Progressive Dimension-Independent Boolean Operations

Abstract

This paper introduces a new progressive multi-resolution approach for representating and processing polyhedral objects of any dimension. Our representation, a variant of BSP trees [Nay90] combined with the Split scheme introduced in [BP96], allows progressive streaming and rendering of solid models at multiple levels of detail (LOD). Boolean set operations are computed progressively by reading in input a stream of incremental refinements of the operands. Each refinement of the input is mapped immediately to a refinement of the output so that the result is also represented as a stream of progressive refinements. The computation of complex models results in a tree of pipelined processes that make continuous progress concurrently, so that coarse approximations of the final results are obtained nearly instantly, long before the input operands are fully processed. We demonstrate the practical effectiveness of this approach with models constructed with our prototype system.