Geometric modeling
Curve intersection using Be´zier clipping
Computer-Aided Design - Special Issue: Be´zier Techniques
A Method for Registration of 3-D Shapes
IEEE Transactions on Pattern Analysis and Machine Intelligence - Special issue on interpretation of 3-D scenes—part II
Numerical recipes in C (2nd ed.): the art of scientific computing
Numerical recipes in C (2nd ed.): the art of scientific computing
The NURBS book
Optimization: algorithms and consistent approximations
Optimization: algorithms and consistent approximations
An acceleration of Newton's method: Super-Halley method
Applied Mathematics and Computation
Geometric constraint solver using multivariate rational spline functions
Proceedings of the sixth ACM symposium on Solid modeling and applications
Shape Interrogation for Computer Aided Design and Manufacturing
Shape Interrogation for Computer Aided Design and Manufacturing
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
Improved Algebraic Algorithm on Point projection for Béziercurves
IMSCCS '07 Proceedings of the Second International Multi-Symposiums on Computer and Computational Sciences
Accelerating geometric queries using the GPU
2009 SIAM/ACM Joint Conference on Geometric and Physical Modeling
Computing the Hausdorff distance between two B-spline curves
Computer-Aided Design
Contour curve reconstruction from cloud data for rapid prototyping
Robotics and Computer-Integrated Manufacturing
A comparison of numerical iteration based algorithms in blank optimization
Finite Elements in Analysis and Design
Efficient point projection to freeform curves and surfaces
GMP'10 Proceedings of the 6th international conference on Advances in Geometric Modeling and Processing
Efficient point-projection to freeform curves and surfaces
Computer Aided Geometric Design
ScolioMedIS: Web-oriented information system for idiopathic scoliosis visualization and monitoring
Computer Methods and Programs in Biomedicine
Direct manipulation of free-form deformation using curve-pairs
Computer-Aided Design
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A new method is presented for computing the minimum distance between a point and a NURBS curve. It utilizes a circular clipping technique to eliminate the curve parts outside a circle with the test point as its center point. The radius of the elimination circle becomes smaller and smaller during the subdivision process. A simple condition for terminating the subdivision process is provided, which leads to very few subdivision steps in the new method. Examples are shown to illustrate the efficiency and robustness of the new method.