Computing zeroes of spline functions
Computer Aided Geometric Design
Ray tracing trimmed rational surface patches
SIGGRAPH '90 Proceedings of the 17th annual conference on Computer graphics and interactive techniques
A new approach to the surface intersection problem
Computer Aided Geometric Design
Representations for Rigid Solids: Theory, Methods, and Systems
ACM Computing Surveys (CSUR)
Set Membership Classification: A Unified Approach to Geometric Intersection Problems
IEEE Transactions on Computers
Classifying points for sweeping solids
Computer-Aided Design
Single-set and class-of-sets semantics for geometric models
Computer-Aided Design
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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.