Geometry-based triangulation of trimmed NURBS surfaces

Computer-Aided Design, Elsevier, Vol 30, Num 1, pp.11-18, 1998

MESHING
RESEARCH
CORNER

Department of Computer Science and Engineering, University of South Florida, 4202 Fowler Avenue, ENG 118, Tampa, FL 33620, USA

Abstract
An algorithm for obtaining a piecewise triangular approximation of a trimmed NURBS surface is presented. The algorithm is geometry based, i.e. the surface is subdivided into triangular facets based on its geometric characteristics and not on its parametrization. No assumption is made about the surface's parametrical representation; it does not have to be continuously differentiable, only C^0 continuity is assumed. The surface subdivision is performed in model space, however, the triangulation is carried out in parameter space using the parametric vertices of subdivision rectangles. Along with computing the triangulation, the method produces a compact database for browsing in the triangular irregular network, e.g. finding all neighbors of a given triangle.