Vortices are commonly understood as rotating motions in fluid flows. The analysis of vortices
plays an important role in numerous scientific applications, such as in engineering …

Vector fields are a common concept for the representation of many different kinds of flow
phenomena in science and engineering. Methods based on vector field topology are known …

Motivated by the vast success of deep convolutional networks, there is a great interest in
generalizing convolutions to non-Euclidean manifolds. A major complication in comparison …

Direction fields and vector fields play an increasingly important role in computer graphics
and geometry processing. The synthesis of directional fields on surfaces, or other spatial …

Many algorithms in computer graphics and geometry processing use two orthogonal smooth
direction fields (unit tangent vector fields) defined over a surface. For instance, these …

We present a robust method for computing locally bijective global parametrizations aligned
with a given cross-field. The singularities of the parametrization in general agree with …

Many algorithms in texture synthesis, nonphotorealistic rendering (hatching), or remeshing
require to define the orientation of some features (texture, hatches, or edges) at each point of …

We describe a method for the generation of seamless surface parametrizations with
guaranteed local injectivity and full control over holonomy. Previous methods guarantee …

The computation of smooth fields of orthogonal directions within a volume is a critical step in
hexahedral mesh generation, used to guide placement of edges and singularities. While this …

The efficient and practical representation and processing of geometrically or topologically
complex shapes often demands a partitioning into simpler patches. Possibilities range from …