Ray Casting Implicit Procedural Noises with Reduced Affine Arithmetic

A method for ray casting implicit surfaces, defined with procedural noise models, is presented. The method is robust in that it is able to guarantee correct intersections at all image pixels and for all types of implicit surfaces. This robustness comes from the use of an affine arithmetic representation for the quantity that expresses the variation of the implicit function along a ray. Affine arithmetic provides a bounding interval estimate which is tighter than the interval estimates returned by conventional interval arithmetic. Our ray casting method is also efficient due to a proposed modification in the data structure used to hold affine arithmetic quantities. This modified data structure ultimately leads to a reduced affine arithmetic model. We show that such a reduced affine arithmetic model is able to retain all the tight estimation capabilities of standard affine arithmetic, in the context of ray casting implicit procedural noises, while being faster to compute and more efficient to store. We also show that, without this reduced model, affine arithmetic would not have any advantage over the more conventional interval arithmetic for ray casting the class of implicit procedural surfaces that we are interested in visualizing.