Related papers: Global Illumination of non-Euclidean spaces
Humans have the remarkable ability to construct consistent mental models of an environment, even under limited or varying levels of illumination. We wish to endow robots with this same capability. In this paper, we tackle the challenge of…
Modern computer vision algorithms have brought significant advancement to 3D geometry reconstruction. However, illumination and material reconstruction remain less studied, with current approaches assuming very simplified models for…
Non-Euclidean triangle centers can be described using homogeneous coordinates that are proportional to the generalized sines of the directed distances of a given center from the edges of the reference triangle. Identical homogeneous…
Geometric optics is often described as tracing the paths of non-diffracting rays through an optical system. In the paraxial limit, ray traces can be calculated using ray transfer matrices (colloquially, ABCD matrices), which are 2x2…
We establish a region of convergence for the proto-typical non-convex Douglas-Rachford iteration which finds a point on the intersection of a line and a circle. Previous work on the non-convex iteration [2] was only able to establish local…
Optics related to non-Euclidean geometry has been attracting growing interest for emerged novel phenomena and the analog for general relativity, while most studies are limited to the free space on rotationally-symmetric surfaces. In this…
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…
We describe algorithms that produce accurate real-time interactive in-space views of the eight Thurston geometries using ray-marching. We give a theoretical framework for our algorithms, independent of the geometry involved. In addition to…
Non-line-of-sight (NLOS) imaging techniques use light that diffusely reflects off of visible surfaces (e.g., walls) to see around corners. One approach involves using pulsed lasers and ultrafast sensors to measure the travel time of…
We present a deep learning solution for estimating the incident illumination at any 3D location within a scene from an input narrow-baseline stereo image pair. Previous approaches for predicting global illumination from images either…
This paper proposes fast and novel methods to jointly estimate the target's unknown 3D shape and dynamics. Measurements are noisy and sparsely distributed 3D points from a light detection and ranging (LiDAR) sensor. The methods utilize…
In this short note, we study compact K\"ahler surfaces whose universal cover can be realized as a quasi-projective (or quasi-K\"ahler) surface. In particular, we show that such a surface is a quotient of a torus if the universal cover is…
We present a lightweight solution for estimating spatially-coherent indoor lighting from a single RGB image. Previous methods for estimating illumination using volumetric representations have overlooked the sparse distribution of light…
Orbifolds are a modern mathematical concept that arises in the research of hyperbolic geometry with applications in computer graphics and visualization. In this paper, we make use of rooms with mirrors as the visual metaphor for orbifolds.…
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…
In this paper we suggest the use of light for performing useful computations. Namely, we propose a special device which uses light rays for solving the Hamiltonian path problem on a directed graph. The device has a graph-like representation…
Modeling the wave nature of light and the propagation and diffraction of electromagnetic fields is crucial for the accurate simulation of many phenomena, yet wave simulations are significantly more computationally complex than classical…
We classify $n$-dimensional geometric graph manifolds with nonnegative scalar curvature, and first show that if $n>3$, the universal cover splits off a codimension 3 Euclidean factor. We then proceed with the classification of the…
Decomposing an object's appearance into representations of its materials and the surrounding illumination is difficult, even when the object's 3D shape is known beforehand. This problem is especially challenging for diffuse objects: it is…
We have developed a universal approach to compute accurately the brightness of eclipsing binary systems during the transit of a planet in front of the stellar disk. This approach is uniform for all values of the system parameters and…