Guaranteed ray intersections with implicit surfaces
SIGGRAPH '89 Proceedings of the 16th annual conference on Computer graphics and interactive techniques
Robust ray intersection with interval arithmetic
Proceedings on Graphics interface '90
Fundamentals of Computer Graphics
Fundamentals of Computer Graphics
Interval Methods for Ray Casting Implicit Surfaces with Affine Arithmetic
SIBGRAPI '99 Proceedings of the XII Brazilian Symposium on Computer Graphics and Image Processing
Beam tracing polygonal objects
SIGGRAPH '84 Proceedings of the 11th annual conference on Computer graphics and interactive techniques
Geometric computations with interval and new robust methods: applications in computer graphics, GIS and computational geometry
Guaranteed Adaptive Antialiasing Using Interval Arithmetic
ICCS '07 Proceedings of the 7th international conference on Computational Science, Part II
Efficient ray tracing using interval analysis
PPAM'07 Proceedings of the 7th international conference on Parallel processing and applied mathematics
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This paper presents a fast and reliable method to trim non-solution regions in an interval ray tracing process. The “trimming algorithm” uses interval analysis to perform rejection tests in a set of pixels simultaneously, instead of individual pixels at each time. With this approach, the presented algorithm runs faster than the traditional interval ray tracing algorithm. Also, an interval algorithm to remove aliasing in the rendering of implicit surfaces is introduced. This algorithm obtains better visualizations than the traditional point sampling. This algorithm can render thin features that would be impossible to obtain with point sampling algorithms.