Output details

Extending Revised Affine Arithmetic for Fast Reliable Ray-tracing of Procedurally Defined Implicit Surfaces

Context:

As for output number 1.

Related Previous Work:

In the paper submitted as output 1 (entitled “Fast Reliable Interrogation of Procedurally Defined Implicit Surfaces Using Extended Revised Affine Arithmetic”) we developed the concept of the Revised Affine Arithmetic technique which allowed us to quickly and reliably (robustly) interrogate implicit surfaces and we proceeded to develop a new ray-tracing technique for the rendering of scenes composed of implicit surfaces.

In this Paper:

We present a further refinement of the Revised Affine Arithmetic technique and we show how this surface interrogation technique can be used for the fast and reliable (robust) ray-tracing of a wide range of procedurally defined implicit objects, including polynomial surfaces, constructive solids, pseudo-random objects, procedurally defined microstructures, and others. Here we also introduce a technique for optimising the proposed ray-tracing procedure by using argument pruning applied to the Revised Affine Arithmetic technique. Additionally we present timings produced by our GPU implementation of our Extended Revised Affine Arithmetic based ray-tracing technique and compare these with the timings of other previously reported ray-tracing methods based on other interval techniques.

Originality:

1 Introduction and mathematical development of the Extended Revised Affine Arithmetic technique.

2 Design and development of a real-time ray-tracing algorithm for implementation on the GPU.

3. Reliable (accurate) rendering of models with an internal structure, stochastic procedural models with disjointed components and even procedurally-defined hair.

4 Accurate rendering of models with complex scenes with a number of procedurally defined implicit surfaces and containing many thin and or small elements. Such scenes do not work well with rendering techniques implemented using approximate techniques or using polygonization.

Significance:

Given the robustness and speed of our real-time ray-tracing algorithm, it sets a new benchmark for the development of future algorithms.

Rigour:

Detailed mathematical derivations, a real-time ray-tracing algorithm and numerical comparison data were presented.