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.

Point-Based Rendering of Non-Manifold Surfaces

Computer Graphics Forum, 2008

We present a point based rendering technique that uses iterated function systems to render parametric and implicit surfaces with singularities and non manifold features, to the pixel precision of the image. Its advantage over existing point based techniques is the simplicity of its implementation, an advantage it also enjoys over polygonisaton, scan line and ray tracing techniques. It only requires evaluations of the surface functions and gradients to render shaded images. It can render arbitrary parametric surfaces, but for arbitrary implicit surfaces, its current form is very slow. It can efficiently render implicit surfaces where one variable can be expressed in terms of the other two, effectively reducing them to one or more parametric surfaces. The technique also allows for hidden surface elimination using a z-buffer and shadow casting using a shadow buffer.

Sphere tracing: A geometric method for the antialiased ray tracing of implicit surfaces

Sphere tracing is a new technique for rendering implicit surfaces that uses geometric distance. Sphere tracing marches along the ray toward its first intersection in steps guaranteed not to penetrate the implicit surface. It is particularly adept at rendering pathological surfaces. Creased and rough implicit surfaces are defined by functions with discontinuous or undefined derivatives. Sphere tracing requires only a bound on the magnitude of the derivative, robustly avoiding problems where the derivative jumps or vanishes. It is an efficient direct visualization system for the design and investigation of new implicit models. Sphere tracing efficiently approximates cone tracing, supporting symbolicprefiltered antialiasing. Signed distance functions for a variety of primitives and operations are derived.

Ray Tracing

Field Guide to Astronomical Instrumentation

We describe a methodology for implementing a ray tracer which provides both a convenient testbed for developing new algorithms and a way to exploit the growing number of acceleration techniques. These bene ts are a natural consequence of a collection of data abstractions called the ray tracing kernel. By de ning an object in a broad sense, the kernel allows a single abstraction to encapsulate a wide spectrum of concepts including geometric primitives, acceleration techniques, CSG operators, and object transformations. Through hierarchical nesting of instances of these objects we are able to construct and eciently render complex environments.

Dynamic ray tracing on Lagrangian manifolds

Geophysical Journal International, 1984

We show that Maslov's extension of the WKBJ method allows an extension of the dynamic ray tracing to wavefields involving caustics of arbitrary form. If the receiver lies off the caustics, then the synthetic seismogram can be obtained by integrating the DRT system along a single I-ay joining the receiver to the source which may touch caustics. If the rcceiveilies in the vicinity of a caustic then DRT has to be carried out along a bunch of rays covering a neighbourhood of the receiver. Our approach encompasses pre-stressed and/or anisotropic media. Initial boundary conditions for a point source embedded in an anisotropic elastic medium are also presented.