Bicubic Polar Subdivision (2009)
We describe and analyze a subdivision scheme that generalizes bicubic spline subdivision to control nets with polar structure. Such control nets appear naturally for surfaces with the combinatorial...
On the curvature of guided surfaces (2009)
Following [KP07], we analyze surfaces arising as an infinite sequence of guided C 2 surface rings. However, here we focus on constructions of too low a degree to be curvature continuous also at the...
A C 2 Polar Jet Subdivision (2009)
Konrad Polthier, Alla Sheffer (editors, K. Karčiauskas, A. Myles, J. Peters
We describe a subdivision scheme that acts on control nodes that each carry a vector of values. Each vector defines partial derivatives, referred to as jets in the following and subdivision computes...
Parameterization transition for guided c 2 surfaces of low degree (2009)
Abstract. By separating shape design from representation, the guided approach to surface construction [KP07] allows to routinely construct everywhere C 2 surfaces with (infinite) subdivision...
We describe and analyze a subdivision scheme that generalizes bicubic spline subdivision to control nets with polar structure. Such control nets appear naturally for surfaces with the combinatorial...
Guided C 2 Spline Surfaces with V-shaped tessellation (2008)
Abstract. The guided spline approach to surface construction separates surface design and surface representation by constructing local guide surfaces and sampling these by splines of moderate degree....
A multi-sided hole in a surface can be filled by a sequence of nested, smoothly joined surface rings. We show how to generate such a sequence so that (i) the resulting surface is C 2 (also in the...
Surfaces with polar structure (2006)
We describe the structure and general properties of surfaces with polar layout. Polar layout is particularly suitable for high valences and is, for example, generated by a new class of subdivision...
Curvature continuous surfaces with subdivision structure are constructed by higher-order sampling of a piecewise polynomial guide surface, at positions defined and derivatives weighted by a special,...
U.: Shape characterization of subdivision surfaces – case studies (2004)
K. Karčiauskas, Jörg Peters, U. Reif C
For subdivision surfaces, it is important to characterize local shape near flat spots and points where the surface is not twice continuously differentiable. Applying general principles derived in...