DEPARTMENT OF COMPUTER SCIENCE
MONASH UNIVERSITY

Clayton, Victoria 3168 Australia


TECHNICAL REPORT 97/324


Creating and Rendering Convolution Surfaces

J McCormack and A Sherstyuk

ABSTRACT

Implicit surfaces obtained by convolution of multi-dimensional primitives with some potential function, are a generalisation of popular implicit surface models: blobs, meatballs and soft objects. These models differ in their choice of potential functions but agree upon the use of underlying modelling primitives, namely, points. In this paper a method is described for modelling and rendering implicit surfaces built upon an expanded set of skeletal primitives: points, line segments, polygons, arcs and planes. An algorithm for ray-tracing the surfaces formed through convolution of any combination of these primitives is also presented. The algorithm employs analytical methods only, which makes it computationally effective.

Keywords: convolution surfaces, geometric modelling, implicit surfaces, ray-tracing.