Polar NURBS Surface with Curvature Continuity

Curvature and Continuity Control in Particle-Based Surface Models

This paper develops techniques to locally control curvature and continuity in particle-based surface models. Such models are a generalization of traditional spline surfaces built out of triangular patches. Traditional splines require the topology of the triangular mesh to be specified ahead of time. In contrast, particle-based surface models compute the topology dynamically as a function of the...

NURBS approximation of surface/surface intersection curves

We use a combination of both symbolic and numerical techniques to construct a degree bounded C-continuous, rational B-spline -approximations of real algebraic surface-surface intersection curves. The algebraic surfaces could be either in implicit or rational parametric form. At singular points we use the classical Newton power series factorizations to determine the distinct branches of the spac...

Finite Curvature Continuous Polar Patchworks

We present an algorithm for completing a C surface of up to degree bi-6 by capping an n-sided hole with polar layout. The cap consists of n tensor-product patches, each of degree 6 in the periodic and degree 5 in the radial direction. To match the polar layout, one edge of these patches is collapsed. We explore and compare with alternative constructions, based on more pieces or using total-degr...

Curvature continuity between adjacent rational Bézier patches

Zheng, J., G Wang and Y. Liang, Curvature continuity between adjacent rational B&ier patches, Computer Aided Geometric Design 9 (1992) 321-335. This paper discusses the cutvature continuity between two adjacent rational BCzier surfaces which may be rectangular or triangular patches. The necessary and sufficient conditions are derived, and further, a series of simple sufficient conditions are de...

Triangular NURBS Surface Modeling of Scattered Data