1996
DOI: 10.1111/1467-8659.1540205
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Topologically exact evaluation of polyhedra defined in CSG with loose primitives

Abstract: Floating point round-off causes erroneous and inconsistent decisions in geometric modelling

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Cited by 27 publications
(19 citation statements)
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“…In a number of cases, such results are used only to establish topological relationships amongst primitives. This can be efficiently done by using sufficiently accurate (as opposed to exact) arithmetic [3,9,15]. Most of the research in graphics dealing with limiting the precision of vertex coordinates has focused on rounding-off the vertex coordinates (perhaps with attributes) independently of the topological structure defined by the vertices.…”
Section: Previous and Related Workmentioning
confidence: 99%
“…In a number of cases, such results are used only to establish topological relationships amongst primitives. This can be efficiently done by using sufficiently accurate (as opposed to exact) arithmetic [3,9,15]. Most of the research in graphics dealing with limiting the precision of vertex coordinates has focused on rounding-off the vertex coordinates (perhaps with attributes) independently of the topological structure defined by the vertices.…”
Section: Previous and Related Workmentioning
confidence: 99%
“…The developers of a modeling system must ensure that these round-off errors do not lead to logical errors, to software crashes, or to wrong design decisions [Hoffmann89]. Exact arithmetic packages do not suffer from round-off problems [Agrawal94], but are usually only effective for polyhedral geometries and significantly slower, unless used with quantized parameters [Banerjee96].…”
Section: Numeric Accuracymentioning
confidence: 99%
“…The most delicate computation in this process is the segmentation of the curve neighborhood, because it involves computing a circular order of surfaces around their common edge. The process may be numerically unreliable and mathematically challenging, if the surfaces are non-planar and are not simple quadrics, and especially when they have identical tangent planes and curvature measures at P. When all surfaces are planar and are represented by fixed-precision numbers, the neighborhood evaluation may be done exactly and efficiently [Banerjee96] using fixed-length arithmetic.…”
Section: Point Membership Classification For Csgmentioning
confidence: 99%
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“…For instance, boundaries of CSG models with polyhedra primitives may be pre-computed reliably [12], triangulated, and used for realtime rendering. However, such a boundary evaluation is too slow (even for polyhedral models) to be invoked at each frame during interactive editing or when the tessellations of the primitive boundaries must be refined through subdivision during camera motions.…”
Section: Introductionmentioning
confidence: 99%