相关论文: Ray-marching Thurston geometries
A study of real quadratic maps with real critical points, emphasizing the effective construction of critically finite maps with specified combinatorics. We discuss the behavior of the Thurston algorithm in obstructed cases, and in one…
In this expository paper, we present a survey about the history of the geometrization conjecture and the background material on the classification of Thurston's eight geometries. We also discuss recent techniques for immersive visualization…
Recent advances in neural rendering have introduced numerous 3D scene representations. Although standard computer vision metrics evaluate the visual quality of generated images, they often overlook the fidelity of surface geometry. This…
Particle-based representations of radiance fields such as 3D Gaussian Splatting have found great success for reconstructing and re-rendering of complex scenes. Most existing methods render particles via rasterization, projecting them to…
A stochastic method is introduced for geometric modeling aerosol surface roughness with random field and discrete differential geometry theory. Optical scattering properties are computed for randomly oriented spheroidal particles with…
Neural Radiance Fields (NeRFs) provide a high fidelity, continuous scene representation that can realistically represent complex behaviour of light. Despite works like Ref-NeRF improving geometry through physics-inspired models, the ability…
Visualization of implicit surfaces is an actively researched topic. While raytracing can produce high quality images, it is not well suited for creating a quick preview of the surface. Indirect algorithms (e.g. Marching Cubes) create an…
Consider scene understanding problems such as predicting where a person is probably reaching, or inferring the pose of 3D objects from depth images, or inferring the probable street crossings of pedestrians at a busy intersection. This…
This draft summarizes some basics about geometric computer vision needed to implement efficient computer vision algorithms for applications that use measurements from at least one digital camera mounted on a moving platform with a special…
Rendering realistic cloth has always been a challenge due to its intricate structure. Cloth is made up of fibers, plies, and yarns, and previous curved-based models, while detailed, were computationally expensive and inflexible for large…
We present an effective method for visualizing flat surfaces using ray marching. Our approach provides an intuitive way to explore translation surfaces, mirror rooms, unfolded polyhedra, and translation prisms while maintaining…
Given the necessity of connecting the unconnected, covering blind spots has emerged as a critical task in the next-generation wireless communication network. A direct solution involves obtaining a coverage manifold that visually showcases…
Illumination effects cause problems for many computer vision algorithms. We present a user-friendly interactive system for robust illumination-invariant image generation. Compared with the previous automated illumination-invariant image…
We introduce and study a class of Thurston maps from the 2-sphere to itself which we call nearly Euclidean Thurston (NET) maps. These are simple generalizations of Euclidean Thurston maps.
We give a generalization of Thurston's Bounded Image Theorem for skinning maps, which applies to pared 3-manifolds with incompressible boundary that are not necessarily acylindrical. Along the way we study properties of divergent sequences…
Neural Radiance Fields achieve high-fidelity scene representation but suffer from costly training and rendering, while 3D Gaussian splatting offers real-time performance with strong empirical results. Recently, solutions that harness the…
Many lighting methods used in computer graphics such as indirect illumination can have very high computational costs and need to be approximated for real-time applications. These costs can be reduced by means of upsampling techniques which…
Textured meshes significantly enhance the realism and detail of objects by mapping intricate texture details onto the geometric structure of 3D models. This advancement is valuable across various applications, including entertainment,…
Lobster eye telescopes are ideal monitors to detect X-ray transients, because they could observe celestial objects over a wide field of view in X-ray band. However, images obtained by lobster eye telescopes are modified by their unique…
While there may be many Thurston metric geodesics between a pair of points in Teichm\"uller space, we find that by imposing an additional energy minimization constraint on the geodesics, thought of as limits of harmonic map rays, we select…