We present a subdivision framework that adds extraordinary vertices to NURBS of arbitrarily
high degree. The surfaces can represent any odd degree NURBS patch exactly. Our rules …

Subdivision surfaces allow smooth free‐form surface modelling without topological
constraints. They have become a fundamental representation for smooth geometry …

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 …

We compare curvature-based surface functionals by comparing the aesthetic properties of
their minimizers. We introduce an enhancement to the original inline curvature variation …

Megapixel single-photon avalanche diode (SPAD) arrays have been developed recently,
opening up the possibility of deploying SPADs as generalpurpose passive cameras for …

We provide asymptotic expansions for the fundamental forms, the Weingarten map, the
principal curvatures, and the principal directions of surfaces generated by linear stationary …

The main roadblock that has limited the usage of subdivision surfaces in computer-aided
design (CAD) systems is the lack of quality and precision that a model must achieve for …

Two main technologies are available to design and represent freeform surfaces: Non-
Uniform Rational B-Splines (NURBS) and subdivision surfaces. Both representations are …

This paper summarizes the structure and analysis of subdivision surfaces and characterizes
the inherent similarities and differences to parametric spline surfaces. Besides presenting …

Subdivision surfaces have become a standard geometric modeling tool for a variety of
applications. This survey is an introduction to subdivision algorithms for arbitrary meshes …