Abstract: Meshes with T-joints (T-meshes) and related high-order surfaces have many advantages in situations where flexible local refinement is needed. At the same time, designing subdivision rules and bases for T-meshes is much more difficult, and fewer options are available. For common geometric modeling tasks it is desirable to retain the simplicity and flexibility of commonly used subdivision surfaces, and extend them to handle T-meshes.

We propose a subdivision scheme extending Catmull-Clark and NURSS to a special class of quad T-meshes, dyadic T-meshes, which have no more than one T-joint per edge. Our scheme is based on a factorization with the same structure as Catmull-Clark subdivision. On regular T-meshes it is a refinement scheme for a subset of standard T-splines. While we use more variations of subdivision masks compared to Catmull-Clark and NURSS, the minimal size of the stencil is maintained, and all variations in formulas are due to simple changes in coefficients.

Abstract: The creation, manipulation and display of piecewise smooth surfaces has been a fundamental topic in computer graphics since its inception. The applications range from highest-quality surfaces for manufacturing in CAD, to believable animations of virtual creatures in Special Effects, to virtual worlds rendered in real-time in computer games.

Our focus is on improving the a) mathematical representation and b) automatic construction of such surfaces from finely sampled meshes in the presence of features. Features can be areas of higher geometric detail in an otherwise smooth area of the mesh, or sharp creases that contrast the overall smooth appearance of an object.

Abstract: We present a simple and efficient technique to add curvature-dependent anisotropy to harmonic parameterization and improve the approximation error of the quadrangulations. We use a metric derived from the shape operator which results in a more uniform error distribution, decreasing the error near features.

Abstract: In this paper, we propose an approach to constructing patch layouts consisting of small numbers of quadrilateral patches while maintaining good feature alignment. To achieve this, we use quadrilateral T-meshes, for which the intersection of two faces may not be the whole edge or vertex, but a part of an edge. T-meshes offer more flexibility for reduction of the number of patches and vertices in a base domain while maintaining alignment with geometric features.

Abstract: We present an extension of recently developed Loop and Schaefer’s approximation of Catmull-Clark surfaces (ACC) for surfaces with creases and corners which are essential for most applications. We discuss the integration of ACC into Valve’s Source game engine and analyze the performance of our implementation.

Abstract: Nonlinear Galerkin methods utilize approximate inertial manifolds to reduce the spatial error of the standard Galerkin method. For certain scenarios, where a rough forcing term is used, a simple postprocessing step yields the same improvements that can be observed with nonlinear Galerkin. We show that this improvement is mainly due to the information about the forcing term that is neglected by standard Galerkin. Moreover, we construct a simple postprocessing scheme that uses only this neglected information but gives the same increase in accuracy as nonlinear or postprocessed Galerkin methods.