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Published July 2000 | Published
Journal Article Open

Perturbation methods for interactive specular reflections


We describe an approach for interactively approximating specular reflections in arbitrary curved surfaces. The technique is applicable to any smooth implicitly defined reflecting surface that is equipped with a ray intersection procedure; it is also extremely efficient as it employs local perturbations to interpolate point samples analytically. After ray tracing a sparse set of reflection paths with respect to a given vantage point and static reflecting surfaces, the algorithm rapidly approximates reflections of arbitrary points in 3-space by expressing them as perturbations of nearby points with known reflections. The reflection of each new point is approximated to second-order accuracy by applying a closed-form perturbation formula to one or more nearby reflection paths. This formula is derived from the Taylor expansion of a reflection path and is based on first and second-order path derivatives. After preprocessing, the approach is fast enough to compute reflections of tessellated diffuse objects in arbitrary curved surfaces at interactive rates using standard graphics hardware. The resulting images are nearly indistinguishable from ray traced images that take several orders of magnitude longer to generate.

Additional Information

© 2000 IEEE. The authors wish to thank Anil Hirani and Al Barr for many valuable discussions, Don Mitchell and Pat Hanrahan for their patience in answering our questions, and Mark Meyer for helpful comments. This work was supported in part by the NSF Science and Technology Center for Computer Graphics and Scientific Visualization, the Army Research Office Young Investigator Program (DAAH04-96-100077), and the Alfred P. Sloan Foundation.

Attached Files

Published - Perturbation_20Methods_20for_20Interactive_20Specular_20Reflections_20TVCG-2000.pdf



Additional details

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October 25, 2023