T-splines and T-NURCCs

Authors:
Thomas W. Sederberg;Jianmin Zheng;Almaz Bakenov;Ahmad Nasri
Affiliations:
Brigham Young University;Brigham Young University;Embassy of Kyrgyz Republic, Washington, D.C.;American University of Beirut
Venue:
ACM SIGGRAPH 2003 Papers
Year:
2003

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Abstract

This paper presents a generalization of non-uniform B-spline surfaces called T-splines. T-spline control grids permit T-junctions, so lines of control points need not traverse the entire control grid. T-splines support many valuable operations within a consistent framework, such as local refinement, and the merging of several B-spline surfaces that have different knot vectors into a single gap-free model. The paper focuses on T-splines of degree three, which are C2 (in the absence of multiple knots). T-NURCCs (Non-Uniform Rational Catmull-Clark Surfaces with T-junctions) are a superset of both T-splines and Catmull-Clark surfaces. Thus, a modeling program for T-NURCCs can handle any NURBS or Catmull-Clark model as special cases. T-NURCCs enable true local refinement of a Catmull-Clark-type control grid: individual control points can be inserted only where they are needed to provide additional control, or to create a smoother tessellation, and such insertions do not alter the limit surface. T-NURCCs use stationary refinement rules and are C2 except at extraordinary points and features.