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 …

This article describes a method for efficiently computing parallel transport of tangent vectors
on curved surfaces, or more generally, any vector-valued data on a curved manifold. More …

In this paper, we introduce complex functional maps, which extend the functional map
framework to conformal maps between tangent vector fields on surfaces. A key property of …

Geometry processing of surface meshes relies heavily on the discretization of differential
operators such as gradient, Laplacian, and covariant derivative. While a variety of discrete …

While scalar fields on surfaces have been staples of geometry processing, the use of
tangent vector fields has steadily grown in geometry processing over the last two decades …

We propose a method for computing global Chebyshev nets on triangular meshes. We
formulate the corresponding global parameterization problem in terms of commuting …

This paper presents a new preconditioning technique for large‐scale geometric optimization
problems, inspired by applications in mesh parameterization. Our positive (semi‐) definite …

We study discrete geodesic foliations of surfaces—foliations whose leaves are all
approximately geodesic curves—and develop several new variational algorithms for …

Previous research on animations of soap bubbles, films, and foams largely focuses on the
motion and geometric shape of the bubble surface. These works neglect the evolution of the …

In geometry processing, smoothness energies are commonly used to model scattered data
interpolation, dense data denoising, and regularization during shape optimization. The …