Bivariate splines over triangular meshes for freeform surface modeling with sharp features

ABSTRACT

This paper presents a novel scheme for constructing bivariate spline surfaces over triangular meshes which are topologically equivalent to a disk. The core part of the scheme is a set of knot selection rules that define local configurations of a triangulation called the directed-one-ring-cycle (D1RC) configurations and bivariate splines defined over a D1RC configuration that are new non-tensor-product splines and possess many nice properties of a univariate B-spline. Using D1RC splines, we take an input triangular mesh as a control mesh and define a bivariate spline surface from the control mesh, which mimics the standard NURBS modeling. Moreover, we can introduce sharp features into the overall smooth spline surface by simply setting special D1RC configurations. As a result, the proposed scheme can define spline surfaces in a way similar to that of NURBS, but has less restriction on the connectivity of the input control mesh.

GRAPHICAL ABSTRACT

KEYWORDS:

• Surface modeling
• bivariate splines
• triangular meshes
• sharp features

Acknowledgements

This work was supported by MOE AcRF Tier 1 Grant of Singapore [RG26/15], National Nature Science Foundation of China [61100105, 61472332], the Natural Science Foundation of Fujian Province of China [2015J01273] and the Fundamental Research Funds for the Central Universities [20720150002].

ORCID

Juan Cao http://orcid.org/0000-0002-8154-4397

Jianmin Zheng http://orcid.org/0000-0002-5062-6226