Hierarchical Penumbra Casting

Samuli Laine

Timo Aila

Helsinki University of Technology

Hybrid Graphics, Ltd.

Introduction

• Rendering soft shadows– As usual, area light sources are sampled with

a number of light samples– Multiple receiver points to be shaded

• The main problem is solving the visibility– which light samples are visible to which

receiver points

Light source

What’s Happening?

Light samples

Shadow caster

Visible surface

Receiver points

On the Scale of the Problem

• With R receiver points and L light samples there are RL visibility relations to solve– For example, 1024×768 resolution and 256

light samples gives over 200 million relations

• Ray casting is the usual solution for solving the visibility relations– With T triangles, the cost of casting one

shadow ray is O(log T)– Total cost becomes O(RL log T)

About Ray Casting

• The standard ray casting approach considers only one ray at a time– This inevitably leads to linear performance

with respect to RL

• However, this is highly flexible– We need to generate only one ray at a time

• Sub-linear complexity with respect to T is achieved by placing the triangles into an acceleration hierarchy

Transposing the Algorithm

Our Approachfor each triangle T find all l r rays blocked by T

Ray Tracingfor each receiver point r for each light sample l find triangle that blocks ray l r

• Goal: sub-linear complexity w.r.t. RL

• Requires rearranging the rendering loop

linear to Rlinear to Lsub-linear to T

linear to Tsub-linear to RL

About Our Algorithm

• Sub-linear complexity with respect to RL is achieved by placing the receiver points and light samples into acceleration hierarchies– Therefore, all receiver points must be

gathered before computing the shadows

• We process one triangle at a time– Good: no need for triangle BSP– Bad: linear complexity with respect to T

About Our Algorithm, part 2

• The full rendering process goes as follows:

1. Ray-trace or rasterize the image without shadows to get the receiver points

2. Build the acceleration structures for receiver points and light samples

3. Process all triangles to solve the visibility relations between light samples and receiver points

4. Perform shading

The Acceleration Structures

• Fixed three-level bounding volume hierarchy is used for the light samples– Assuming a polygonal light source, bounding

“volumes” are actually bounding polygons

• Standard bounding volume hierarchy is used for the receiver points – Axis-aligned boxes as bounding volumes

Light Sample Hierarchy

• Three levels

• All nodes have a bounding volume

Entire light source Light sample groups Light samples

Root node Middle nodes Leaf nodes

Storing the visibility information

• A bit mask with L bits is assigned for every receiver point– bit = 0: light sample is visible– bit = 1: light sample is occluded

• Initially, all bits are zero

• When a triangle is found to occlude a light sample from a receiver point, the corresponding bit is set to one

• All points where a triangle may block a ray from a bounding volume are inside the corresponding penumbra volume

Penumbra Volumes

Penumbra volumeBounding

volume in light hierarchy

Triangle

Processing a Triangle

• First build penumbra volumes for all nodes in the light sample hierarchy

• For individual light samples (leaf nodes) these become hard shadow volumes

Processing a Triangle

• Traverse down the receiver point hierarchy

• Step 1: Test intersection between main penumbra volume and bounding volume of receiver node

Main penumbra volumeBounding

volume of entire light source

Triangle

Receiver node

Processing a Triangle

• Step 2: Update the list of active light sample groups– At beginning of traversal, all groups are active

Bounding volumes of light sample groups

Receiver node

Triangle

Remove from active group list

Processing a Triangle

• Step 3: Recurse into child nodes in receiver hierarchy– With pruned list of active light sample groups

Main penumbra volumeBounding

volume of entire light source

Triangle

Child nodes

Processing a Triangle

• Step 4: In leaf node, test receiver points vs. hard shadow volumes of light samples– Update the visibility relation bits

Light samples in active groups

Receiver points

Triangle

Summary of Recursion

• Traverse down the receiver point hierarchy– Maintain list of active light sample groups

• Initially all groups are active

– First ensure that receiver node intersects the main penumbra volume, terminate otherwise

– Then prune the active light sample group list by intersecting receiver node vs. penumbra volumes of active light sample groups

– In leaf node, test receiver points against hard shadow volumes of remaining light samples

Optimizations

• Umbra bits for early traversal termination– With receiver hierarchy rebuilding to ensure

balance

• Active plane sets

• Lazy penumbra volume and hard shadow volume construction

• On-demand bit mask allocation

• Coarse blocker sorting

Extensions

• Multiple light sample sets– To remove banding artifacts

• Alpha matte textures– Often used in e.g. vegetation textures

• Adaptive antialiasing

• Volumetric light sources

Results

• Compared against Mental Ray 3.2

• Benchmarked only the solving of the visibility relations– For Mental Ray, computed both with and

without shadows and took the difference

• More detailed results in the paper

Resolution Peak mem usage Speedup factor

1280×9600 058M 13.5

2560×1920 228M 16.7

Grids

32K triangles256 light samples

Resolution Peak mem usage Speedup factor

1280×9600 039M 3.5

2560×1920 154M 7.8

Flowers

903K triangles256 light samples

Resolution Peak mem usage Speedup factor

1280×9600 062M 8.2

2560×1920 244M 11.4

Sponza

1.27M triangles256 light samples

Results: Analysis

• Sub-linearity with respect to R– Increasing output resolution gives better

relative performance– Due to hierarchical processing of receiver

points

• Sub-linearity with respect to L– Using more light samples gives better relative

performance (results in the paper)– Due to using analytic penumbra volumes that

represent many light samples at once

Results: More Analysis

• Somewhat high memory usage– Depends on the output resolution– Depends on the complexity of the shadows– Does not depend on the number of triangles

in the scene

• New problem: dependence on the spatial size of light source– Penumbra volumes become larger– Leads to lower performance

Conclusions

• Nice properties+ Exactly the same result as with ray casting+ No need to store all triangles at any point+ Sub-linear dependence on output resolution

and number of light samples

• Not so nice properties– Linear dependence on triangle count– Memory usage can be high– Dependence on the spatial size of light source

Future Work

• Process multiple triangles at a time?

• Could experiment with full light sample hierarchy, which should (in theory) have better performance

Thank You

• Questions

Funding: National Technology Agency of Finland, Bitboys, Hybrid Graphics, Remedy Entertainment, Nokia, ATI