Ray tracing trimmed rational surface patches
SIGGRAPH '90 Proceedings of the 17th annual conference on Computer graphics and interactive techniques
Curve intersection using Be´zier clipping
Computer-Aided Design - Special Issue: Be´zier Techniques
Geometric constraint solver using multivariate rational spline functions
Proceedings of the sixth ACM symposium on Solid modeling and applications
Efficient Collision Detection Using Bounding Volume Hierarchies of k-DOPs
IEEE Transactions on Visualization and Computer Graphics
Point inversion and projection for NURBS curve and surface: control polygon approach
Computer Aided Geometric Design
Minimum distance queries for haptic rendering
Minimum distance queries for haptic rendering
Numerical Recipes 3rd Edition: The Art of Scientific Computing
Numerical Recipes 3rd Edition: The Art of Scientific Computing
Computing the minimum distance between a point and a NURBS curve
Computer-Aided Design
Computing the minimum distance between two Bézier curves
Journal of Computational and Applied Mathematics
A torus patch approximation approach for point projection on surfaces
Computer Aided Geometric Design
A second order algorithm for orthogonal projection onto curves and surfaces
Computer Aided Geometric Design
Improved algorithms for the projection of points on NURBS curves and surfaces
Computer Aided Geometric Design
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We present an efficient algorithm for projecting a given point to its closest point on a family of freeform C1-continuous curves and surfaces. The algorithm is based on an efficient culling technique that eliminates redundant curves and surfaces which obviously contain no projection from the given point. Based on this scheme, we can reduce the whole computation to considerably smaller subproblems, which are then solved using a numerical method. In several experimental results, we demonstrate the effectiveness of the proposed approach.