Single-set and class-of-sets semantics for geometric models

Qi, Jianchang; Shapiro, Vadim; Stewart, Neil F.

doi:10.1016/j.cad.2006.06.006

Cited by 3 publications

(2 citation statements)

References 23 publications

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“…Now the winding number can be computed more precisely, but this precision should not be trusted if P is within (or close to) the bounding rectangle of one of the added segments. For more on these issues, see [9].…”

Section: Two Dimensionsmentioning

confidence: 98%

“…It should be noted that Poincaré found a more efficient way to compute the winding number of a point with respect to a polygon that does not involve computing any of the angles between segments; see [9] for details. However, it is not clear how to make his two-dimensional algorithm work in three dimensions, so I will not take advantage of it here.…”

Section: Two Dimensionsmentioning

confidence: 99%

See 1 more Smart Citation

A New Approach to Point Membership Classification in B-rep Solids

Klein

2009

Mathematics of Surfaces XIII

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Abstract.A fundamental problem in computational geometry is determining whether a point is inside a B-rep solid. Methods currently used for such point classification are unreliable or inefficient or both. A new approach is illustrated by showing how a simple method for loops of planar curves represented by B-splines can be extended from two dimensions to three. The plan in two dimensions is to construct a polygon so that the point will be inside the loop if and only if it is inside the polygon. Once such a polygon is found, it is easy to compute its winding number with respect to the point. In three dimensions, an analogous (although more complicated) method is robust and efficient.

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Section: Two Dimensionsmentioning

confidence: 98%

Section: Two Dimensionsmentioning

confidence: 99%