Geometric modeling
Optimization: algorithms and consistent approximations
Optimization: algorithms and consistent approximations
Point inversion and projection for NURBS curve and surface: control polygon approach
Computer Aided Geometric Design
A second order algorithm for orthogonal projection onto curves and surfaces
Computer Aided Geometric Design
Distance extrema for spline models using tangent cones
GI '05 Proceedings of Graphics Interface 2005
Improved algorithms for the projection of points on NURBS curves and surfaces
Computer Aided Geometric Design
A counterexample on point inversion and projection for NURBS curve
Computer Aided Geometric Design
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The computation of the minimum distance between a point and a surface is important for the applications such as CAD/CAM, NC verification, robotics and computer graphics. This paper presents a spherical clipping method to compute the minimum distance between a point and a clamped B-spline surface. The surface patches outside the clipping sphere which do not contain the nearest point are eliminated. Another exclusion criterion whether the nearest point is on the boundary curves of the surface is employed, which is proved to be superior to previous comparable criteria. Examples are also shown to illustrate efficiency and correctness of the new method.