Semi‐sharp Creases on Subdivision Curves and Surfaces

Abstract

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 surfaces.

Non‐Uniform Subdivision Surfaces with Sharp Features

“…Similar to [KSD14a] and [DKT98], our method can also produce semi‐sharp features by interactively mixing the sharp rule and smooth rule throughout the subdivision process. Specifically, after subdividing a tagged initial mesh several times, we clear the tagged information in the control mesh and continue to subdivide until the limit surface is obtained.…”

“…Subdivision surfaces are also attractive because they are conceptually simple and can be easily modified to create surface features without making major changes to the original subdivision rules. Lots of approaches [HDD*94, DKT98, BLZ00, BMZB02, KSD14a, KS99, NLG12] have been proposed to produce sharp features for subdivision surfaces. These schemes are directly modified from Catmull–Clark [CC78] or Loop [Loo87] subdivision rules.…”

Converting a CAD model into a non-uniform subdivision surface

“…(2) Models that require a mix of accurate continuity at the joined corner. In such cases, methods such as those of Kosinka et al (2014a) need to be used.…”

“…We considered several alternatives including those proposed by Sederberg et al (1998), Müller et al (2006Müller et al ( , 2010 and Kosinka et al (2014b). We opted for a modification of Cashman's (2010) framework, which we based on a generalisation of both Pixar rules (DeRose et al, 1998) and ghost points (Kosinka et al, 2014a) to the non-uniform setting required in our method.…”

Variational reconstruction using subdivision surfaces with continuous sharpness control

“…Although DeRose et al's approach [3] provides a simple way to model semi-sharp features, and has been extended from the cubic case [4] to arbitrary degree for semi-sharp creases in Ref. [5], these methods of controlling the iterations of geometry preserving subdivision are inconvenient for reverse engineering where such sharpness control must be determined. Ideally, such a sharpness parameter should be continuously controllable.…”