Ray Tracing in Curved Spaces (original) (raw)

Visualization of Non-Euclidean Spaces using Ray Tracing

2019

This paper presents a system for immersive visualization of Non-Euclidean spaces using real-time ray tracing. It exploits the capabilities of the new generation of GPU's based on the NVIDIA's Turing architecture in order to develop new methods for intuitive exploration of landscapes featuring nontrivial geometry and topology in virtual reality.

GPU Ray Tracing in Non-Euclidean Spaces

Synthesis Lectures on Visual Computing, 2022

This series presents lectures on research and development in visual computing for an audience of professional developers, researchers, and advanced students. Topics of interest include computational photography, animation, visualization, special effects, game design, image techniques, computational geometry, modeling, rendering, and others of interest to the visual computing system developer or researcher.

Design and visualization of Riemannian metrics

ArXiv, 2020

Local and global illumination were recently defined in Riemannian manifolds to visualize classical Non-Euclidean spaces. This work focuses on Riemannian metric construction in mathbbR3\mathbb{R}^3mathbbR3 to explore special effects like warping, mirages, and deformations. We investigate the possibility of using graphs of functions and diffeomorphism to produce such effects. For these, their Riemannian metrics and geodesics derivations are provided, and ways of accumulating such metrics. We visualize, in "real-time", the resulting Riemannian manifolds using a ray tracing implemented on top of Nvidia RTX GPUs.

On ray tracing parametric surfaces

ACM Siggraph Computer Graphics, 1985

A new method for ray tracing parametric surfaces is presented. The new algorithm solves the ray surface intersection directly using multivariate Newton iteration. This provides enough generality to render surfaces which could not be ray traced using existing methods. To overcome the problem of finding a starting point for the Newton algorithm, techniques from Interval Analysis are employed. The results are presented in terms of solving a general nonlinear system of equations f(x) = 0, and thus can be extended to a large class of problems which arise in computer graphics.

Ray-VR: Ray Tracing Virtual Reality in Falcor

ArXiv, 2020

NVidia RTX platform has been changing and extending the possibilities for real time Computer Graphics applications. It is the first time in history that retail graphics cards have full hardware support for ray tracing primitives. It still a long way to fully understand and optimize its use and this task itself is a fertile field for scientific progression. However, another path is to explore the platform as an expansion of paradigms for other problems. For example, the integration of real time Ray Tracing and Virtual Reality can result in interesting applications for visualization of Non-Euclidean Geometry and 3D Manifolds. In this paper we present Ray-VR, a novel algorithm for real time stereo ray tracing, constructed on top of Falcor, NVidia's scientific prototyping framework.

Special Relativistic Visualization by Local Ray Tracing

IEEE Transactions on Visualization and Computer Graphics, 2010

Special relativistic visualization offers the possibility of experiencing the optical effects of traveling near the speed of light, including apparent geometric distortions as well as Doppler and searchlight effects. Early high-quality computer graphics images of relativistic scenes were created using offline, computationally expensive CPU-side 4D ray tracing. Alternate approaches such as image-based rendering and polygon-distortion methods are able to achieve interactivity, but exhibit inferior visual quality due to sampling artifacts. In this paper, we introduce a hybrid rendering technique based on polygon distortion and local ray tracing that facilitates interactive high-quality visualization of multiple objects moving at relativistic speeds in arbitrary directions. The method starts by calculating tight image-space footprints for the apparent triangles of the 3D scene objects. The final image is generated using a single image-space ray tracing step incorporating Doppler and searchlight effects. Our implementation uses GPU shader programming and hardware texture filtering to achieve high rendering speed.

Global ray-bundle tracing with hardware acceleration

… , Austria, June 29-July 1, 1998, 1998

The paper presents a single-pass, view-dependent method to solve the general rendering equation, using a combined finite element and random walk approach. Applying finite element techniques, the surfaces are decomposed into planar patches on which the radiance is assumed to be combined from finite number of unknown directional radiance functions by predefined positional basis functions. The directional radiance functions are then computed by random walk or by stochastic iteration using bundles of parallel rays. To compute the radiance transfer in a single direction, several global visibility methods are considered, including the global versions of the painter's, z-buffer, Weiler-Atherton's and planar graph based algorithms. The method requires no preprocessing except for handling point lightsources, for which a first-shot technique is proposed. The proposed method is particularly efficient for scenes including not very specular materials illuminated by large area lightsources or sky-light. In order to increase the speed for difficult lighting situations, walks can be selected according to their importance. The importance can be explored adaptively by the Metropolis and VEGAS sampling techniques.

Adaptive Ray-Tracing on Spatial Patches

2000

Spatial patch is a new kind of rendering primitive that allows convenient and compact representation of surfaces for real-life 3D objects. In [1] and [2], several algorithms for z-buffer visualization of spatial patches are presented. However, zbuffering approach cannot provide photo-realistic quality of rendering. On the contrary, such quality can be obtained by means of ray tracing -a well-known method of realistic image synthesis. Being quite distinct from most of traditional ray tracing primitives, spatial patches possess different challenging features, which can be efficiently exploited by the modification of this technique. In order to exploit them, we propose to find parameters of ray -surface intersection approximately, where precision of operation is naturally defined by a size of a pixel. In case of spatial patches, such an assumption gives significant speed-up and possibility of rendering with optimal level of details. In this paper, an efficient algorithm for ray-patch and ray-patched scene intersections calculation is presented. The paper starts with a method of representing spatial patches as hierarchies of bounding boxes. Employing existing techniques, these hierarchies can be linked into a single one that represents the whole scene. Then, the calculation of ray-tree approximate intersection is discussed. Experimental results, proving ray-tracing suitability of spatial patches, are presented as well.

Global ray-bundle tracing with infinite number of rays

Computers & Graphics, 1999

The paper presents a combined nite element and quasi-random walk method to solve the general rendering equation. Applying nite element techniques, the surfaces are decomposed into planar patches that are assumed to have position independent, but not direction independent (that is non-di use) radiance. The direction dependent radiance function is then computed by quasi-random walk. Since quasi-Monte Carlo quadrature is applied here to an integrand of nite variation, this method can take advantage of the superior convergence of quasi-Monte Carlo integration.