadow map.
In the second video we demonstrate our algorithm and the significantly improvement in quality that we achieve
standard shadow map
LogPSM

14. Aliasing error light shadow plane eye view frustum
Let’s briefly discuss why aliasing error occurs
Suppose we have a light above the view frustum. We will consider the intersection of a beam through from the eye through a pixel in the image and a beam from the light through a texel in the shadow map.
eye
view frustum

15. Aliasing error ' wl ' wi ' wi ' wi ' wl ' wi light beam image beam
The beams project onto a surface, each with footprints of a certain size.
When the light beam footprints are larger than the image beam footprints, they are covered by multiple image beams and can be clearly distinguished as jagged shadow edges in the image. ' wi

16. Perspective warping eye view light view shadow map
This video sequence shows the effect of perspective warping. On the left we show the view from the eye. In the middle we show the view from the light. We see the view frustum surrounded by the light’s frustum used to render the shadow map. On the right we show the shadow map. Grid lines are shown for reference.
Note how as we increase the perspective warping, the light frustum is transformed to match the view frustum. This causes the regions of the scene closer to the viewer to occupy a larger portion of the shadow map, thus reducing aliasing.
eye view
light view
shadow map

17. Shadow map res. / image res.
Comparison 10 1 2 3 4 6 8
f / n
Shadow map res. / image res.
Standard
Perspective
Here we see the difference that the parameterization can make
The graph shows how large the shadow map must be relative to a square image in order to eliminate perspective aliasing.
The required resolution depends on the ratio of the far to near plane distances of the view frustum.
On this log scale plot we can see that perspective warping can produce notable improvements over a standard shadow map. However, perspective warping is only a rough approximation to the optimal parameterization. A combination of a logarthmic transformation with a perspective parameterization produces much better results that are close to optimal
LogPSM
frustum fov = 60○

18. Comparison video
In this video we compare standard shadow maps, perspective warping techniques, and cascaded shadow maps to our LogPSM algorithm

19. Hardware support for logarithmic rasterization
Requires only incremental enhancements to current graphics hardware
Trades a modest increase in computation for significant reductions in memory bandwidth and storage
Aligns well with current trends
memory
interface
depth
compression
color
fragment processor
vertex processor
rasterizer
alpha, stencil,
& depth tests
blending
clip & back-face cull
Therefore we propose supporting Logarithmic rasterization directly in graphics hardware to support rendering of LogPSMs at the same rates as other shadow map algorithms. We require only incremental enhancements to the current hardware. The hardware units that must be modified are shown here in orange.
These enhancements require increased computation but they bring significant savings in bandwidth and storage – both of which are limiting factors to performance on current GPUs.
Since the cost of computation continues to decrease relative to the cost of memory bandwidth, these modifications align well with current trends

20. Results
In this video we show our algorithm on a robot scene

21. Comparison – directional light
Here we compare LogPSMs to several other algorithms. The images show a view of the town scene from under a tree with a directional light overhead. The top row shows the texel grid of the shadow map projected onto the scene so that the quality of the parameterization can be seen more easily. On the bottom row we show the same scene color coded with an aliasing error metric. Standard shadow maps have extremely high aliasing. An algorithm that partitions the frustum into regions corresponding to its faces and applies perspective warping to each partition has considerable lower error. A cascaded shadow map combined with perspective warping has even lower error near the viewer. LogPSMs however have the lowest error of all.
Face partitioning + persp. warp
Cascaded +
persp. warp
Standard
LogPSM

22. Comparisons – point light
Here we compare algorithms for a point light. Perspective warping provides marked improvement over a shadow map created from a standard cube map. LogPSMs produce significant error reductions.
The videos show animations with a point light
Standard
cube map
Persp. warped cube map
LogPSM

23. Conclusion: A practical shadow solution
LogPSM algorithm
Significantly lower error
Significantly lower memory bandwidth and storage
Hardware architecture for log rasterization
Requires only small enhancements to current graphics hardware
Exploits current hardware trends