Mapping a triangulated surface to 2D space (or a tetrahedral mesh to 3D space) is an
important problem in geometry processing. In computational physics, untangling plays an …

Constructing an analysis-suitable parameterization for the computational domain from its
boundary representation plays a crucial role in the isogeometric design-through-analysis …

Constructing spline parameterizations for computational domains is one of the fundamental
problems in isogeometric analysis. In this paper, we present an efficient method for …

We aim to tackle the challenge of generating unstructured high-order meshes of complex
three-dimensional bodies, which remains a significant bottleneck in the wider adoption of …

In isogeometric analysis, constructing bijective and low-distorted parameterizations is a
fundamental task. Compared with the planar problem, the volumetric case is more …

A variational method that can provably construct 3D quasi-isometric mappings between
domains of a complex shape is introduced. A local maximum principle for polyconvex mesh …

Isogeometric analysis has brought a paradigm shift in integrating computational simulations
with geometric designs across engineering disciplines. This technique necessitates analysis …

Computing injective maps with low distortions is a long-standing problem in computer
graphics. Such maps are particularly challenging to obtain in the presence of positional …

Optimal mapping is one of the longest-standing problems in computational mathematics. It is
natural to measure the relative curve length error under map to assess its quality. The …

The generation of sufficiently high quality unstructured high-order meshes remains a
significant obstacle in the adoption of high-order methods. However, there is little consensus …