Afrigraph 2004Interactive Ray-Tracing of

Free-Form Surfaces

Carsten Benthin Ingo Wald Philipp Slusallek

Computer Graphics Lab

Saarland University, Germany

http://graphics.cs.uni-sb.de

Motivation

Why ray-tracing of free-form surfaces ?

Tessellating surfaces has disadvantages:• Scene size complexity• Accuracy• Time complexity (preprocessing step)• Workflow (Animation Tools, CAD)

Want directly ray-trace Splines,

NURBS, Subdivision Surfaces, ...

Previous Approaches

Splines and NURBS• Bezier Clipping

– Nishita, Campagna, Wang

• Newton Iteration– Wang, Martin

Subdivision Surfaces• Adaptive refinement

– Kobbelt, Mueller

Too slow for interactive use

Interactive Ray-Tracing (IRT)OpenRT• Wald, Benthin, Dietrich• Interactive performance

even on a commodity PC• Limited to triangles

Utah RTRT• Shirley, Parker• Supports even spline surfaces• Need large parallel supercomputer

for interactive performance

Outline

Analysis of existing approaches (ray/primitive test)

Our simple and generic approach

Implementation: Bicubic Bezier, Loop Subdivision

Complex Scenes

Results

Conclusion & Future Work

Analysis I

Performance „killers“ of current CPU architectures• Memory latency cache misses • Long pipelines branch mispredictions• Complex control flow low instruction level parallelism

Code Optimization• Ensure data locality & memory access pattern• Simple code control flow (streamline)• Data level parallelism (SIMD), e.g. Intel‘s SSE Instructions

Analysis II

Analytical/Iterative algorithms• Algorithmic complexity• Numerical problems• Handling many special cases• Complex control flow

Adaptive refinement algorithms• Test for required refinement is costly• Crack prevention additional book-keeping data structures• Complex control flow

Our Approach I

Simple and generic „divide and conquer“

Fixed number of refinement steps

Our Approach II

• Few core operations– Refinement– Pruning– Final Intersection

• No refinement test• No crack handling • Constant memory costs

• 4x4 control points, suited for 4-way-SIMD• Optimized data layout for maximize SIMD performance

– SOA instead AOS

• Pruning: Ray as intersection of two planes (half-space criteria)• Refinement: deCasteljau algorithm (alternate direction)• Final Intersection: Triangulation + Ray/Triangle-Tests

Implementation for Bicubic Bezier Surfaces

Implementation forLoop Subdivision Surfaces

• AOS data layout• Regular/Irregular Triangles

– One refinement step max one irregular vertex

• Pruning: Two planes critera (1-neighborhood)• Refinement: Loop subdivision four new triangles• Final Intersection: Triangle test

Core Performance (Cycles)

Bicubic Bezier Loop Subdivision

Pruning 86 172/222

Refinement 168/244 405/600

Final Intersection

294-366 169

Subdivision core operations more complex higher cost

Free-Form Objects

Reduce tested primitives/ray• Use spatial acceleration structure (KD-Tree)

– Construct KD-Tree out of AABBs– Use fast traversal from IRT

• Surface Area Heuristics better KD-Tree• Mailboxing• Reduction: up to 92% (78%)

Dynamic Objects• Less primtives KD-Tree reconstruction every frame

Results (Bezier Surfaces)

P4 CPU 2.2 GHz, 640x480, #tris = #primitives * 2^steps * 18

Results (Subdivision Surfaces)

P4 CPU 2.2 GHz, 640x480, 640x480, #tris = #primitives * 4^steps

Video

Conclusion

Pros• Simple and robust approach • Interactive performance on single CPU• Memory efficient, compute bounded ray/primitive test• Support for trimming curves• Half the speed compared to triangle approach• Can easily integrated into existing ray-tracers (OpenRT)

Cons• Over-refinement• Subdivision Surface implementation not optimal

Current & Future Work

• Key to performance: tracing ray bundles (e.g. 16 rays)– Amortize core operation costs over rays

• Different variants for final intersection step– Plücker triangle test– Bilinear Patch

• Very fast KD-Tree reconstruction code– Multithreading

• Higher order bezier patches or even direct NURBS support• Improve implementation for Subdivision Surfaces

Questions ?