Point inversion and projection for NURBS curve and surface: control polygon approach

Authors:
Ying Liang Ma;W. T. Hewitt
Affiliations:
Manchester Visualization Centre, University of Manchester, M13 9PL, UK;Manchester Visualization Centre, University of Manchester, M13 9PL, UK
Venue:
Computer Aided Geometric Design
Year:
2003

Citing 4
Cited 23

Geometric modeling

Geometric modeling
Making the Oslo algorithm more efficient

SIAM Journal on Numerical Analysis
The NURBS book

The NURBS book
On NURBS: a Survey

IEEE Computer Graphics and Applications

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
A counterexample on point inversion and projection for NURBS curve

Computer Aided Geometric Design
Computing the minimum distance between a point and a NURBS curve

Computer-Aided Design
Computing the minimum distance between a point and a clamped B-spline surface

Graphical Models
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
Automatic least-squares projection of points onto point clouds with applications in reverse engineering

Computer-Aided Design
Some applications of scalar and vector fields to geometric processing of surfaces

Computers and Graphics
Virtual fixture based haptic rendering of handwriting

VECIMS'09 Proceedings of the 2009 IEEE international conference on Virtual Environments, Human-Computer Interfaces and Measurement Systems
Computing the Hausdorff distance between two B-spline curves

Computer-Aided Design
Algorithm for orthogonal projection of parametric curves onto B-spline surfaces

Computer-Aided 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
Computing the Hausdorff distance between NURBS surfaces using numerical iteration on the GPU

Graphical Models
An adaptive process planning approach of rapid prototyping and manufacturing

Robotics and Computer-Integrated Manufacturing
Iterative, simulation-based shape modification by free-form deformation of the NC programs

Advances in Engineering Software
Direct manipulation of free-form deformation using curve-pairs

Computer-Aided Design
A hybrid and adaptive tool-path generation approach of rapid prototyping and manufacturing for biomedical models

Computers in Industry
A geometric strategy for computing intersections of two spatial parametric curves

The Visual Computer: International Journal of Computer Graphics
Special Section on CAD/Graphics 2013: Projecting points onto planar parametric curves by local biarc approximation

Computers and Graphics

Quantified Score

Hi-index	0.00

Visualization

Abstract

This paper presents an accurate and efficient method to solve both point projection and point inversion for NURBS curves and surfaces. We first subdivide the NURBS curve or surface into a set of Bézier subcurves or patches. Based on the relationship between the test point and the control polygon of Bézier curve or the control point net of the Bézier patch, we extract candidate Bézier subcurves or Bézier patches and then find the approximate candidate points. Finally, by comparing the distances between the test point and candidate points, we are able to find the closest point. We improve its accuracy by using the Newton-Raphson method.