Reliable algorithms for ray intersection in computer graphics based on interval arithmetic

Abstract

We study the reliability and performance of interval arithmetic for ray tracing implicit surfaces. We analyze when and how to use interval arithmetic as an alternative to the methods used in POV-Ray for ray intersection. Interval methods are applied as robust approaches for solving the ray-surface intersection problem; i.e. to find the minimal root in a set of analytic functions. POV-Ray is able to solve this problem efficiently for relatively simple objects (objects that can be bounded in a box). Interval based algorithms can speed up the rendering process for scenes with some infinite implicit surfaces, including nondifferentiable ones, where the automatic bounding box cannot be applied. Interval methods have the advantage of not needing to provide the interval guess of the maximum gradient, as recursive subdivision equipotential methods (used by POV-Ray) does. Experimental results were obtained from the evaluation of our interval algorithms and the methods used in POV-Ray in scenes with single objects and in complex scenes with several objects.