Related papers: Density-equalizing maps for simply-connected open …
In this paper, we present an approach to enhance and improve the current normal map rendering technique. Our algorithm is based on semi-discrete Optimal Mass Transportation (OMT) theory and has a solid theoretical base. The key difference…
Diffusion maps are an emerging data-driven technique for non-linear dimensionality reduction, which are especially useful for the analysis of coherent structures and nonlinear embeddings of dynamical systems. However, the computational…
Modeling folding surfaces with nonzero thickness is of practical interest for mechanical engineering. There are many existing approaches that account for material thickness in folding applications. We propose a new systematic and broadly…
Conformal mapping, a classical topic in complex analysis and differential geometry, has become a subject of great interest in the area of surface parameterization in recent decades with various applications in science and engineering.…
In this paper we introduce flat grafting as a deformation of quadratic differentials on a surface of finite type that is analogous to the grafting map on hyperbolic surfaces. Flat grafting maps are generic in the strata structure and…
A rigorous mathematical model and an efficient computational method are proposed to solving the inverse elastic surface scattering problem which arises from the near-field imaging of periodic structures. We demonstrate how an enhanced…
We demonstrate a method for filtering images defined on curved surfaces embedded in 3D. Applications are noise removal and the creation of artistic effects. Our approach relies on in-surface diffusion: we formulate Weickert's edge/coherence…
Spectral analysis of open surfaces is gaining momentum for studying surface morphology in engineering, computer graphics, and medical domains. This analysis is enabled using proper parameterization approaches on the target analysis domain.…
We use conformal maps to study a free boundary problem for a two-fluid electromechanical system, where the interface between the fluids is determined by the combined effects of electrostatic forces, gravity and surface tension. The free…
Density map is an effective visualization technique for depicting the scalar field distribution in 2D space. Conventional methods for constructing density maps are mainly based on Euclidean distance, limiting their applicability in urban…
Motivated by geometry processing for surfaces with non-trivial topology, we study discrete harmonic maps between closed surfaces of genus at least two. Harmonic maps provide a natural framework for comparing surfaces by minimizing…
The traditional wisdom for achieving transparency is to minimize disordered scattering within and on the surface of materials, so as to avoid translucency. However, the lack of disordered scattering also deprives the possibility of…
We use mass-transportation as a tool to compare surfaces (2-manifolds). In particular, we determine the "similarity" of two given surfaces by solving a mass-transportation problem between their conformal densities. This mass transportation…
This paper proposes a method for computing the visible occluding contours of subdivision surfaces. The paper first introduces new theory for contour visibility of smooth surfaces. Necessary and sufficient conditions are introduced for when…
We propose DeMapGS, a structured Gaussian Splatting framework that jointly optimizes deformable surfaces and surface-attached 2D Gaussian splats. By anchoring splats to a deformable template mesh, our method overcomes topological…
A regular map is a surface together with an embedded graph, having properties similar to those of the surface and graph of a platonic solid. We analyze regular maps with reflection symmetry and a graph of density strictly exceeding 1/2, and…
In this article, we discuss the numerical solution of diffusion equations on random surfaces within the isogeometric framework. We describe in detail, how diffusion problems on random surfaces can be modelled and how quantities of interest…
This paper proposes a fast and accurate surface normal estimation method which can be directly used on depth maps (organized point clouds). The surface normal estimation process is formulated as a closed-form expression. In order to reduce…
We consider chains of one-dimensional, piecewise linear, chaotic maps with uniform slope. We study the diffusive behaviour of an initially nonuniform distribution of points as a function of the slope of the map by solving Frobenius-Perron…
In this article we describe an algorithm that can be applied for the generation of various classes of maps on orientable surfaces. It uses existing generators for abstract graphs and combines them with an efficient embedding and isomorphism…