A Caltech Library Service

Guaranteed ray intersections with implicit surfaces

Kalra, Devendra and Barr, Alan H. (1989) Guaranteed ray intersections with implicit surfaces. ACM SIGGRAPH Computer Graphics, 23 (3). pp. 297-306. ISSN 0097-8930. doi:10.1145/74334.74364.

Full text is not posted in this repository. Consult Related URLs below.

Use this Persistent URL to link to this item:


In this paper, we present a robust and mathematically sound ray-intersection algorithm for implicit surfaces. The algorithm is guaranteed to numerically find the nearest intersection of the surface with a ray, and is guaranteed not to miss fine features of the surface. It does not require fine tuning or human choice of interactive parameters. Instead, it requires two upper bounds: "L" that limits the net rate of change of the implicit surface function f(x,y,z) and "G" that limits the rate of change of the gradient. We refer to an implicit surface with these rate limits as an "LG-implicit surface."Existing schemes to intersect a ray with an implicit surface have typically been guaranteed to work only for a limited set of implicit functions, such as quadric surfaces or polynomials, or else have been ad-hoc and have not been guaranteed to work. Our technique significantly extends the ability to intersect rays with implicit surfaces in a guaranteed fashion.

Item Type:Article
Related URLs:
URLURL TypeDescription
Additional Information:© 1989 ACM. We would like to thank Steve Gabriel for his helpful comments and also to Harold Zatz. Thanks also are due to our sponsors for this work, Apple Computer, AT&T, Hewlett Packard, IBM, and the National Science Foundation.
Funding AgencyGrant Number
Subject Keywords:Implicit Surfaces, Ray Tracing, Rendering, Sampling, Subdivision, Lipschitz Constant
Issue or Number:3
Classification Code:1.3.3 (Picture/Image Generation) - display algorirthms; 1.3.5 (Computational Geometry and Object Modeling) - Curve, surface, solid and object represen- tations, Geometric algorithms, languages and systems; 1.3.7 (Three- Dimensio
Record Number:CaltechAUTHORS:20161110-132143128
Persistent URL:
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:71915
Deposited On:10 Nov 2016 22:44
Last Modified:11 Nov 2021 04:53

Repository Staff Only: item control page