Topology preserving voxelisation of rational Bezier and NURBS curves
The development of volume graphics systems has attracted numerous researchers. These systems are able to synthesise geometric models and natural objects such as those in 3D medical imaging into a complex graphics scene, extending the domain of graphics applications. Voxelisation of geometric models is a fundamental and crucial issue in such systems; especially, voxelisation of free-form models has been proven challenging. This paper is a report on our research in free-form voxelisation. It presents a novel method and algorithm for voxelisation of the most widely used rational Bezier and NURBS curves. Voxelisation of a NURBS curve is realised through first converting it into a piecewise rational Bezier curve. Different kinds of topological connectivity of the voxelised curves are discussed. The proposed algorithm employs the forward difference technique to speed up the voxelisation process while the desired topological connectivity is preserved. (C) 2002 Elsevier Science Ltd. All rights reserved.
voxelisation nurbs volume graphics algorithm rational bezier curve forward difference