Related papers: BPM: Blended Piecewise Moebius Maps
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.…
We describe a method for discretizing planar C2-regular domains immersed in non-conforming triangulations. The method consists in constructing mappings from triangles in a background mesh to curvilinear ones that conform exactly to the…
Finding appropriate notions of discrete holomorphic maps and, more generally, conformal immersions of discrete Riemann surfaces into 3-space is an important problem of discrete differential geometry and computer visualization. We propose an…
Surface mapping plays an important role in geometric processing. They induce both area and angular distortions. If the angular distortion is bounded, the mapping is called a {\it quasi-conformal} map. Many surface maps in our physical world…
Machine learning has been progressively generalised to operate within non-Euclidean domains, but geometrically accurate methods for learning on surfaces are still falling behind. The lack of closed-form Riemannian operators, the…
We decrease the $rms$ mean curvature and area of a variable surface with a fixed boundary by iterating a few times through a curvature-based variational algorithm. For a boundary with a known minimal surface, starting with a deliberately…
Tube-like surfaces are widely encountered in geometry processing, engineering structures, and medical anatomy, yet their intrinsic longitudinal and circumferential topology is not well preserved by conventional planar annular or rectangular…
Maps from a source manifold $ {\mathcal M}$ to a target manifold ${\mathcal N}$ appear in liquid crystals, colour image enhancement, texture mapping, brain mapping, and many other areas. A numerical framework to solve variational problems…
A fundamental building block for supporting better utilization of radio spectrum involves predicting the impact that an emitter will have at different geographic locations. To this end, fixed sensors can be deployed to spatially sample the…
In this short note we describe a simple adaptation of biharmonic surfaces to interpolate boundary cross-derivatives given in ribbon form, and compare with the recently proposed Generalized B-spline patches.
We propose the Binary Diffusion Probabilistic Model (BDPM), a generative framework specifically designed for data representations in binary form. Conventional denoising diffusion probabilistic models (DDPMs) assume continuous inputs, use…
We examine implicit representations of parametric or point cloud models, based on interpolation matrices, which are not sensitive to base points. We show how interpolation matrices can be used for ray shooting of a parametric ray with a…
We introduce DiffBMP, a scalable and efficient differentiable rendering engine for a collection of bitmap images. Our work addresses a limitation that traditional differentiable renderers are constrained to vector graphics, given that most…
We present simpler algorithms for two closely related morphing problems, both based on the barycentric interpolation paradigm introduced by Floater and Gotsman, which is in turn based on Floater's asymmetric extension of Tutte's classical…
We present an augmented version of our dual messenger algorithm for spin field reconstruction on the sphere, while accounting for highly non-trivial and realistic noise models such as modulated correlated noise. We also describe an…
Recent progress in large-scale text-to-video (T2V) and image-to-video (I2V) diffusion models has greatly enhanced video generation, especially in terms of keyframe interpolation. However, current image-to-video diffusion models, while…
We present the Bilinear Phase Map (BPM), a concept that extends the Kramers-Wannier (KW) transformation to investigate unconventional gapped phases, their dualities, and phase transitions. Defined by a matrix of $\mathbb{Z}_2$ elements, the…
In this work, we introduce a novel method to render, in real-time, Lambertian surfaces with a rough dieletric coating. We show that the appearance of such configurations is faithfully represented with two microfacet lobes accounting for…
A large amount of quantitative geospatial data are collected and aggregated in discrete enumeration units (e.g. countries or states). Smooth pycnophylactic interpolation aims to find a smooth, nonnegative function such that the area…
In this paper we propose a new method to enhance a mapping $\mu(\cdot)$ of a parallel application's computational tasks to the processing elements (PEs) of a parallel computer. The idea behind our method \mswap is to enhance such a mapping…