z Abstract Computer Graphics, 26,2, July 1992 Interval Analysis For Computer Graphics John M. Snyder CaliforniaInstituteof Technology Pasadena, CA 91125 and rendering implicit surfaces [SUFF90], and for ray tracing implicit sur- This paper discusses how interval analysis can be used to solve a wide variety of problems in computer graphics. These problcrna include ray tracing, interference detection, polygonal decomposition of parametric surfaces, and CSO on solids kmnderf by parametric surfaw?s. Ordy two basic afgorhfuna MErequired SOLVE,which computes solutions to a system of constraints, which computes the global minimum of a function, subject and MINIMIZE, faces [MITC90]. Several researchers have also used Lipaehitz bounds, a S*SI CMeof M interval method, in their algorithrrtx to approximate fWSntetric surfaces [VONH87], to compute collisions between time-dependent parametric surfaces [VONH89,VONH90], and to ray trace implicit surfaces [KALR89]. This paper extenda the work of these researchers by showing how a generat set of problems in computer graphics can be solved using only two algorithms that employ interval analysis: constraint solution (SOLVE) and constrained rrdrsirtdzation (MINIMIZE). Many of the ideas presented here are krrowed from recent work in the area of interval amatysis ([IUTS88, ALEF83]), but are new to computer graphics. flrese ideaa inchr& the
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Interval analysis for computer graphics
Snyder, John M.
Follow ACM SIGGRAPH Computer Graphics
, Volume 26 (2)
Association for Computing Machinery – Jul 1, 1992
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