Output details

Fast reliable interrogation of procedurally defined implicit surfaces using extended revised affine arithmetic

Context:

Here we present results produced by our group as part of a long-term research project that involves the development of hybrid geometric modelling techniques for heterogeneous objects and the definition of a novel modelling and animation system that is intended to introduce a paradigm shift in the way artists design and produce VFX and Computer Animation and Games. This project involves research in the areas of modelling, animation and visualisation.

Our team introduced the concept of hybrid modelling which is based on the idea that a single physical object can be described internally by multiple diverse representations that are best suited to the diversity of operations that the user may which to perform on such an object. This makes the internal representation of objects opaque to the user, thus allowing the artist to interact with objects at a higher level and not to be concerned with the details and mechanisms of its internal representation.

In this Paper:

We develop a novel and robust technique for the interrogation of function representations and a faster and more robust ray-tracing rendering algorithm.

Originality:

1 Introduction of Revised Affine Arithmetic to CG.

2 Widening of the scope of reliable ray-tracing and spatial enumeration algorithms for surfaces ranging from algebraic surfaces (defined by polynomials) to general implicit surfaces (defined by function evaluation procedures involving both affine and non-affine operations based on Revised Affine Arithmetic).

3 Introduction of a technique for representing procedural models using special affine forms (set-theoretic operations in the form of R-functions, blending operations and conditional operations).

4 Derivation of special affine forms for arbitrary operators.

Significance:

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

Rigour:

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