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Theory and Application of Specular Path Perturbation

Chen, Min and Arvo, James (2000) Theory and Application of Specular Path Perturbation. ACM Transactions on Graphics (TOG), 19 (4). pp. 246-278. ISSN 0730-0301. https://resolver.caltech.edu/CaltechAUTHORS:20160822-152504191

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Abstract

In this paper we apply perturbation methods to the problem of computing specular reflections in curved surfaces. The key idea is to generate families of closely related optical paths by expanding a given path into a high-dimensional Taylor series. Our path perturbation method is based on closed-form expressions for linear and higher-order approximations of ray paths, which are derived using Fermat’s Variation Principle and the Implicit Function Theorem (IFT). The perturbation formula presented here holds for general multiple-bounce reflection paths and provides a mathematical foundation for exploiting path coherence in ray tracing acceleration techniques and incremental rendering. To illustrate its use, we describe an algorithm for fast approximation of specular reflections on curved surfaces; the resulting images are highly accurate and nearly indistinguishable from ray traced images.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1145/380666.380670DOIArticle
http://dl.acm.org/citation.cfm?doid=380666.380670PublisherArticle
Additional Information:© 2000 ACM. Received: June 1999; revised: November 2000; accepted: January 2001. This work was supported in part by the US National Science Foundation Career Award (CCR9876332), the Army Research Office Young Investigator Program (DAAH04-96-100077), and the Alfred P. Sloan Foundation.
Funders:
Funding AgencyGrant Number
NSFCCR-9876332
Army Research Office (ARO)DAAH04-96-100077
Alfred P. Sloan FoundationUNSPECIFIED
Subject Keywords:Algorithms, Performance, Implicit surfaces, optics, perturbation theory, specular reflection, Taylor series
Issue or Number:4
Classification Code:I.3.3 [Computer Graphics]: Picture/Image Generation— Display algorithms; I.3.6 [Computer Graphics]: Methodology and Techniques—Interaction techniques; I.3.7 [Computer Graphics]: Three-Dimensional Graphics and Realism—Raytracing; G.1.1 [Numerical Analysis]
Record Number:CaltechAUTHORS:20160822-152504191
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20160822-152504191
Official Citation:Min Chen and James Arvo. 2000. Theory and application of specular path perturbation. ACM Trans. Graph. 19, 4 (October 2000), 246-278. DOI=http://dx.doi.org/10.1145/380666.380670
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:69818
Collection:CaltechAUTHORS
Deposited By: Kristin Buxton
Deposited On:22 Aug 2016 22:40
Last Modified:03 Oct 2019 10:25

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