Tunnel-free voxelisation of rational Bézier surfaces

Abstract

To synthesize natural and artificial objects into a hybrid graphics scene represented by a set of voxels, voxelisation of geometric models is necessary. Rational parametric surfaces have been widely used in the representation of free-form surfaces. Voxelisation of these surfaces is therefore of great importance in the development of a voxel-based modeling system. A key issue is to develop a tunnel-free voxelisation algorithm for these continuous surfaces. In this paper, we propose such an algorithm for a rational Bezier surface. We derive the bound of the parametric steps to ensure that the voxelised rational Bezier surface is, by our algorithm, 6-tunnel-free, and we give the mathematical proof of this property. For efficient computation, we employ the forward difference technique in homogeneous form in the implementation of the algorithm. For more general applications, we show that voxelisation of a NURBS surface can be realised by first converting it into a piecewise rational Bezier surface and then voxelising each of the rational Bezier surfaces. We indicate the advantages carrying out this procedure.