This article presents a generalized B-spline surface subdivision scheme of arbitrary order with a tension parameter.We first propose a tensor-product subdivision scheme that produces ku×kv order generalized B-spline limit surfaces. Generalized B-spline surface is the unified and extended form of B-splines, trigonometric B-splines and hyperbolic B-splines (Fang et al. 2010). The tensor product s...

Problem statement: Subdivision surfaces were applied to the entire meshes in order to produce smooth surfaces refinement from coarse mesh. Several schemes had been introduced in this area to provide a set of rules to converge smooth surfaces. However, to compute and render all the vertices are really inconvenient in terms of memory consumption and runtime during the subdivision process. It will...

A sufficient condition for C 1-continuity of subdivision surfaces was proposed by Reif [17] and extended to a more general setting in [22]. In both cases, the analysis of C 1-continuity is reduced to establishing injectivity and regularity of a characteristic map. In all known proofs of C 1-continuity, explicit representation of the limit surface on an annular region was used to establish regul...

Recent research has produced results on subdivision in arbitrary manifolds. These results can be applied to the manifold of lines and thus we can create subdivision schemes especially for ruled surfaces. We present different methods for refining discrete models of ruled surfaces: An algorithm combining subdivision and projection to the manifold of lines in Euclidean three-space. A further algor...

Subdivision schemes provide efficient algorithms both for the design and processing of arbitrary control meshes. Theoretically, these techniques are often considered as an elegant algorithmic way to approximate a desired surface from a given surface. In practice, controlling the accuracy of control meshes with regard to the limit surface remains difficult. In this paper, from a bound of the dis...

Subdivision surfaces refer to a class of modelling schemes that define an object through recursive subdivision starting from an initial control mesh. Similar to B-splines, the final surface is defined by the vertices of the initial control mesh. These surfaces were initially conceived as an extension of splines in modelling objects with a control mesh of arbitrary topology. They exhibit a numbe...

Our goal is to find subdivision rules at creases in arbitrary degree subdivision for piece-wise polynomial curves, but without introducing new control points e.g. by knot insertion. Crease rules are well understood for low degree (cubic and lower) curves. We compare three main approaches: knot insertion, ghost points, and modifying subdivision rules. While knot insertion and ghost points work f...

Subdivision provides an efficient method to generate smooth curves and surfaces. Recently matrixvalued subdivision schemes were introduced to provide more flexibility and smaller subdivision templates for curve and surface design. For matrix-valued subdivision, the input is a set of vectors with the first components being the vertices of the control polygon (or the control net for surface subdi...

Starting with values {f 0 j }j∈Z assigned to the integers, a binary subdivision scheme defines recursively values {fk j }j∈Z, respectively assigned to the binary points {2−kj}j∈Z. The purpose of subdivision analysis is to study the convergence of such processes and to establish the existence of a limit function on R and its smoothness class. A general treatment of uniform subdivision can be fou...