Journal Article10.1016/0097-8493(91)90002-Y
Interval methods in computer graphics
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TL;DR: Interval methods provide a degree of robustness to the algorithms which is difficult to achieve when point sampling alone is used to detect the contours and surfaces.
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About: This article is published in Computers & Graphics. The article was published on 01 Jan 1991. The article focuses on the topics: Computer graphics & Rendering (computer graphics).
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Citations
Self-validated numerical methods and applications
De Figueiredo
- 01 Jan 1997
TL;DR: This monograph gives an overview of the eld of self-validated numerics|computation models in which approximate results are automatically provided with guaranteed error bounds, and focuses on two such models: interval arithmetic and aane arithmetic.
399
Interval analysis for computer graphics
John Snyder
- 01 Jul 1992
TL;DR: This paper discusses how interval analysis can be used to solve a wide variety of problems in computer graphics, including ray tracing, interference detection, polygonal decomposition of parametric surfaces, and CSG on solids bounded byParametric surfaces.
Guaranteeing the topology of an implicit surface polygonization for interactive modeling
Barton T. Stander,John Hart +1 more
- 03 Aug 1997
TL;DR: The impact of this work is a topologically-guaranteed polygonization technique, and the ability to directly and accurately manipulate polygonized implicit surfaces in real time.
Robustness and precision issues in geometric computation
Stefan Schirra
- 01 Jan 1998
TL;DR: A survey on techniques that have been proposed and successfully used to attack robustness and precision problems in the implementation of geometric algorithms.
Robust adaptive polygonal approximation of implicit curves
TL;DR: An algorithm for computing a robust adaptive polygonal approximation of an implicit curve in the plane that is adapted to the geometry of the curve by combining interval arithmetic and automatic differentiation is presented.
41
References
Polygonization of implicit surfaces
TL;DR: A numerical technique that approximates an implicit surface with a polygonal representation, so that the roots to the function need not be solved each time the surface is rendered.
567
Global optimization using interval analysis -- the multi-dimensional case
TL;DR: In this paper, interval analysis is used to compute the global minimum of a function of n variables over ann-dimensional parallelopiped with sides parallel to the coordinate axes, providing infallible bounds on both the globally minimum value of the function and the point(s) at which the minimum occurs.
Interval Methods for Processing Geometric Objects
Sudhir P. Mudur,P. A. Koparkar +1 more
TL;DR: In this approach, the parametric form is applied without the usual computational nightmare, relying on subdivision algorithms.
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