Ray tracing trimmed rational surface patches
SIGGRAPH '90 Proceedings of the 17th annual conference on Computer graphics and interactive 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
Computing the minimum distance between a point and a NURBS curve
Computer-Aided Design
Interactive Hausdorff distance computation for general polygonal models
ACM SIGGRAPH 2009 papers
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
Precise Hausdorff distance computation for planar freeform curves using biarcs and depth buffer
The Visual Computer: International Journal of Computer Graphics
Precise Hausdorff distance computation between polygonal meshes
Computer Aided Geometric Design
Spiral fat arcs - Bounding regions with cubic convergence
Graphical Models
Efficient offset trimming for planar rational curves using biarc trees
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 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. For monotone spiral planar curves with no inflection, we show that a few simple geometric tests are sufficient to guarantee the convergence of numerical methods to the closest point. In several experimental results, we demonstrate the effectiveness of the proposed approach.