ABSTRACT
We have developed an innovative ray-tracing algorithm to describe Relativistic Effects in SpaceTime (“REST”). Our algorithm, called REST-frame, models light rays that have assumed infinite speed in conventional ray-tracing to have a finite speed c in spacetime, and uses general Lorentz Transformation, which connects the spacetime description of a single event in two inertial coordinate systems (frames) that differ by a constant velocity, to perform the relativistic translation and aberration of light rays.
In this paper, we report the extension of our previous work for visualizing relativistic motion in spacetime to include relativistic Doppler color shift and the simulation of complex kinematic systems in which objects of different relativistic velocities coexist. Our simulations have produced non-intuitive images showing anisotropic deformation (warping) of space and intensity concentration/spreading of light sources in spacetime. Images of objects undergoing relativistic Doppler shift are also generated.
By applying state-of-the-art computation technology and simulation techniques to the earlier quests in Physics that were conducted mainly by thought experiment, we demonstrate, through our new revelations, that REST-frame offers a powerful experimentation tool to study and explore some of the most exciting aspects of the natural world; particularly, the rich physical properties associated with the finite speed of light.
- 1.R. Cook and K. Torrance. A reflectance model for cornputer graphics. ACM Trans. Graphics, 1(1):7-24, Jan 1982. Google ScholarDigital Library
- 2.Andrew Glassner. An Introduction to Ray-Tracing. Academic Press Limited, 1989. Google ScholarDigital Library
- 3.R. Goldstein and R. Nagel. 3-D visual simulation. Simulation, 25, 1971.Google ScholarCross Ref
- 4.Ping-Kang Hsiung. Data structures for ray-tracing. Thesis Proposal, Carnegie Mellon University, Feb. 1989.Google Scholar
- 5.Ping-Kang Hsiung and Robert H. P. Dunn. Visualizing relativistic effects in sp~etime. In Proceedings of the Supercomputing '89 Conference, Nov. 13-17, 1989. Google ScholarDigital Library
- 6.Ping-Kang Hsiung and Robert H. Thibadeau. Spacetime visualization of 3D relativistic motion. Unpublished documera, Oct., 1989.Google Scholar
- 7.Ping-Kang Hsiung, Robert H. Thibadeau, and Michael Wu. T-buffer: fast visualization of relativistic effects in spacetime. In 1990 Symposium on Interactive 3D Graphics (to appear), March 18-21, 1990. Google ScholarDigital Library
- 8.T.L. Kay and J.T. Kajiya. Ray tracing complex scenes. Computer Graphics (SIGGRAPH), 269-278, Aug. 1986. Google ScholarDigital Library
- 9.C. M~ller. The Theory of Relativity. Oxford University Press, 1960.Google Scholar
- 10.R. Penrose. The apparent shape of a relativistically moving sphere. Proceedings of the Cambridge Philosophical Society, 55:137-9, July 29 1958.Google ScholarCross Ref
- 11.Bui Phong. Illumination for computer generated pictures. CACM, 18(6):311, June 1975. Google ScholarDigital Library
- 12.Robert Resnick. Introduction to Special Relativity. Rensselaer Polytechnic Institute, 1968.Google Scholar
- 13.E. Taylor and J. Wheeler. Spacetime Physics. M.I.T. / Princeton, 1966.Google Scholar
- 14.J. Terrell. Invisibility of the Lorentz contraction. Physical Review, 116(4):1041, 1959.Google ScholarCross Ref
- 15.K. E. Torrance and E. M. Sparrow. Theory for offspecular reflection from rougheded surfaces. Journal of the Optical Society of America, 1105, 1967.Google ScholarCross Ref
- 16.V.F. Weisskopf. The visual appearance of rapidly moving bodies (section). Physics Today, 13(9):24, 1960.Google ScholarCross Ref
- 17.T. Whitted. An improved illumination model for shaded display. CACM, 343-349, June 1980. Google ScholarDigital Library
Index Terms
- Spacetime visualization of relativistic effects
Recommendations
Visualizing relativistic effects in spacetime
Supercomputing '89: Proceedings of the 1989 ACM/IEEE conference on SupercomputingWe have developed an innovative ray-tracing algorithm to describe Relativistic Effects in SpaceTime (“REST”). Our algorithm, called REST-frame, simulates a generalized world in Spacetime and gives the fine details implicit in the Special Theory of ...
Relativistic effects on information measures for hydrogen-like atoms
Position and momentum information measures are evaluated for the ground state of the relativistic hydrogen-like atoms. Consequences of the fact that the radial momentum operator is not self-adjoint are explicitly studied, exhibiting fundamental ...
Image shading taking into account relativistic effects
This article is concerned with creating more realistic images of 3D scenes which are moving relative to the viewer at such high speeds that the propagation delay of light signals and other relativistic effects can not be neglected. Creating images of 3D ...
Comments