Ray Tracing Spherical Harmonics Glyphs
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Date
2023
Journal Title
Journal ISSN
Volume Title
Publisher
The Eurographics Association
Abstract
Spherical harmonics glyphs are an established way to visualize high angular resolution diffusion imaging data. Starting from a unit sphere, each point on the surface is scaled according to the value of a linear combination of spherical harmonics basis functions. The resulting glyph visualizes an orientation distribution function. We present an efficient method to render these glyphs using ray tracing. Our method constructs a polynomial whose roots correspond to ray-glyph intersections. This polynomial has degree 2k+2 for spherical harmonics bands 0;2; : : : ; k. We then find all intersections in an efficient and numerically stable fashion through polynomial root finding. Our formulation also gives rise to a simple formula for normal vectors of the glyph. Additionally, we compute a nearly exact axis-aligned bounding box to make ray tracing of these glyphs even more efficient. Since our method finds all intersections for arbitrary rays, it lets us perform sophisticated shading and uncertainty visualization. Compared to prior work, it is faster, more flexible and more accurate.
Description
CCS Concepts: Computing methodologies -> Ray tracing; Human-centered computing -> Scientific visualization; Mathematics of computing -> Solvers
@inproceedings{10.2312:vmv.20231223,
booktitle = {Vision, Modeling, and Visualization},
editor = {Guthe, Michael and Grosch, Thorsten},
title = {{Ray Tracing Spherical Harmonics Glyphs}},
author = {Peters, Christoph and Patel, Tark and Usher, Will and Johnson, Chris R.},
year = {2023},
publisher = {The Eurographics Association},
ISBN = {978-3-03868-232-5},
DOI = {10.2312/vmv.20231223}
}