Semi-sharp creases on subdivision curves and surfaces

We explore a method for generalising Pixar semi-sharp creases from the univariate cubic case to arbitrary degree subdivision curves. Our approach is based on solving simple matrix equations. The resulting schemes allow for greater flexibility over existing methods, via control vectors. We demonstrate our results on several high-degree univariate examples and explore analogous methods for subdivision surfacesThis work was supported by the Engineering and Physical Sciences Research Council [EP/H030115/1].This is the author accepted manuscript and will be under embargo until the 23rd of August 2015. The final version has been published in Computer Graphics Forum here: http://onlinelibrary.wiley.com/doi/10.1111/cgf.12447/abstract

Subdivision surfaces with creases and truncated multiple knot lines

We deal with subdivision schemes based on arbitrary degree B-splines. We focus on extraordinary knots which exhibit various levels of complexity in terms of both valency and multiplicity of knot lines emanating from such knots. The purpose of truncated multiple knot lines is to model creases which fair out. Our construction supports any degree and any knot line multiplicity and provides a modelling framework familiar to users used to B-splines and NURBS systems

Creases and boundary conditions for subdivision curves

AbstractOur 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 for arbitrary degrees for B-splines, these methods introduce unnecessary (ghost) control points.The situation is not so simple in modifying subdivision rules. Based on subdivision and subspace selection matrices, a novel approach to finding boundary and sharp subdivision rules that generalises to any degree is presented. Our approach leads to new higher-degree polynomial subdivision schemes with crease control without introducing new control points