相关论文: Ray-marching Thurston geometries

3D scene modeling techniques serve as the bedrocks in the geospatial engineering and computer science, which drives many applications ranging from automated driving, terrain mapping, navigation, virtual, augmented, mixed, and extended…

Radiance fields have revolutionized photo-realistic 3D scene visualization by enabling high-fidelity reconstruction of complex environments, making them an ideal match for light field displays. However, integrating these technologies…

Many problems in computational geometry are not stated in graph-theoretic terms, but can be solved efficiently by constructing an auxiliary graph and performing a graph-theoretic algorithm on it. Often, the efficiency of the algorithm…

We examine a wide class of stochastic approximation algorithms for solving (stochastic) nonlinear problems on Riemannian manifolds. Such algorithms arise naturally in the study of Riemannian optimization, game theory and optimal transport,…

Real-time rendering with global illumination is crucial to afford the user realistic experience in virtual environments. We present a learning-based estimator to predict diffuse indirect illumination in screen space, which then is combined…

Mating is an operation to construct a rational map f from two polynomials, which are not in conjugate limbs of the Mandelbrot set. When the Thurston Algorithm for the unmodified formal mating is iterated in the case of postcritical…

Reconstructing 3D geometry and appearance from a sparse set of fixed cameras is a foundational task with broad applications, yet it remains fundamentally constrained by the limited viewpoints. We show that this bound can be broken by…

We present an algorithm for creating an n-level ray-space hierarchy (RSH) of coherent rays that runs on the GPU. Our algorithm uses rasterization to process the primary rays, then uses those results as the inputs for a RSH, that processes…

Problems in differentiable rendering often involve optimizing scene parameters that cause motion in image space. The gradients for such parameters tend to be sparse, leading to poor convergence. While existing methods address this sparsity…

We address the problem of active mapping with a continually-learned neural scene representation, namely Active Neural Mapping. The key lies in actively finding the target space to be explored with efficient agent movement, thus minimizing…

This paper addresses two problems needed to support four-dimensional ($3d + t$) spacetime numerical simulations. The first contribution is a general algorithm for producing conforming spacetime meshes of moving geometries. Here, the surface…

Here we present a new non-parametric approach to density estimation and classification derived from theory in Radon transforms and image reconstruction. We start by constructing a "forward problem" in which the unknown density is mapped to…

We present a physics-based inverse rendering method that learns the illumination, geometry, and materials of a scene from posed multi-view RGB images. To model the illumination of a scene, existing inverse rendering works either completely…

Many machine learning problems involve regressing variables on a non-Euclidean manifold -- e.g. a discrete probability distribution, or the 6D pose of an object. One way to tackle these problems through gradient-based learning is to use a…

We introduce a deep appearance model for rendering the human face. Inspired by Active Appearance Models, we develop a data-driven rendering pipeline that learns a joint representation of facial geometry and appearance from a multiview…

We present a sampling-based framework for multi-robot motion planning which combines an implicit representation of a roadmap with a novel approach for pathfinding in geometrically embedded graphs tailored for our setting. Our pathfinding…

We introduce an algorithm which can be directly used to feasible and optimum search in linear programming. Starting from an initial point the algorithm iteratively moves a point in a direction to resolve the violated constraints. At the…

Non-isotropic geometries are of interest to low-dimensional topologists, physicists and cosmologists. However, they are challenging to comprehend and visualize. We present novel methods of computing real-time native geodesic rendering of…

We propose Text2Scene, a method to automatically create realistic textures for virtual scenes composed of multiple objects. Guided by a reference image and text descriptions, our pipeline adds detailed texture on labeled 3D geometries in…

We propose a method for estimating high-definition spatially-varying lighting, reflectance, and geometry of a scene from 360$^{\circ}$ stereo images. Our model takes advantage of the 360$^{\circ}$ input to observe the entire scene with…