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While explicit representations of shapes such as triangular and tetrahedral meshes are often used for boundary surfaces and 3D volumes bounded by closed surfaces, implicit representations of planar regions and volumetric regions defined by level-set ...

As key subjects in spectral geometry and combinatorial graph theory, respectively, the (continuous) Hodge Laplacian and the combinatorial Laplacian share similarities in revealing the topological dimension and geometric shape of data and in their ...

Controlling the size and shear of elements is crucial in pure hex or hex-dominant meshing. To this end, non-orthonormal frame fields that are almost everywhere integrable (except for the singularities) can play a key role. However, it is often challenging ...

Locating neck-like features, or locally narrow parts, of a surface is crucial in various applications such as segmentation, shape analysis, path planning, and robotics. Topological methods are often utilized to find the set of shortest loops around ...

Singularity editing of a quadrangle mesh consists in shifting singularities around for either improving the quality of the mesh elements or canceling extraneous singularities, so as to increase mesh regularity. However, the particular structure of a ...

Digital image forensics entails the deduction of the origin, history and authenticity of a digital image. While a number of powerful techniques have been developed for this purpose, much of the focus has been on images depicting natural scenes and ...

We present a compendium of Hodge decompositions of vector fields on tetrahedral meshes embedded in the 3D Euclidean space. After describing the foundations of the Hodge decomposition in the continuous setting, we describe how to implement a five-...

A typical rainfall scenario contains tens of thousands of dynamic sound sources. A characteristic of the large-scale scene is the strong randomness in raindrop distribution, which makes it notoriously expensive to synthesize such sounds with purely ...

We introduce an approach to quadrilateral meshing of arbitrary triangulated surfaces that combines the theoretical guarantees of Morse-based approaches with the practical advantages of parameterization methods. We first construct, through an eigensolver ...

Given a photo collection of “unconstrained” face images of one individual captured under a variety of unknown pose, expression, and illumination conditions, this paper presents a method for reconstructing a 3D face surface model of the ...

In this paper, we propose a controllable embedding method for high- and low-dimensional geometry processing through sparse matrix eigenanalysis. Our approach is equally suitable to perform non-linear dimensionality reduction on big data, or to offer non-...

Decorating the surfaces of 3D printed objects with color textures is still not readily available in most consumer-level or even high-end 3D printers. Existing techniques such as hydrographics color transfer suffer from the issues of air pockets in concave ...

We present a full geometric parameterization of generalized barycentric coordinates on convex polytopes. We show that these continuous and non-negative coefficients ensuring linear precision can be efficiently and exactly computed through a power ...

This paper presents a variational method to generate cell complexes with local anisotropy conforming to the Hessian of any given convex function and for any given local mesh density. Our formulation builds upon approximation theory to offer an ...

The analysis of electromagnetic scattering has long been performed on a discrete representation of the geometry. This representation is typically continuous but not differentiable. The need to define physical quantities on this geometric representation ...

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: they are crucial to encode both directions and sizing on surfaces as commonly ...

In this article, we introduce a discrete definition of connection on simplicial manifolds, involving closed-form continuous expressions within simplices and finite rotations across simplices. The finite-dimensional parameters of this connection are ...

We propose a real-time approach for indoor scene reconstruction. It is capable of producing a ready-to-use 3D geometric model even while the user is still scanning the environment with a consumer depth camera. Our approach features explicit ...

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: they are crucial to encoding directions and sizing on surfaces as commonly ...

We present a model-reduced variational Eulerian integrator for incompressible fluids, which combines the efficiency gains of dimension reduction, the qualitative robustness of coarse spatial and temporal resolutions of geometric integrators, and the ...