Consistent Schemes for Addressing Surfaces when Ray Tracing Transparent CSG Objects

Abstract

Constructive Solid Geometry (CSG) defines the shape of objects, i.e. the inside and the outside regions of objects, but it does not define the material properties of the space in the interior of objects. The definition is ambiguous. There are points of space lying in several primitives, which can consist of different materials. When visualizing transparent objects this ambiguity leads to strange results, which are not consistent with the CSG modelling scheme and must therefore be eliminated. This work describes how an unambiguous model can be built by asymmetric CSG-operators and how correct refraction and shading on material boundaries can be established by separating surface properties from material properties. This separation leads to a consistent view of CSG modelling also concerning materials and surfaces. Ray tracing CSG trees and the shading model are influenced by these asymmetric operators. We introduce an applied classification scheme to handle the requirements of the new operator definition.