相关论文: Ray-marching Thurston geometries

Representing graphs as sets of node embeddings in certain curved Riemannian manifolds has recently gained momentum in machine learning due to their desirable geometric inductive biases, e.g., hierarchical structures benefit from hyperbolic…

This tutorial describes the geometry and algorithms for generating line drawings from 3D models, focusing on occluding contours. The geometry of occluding contours on meshes and on smooth surfaces is described in detail, together with…

Textured high-fidelity 3D models are crucial for games, AR/VR, and film, but human-aligned evaluation methods still fall behind despite recent advances in 3D reconstruction and generation. Existing metrics, such as Chamfer Distance, often…

Exploiting geometric structure to improve the asymptotic complexity of discrete assignment problems is a well-studied subject. In contrast, the practical advantages of using geometry for such problems have not been explored. We implement…

The geometry of weight spaces and functional manifolds of neural networks play an important role towards 'understanding' the intricacies of ML. In this paper, we attempt to solve certain open questions in ML, by viewing them through the…

We develop a computational framework that leverages the features of sophisticated software tools and numerics to tackle some of the pressing issues in the realm of earth sciences. The algorithms to handle the physics of multiphase flow,…

We present a simple, novel method of efficiently rendering ray cast soft shadows on curved terrain by using dynamic programming and maximum mipmaps to rapidly find a global minimum shadow cost in constant runtime complexity. Additionally,…

Projection methods are popular algorithms for iteratively solving feasibility problems in Euclidean or even Hilbert spaces. They employ (selections of) nearest point mappings to generate sequences that are designed to approximate a point in…

We propose a new framework for the sampling, compression, and analysis of distributions of point sets and other geometric objects embedded in Euclidean spaces. Our approach involves constructing a tensor called the RaySense sketch, which…

Information transfer between triangle meshes is of great importance in computer graphics and geometry processing. To facilitate this process, a smooth and accurate map is typically required between the two meshes. While such maps can…

Real-time global illumination is key to enabling more dynamic and physically realistic worlds in performance-critical applications such as games or any other applications with real-time constraints.Hardware-accelerated ray tracing in modern…

Intersection algorithms are very important in computation of geometrical problems. Algorithms for a line intersection with linear or quadratic surfaces are quite efficient. However, algorithms for a line intersection with other surfaces are…

Classical light field rendering for novel view synthesis can accurately reproduce view-dependent effects such as reflection, refraction, and translucency, but requires a dense view sampling of the scene. Methods based on geometric…

Current practice in parameter space exploration in euclidean space is dominated by randomized sampling or design of experiment methods. The biggest issue with these methods is not keeping track of what part of parameter space has been…

Recent literature has shown that symbolic data, such as text and graphs, is often better represented by points on a curved manifold, rather than in Euclidean space. However, geometrical operations on manifolds are generally more complicated…

The Heston model is a well-known two-dimensional financial model. Because the Heston model contains implicit parameters that cannot be determined directly from real market data, calibrating the parameters to real market data is challenging.…

We obtain algorithms for computing Tverberg partitions based on centerpoint approximations. This applies to a wide range of convexity spaces, from the classic Euclidean setting to geodetic convexity in graphs. In the Euclidean setting, we…

Recent 3D Gaussian Splatting (3DGS) representations have demonstrated remarkable performance in novel view synthesis; further, material-lighting disentanglement on 3DGS warrants relighting capabilities and its adaptability to broader…

We design and implement a Python library to help the non-expert using all these powerful tools in a way that is efficient, extensible, and simple to incorporate into the workflow of the data scientist, practitioner, and applied researcher.…

We introduce a novel approach for depth estimation using images obtained from monocular structured light systems. In contrast to many existing methods that depend on image matching, our technique employs a density voxel grid to represent…