Knot removal for parametric B-spline curves and surfaces
Computer Aided Geometric Design
Approximate conversion of rational splines
Computer Aided Geometric Design
Constrained B-spline curve and surface fitting
Computer-Aided Design
Deformable curve and surface finite-elements for free-form shape design
Proceedings of the 18th annual conference on Computer graphics and interactive techniques
Parameter optimization in approximating curves and surfaces to measurement data
Computer Aided Geometric Design
SIGGRAPH '92 Proceedings of the 19th annual conference on Computer graphics and interactive techniques
Detecting cusps and inflection points in curves
Computer Aided Geometric Design
Curves and surfaces for computer aided geometric design (3rd ed.): a practical guide
Curves and surfaces for computer aided geometric design (3rd ed.): a practical guide
Fundamentals of computer aided geometric design
Fundamentals of computer aided geometric design
The NURBS book
Knot removal for B-spline curves
Computer Aided Geometric Design
Computational Geometry for Design and Manufacture
Computational Geometry for Design and Manufacture
Comparing Images Using the Hausdorff Distance
IEEE Transactions on Pattern Analysis and Machine Intelligence
B-spline curve fitting based on adaptive curve refinement using dominant points
Computer-Aided Design
A local fitting algorithm for converting planar curves to B-splines
Computer Aided Geometric Design
Cubic B-spline curve approximation by curve unclamping
Computer-Aided Design
B-spline surface fitting based on adaptive knot placement using dominant columns
Computer-Aided Design
Efficient particle swarm optimization approach for data fitting with free knot B-splines
Computer-Aided Design
B-Spline curve fitting using dominant points
ICCS'06 Proceedings of the 6th international conference on Computational Science - Volume Part II
Geometric point interpolation method in R3 space with tangent directional constraint
Computer-Aided Design
A new iterative mutually coupled hybrid GA-PSO approach for curve fitting in manufacturing
Applied Soft Computing
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This paper addresses the problem of representing a given planar curve in B-splines, where the curve is not so restricted on its initial basis form that it does not have to be compatible with or derivable from B-splines. As B-spline curve approximation is inevitable in this representation process, major concerns are focused both on accuracy control and data reduction to pursue a B-spline curve with fewer control points while keeping the distance between the given curve and the B-spline curve smaller than a specified tolerance. The paper thus presents an error-bounded method for B-spline curve approximation to the given curve within the accuracy. The method adopts an approach of B-spline curve refitting accomplished via polygonal approximation of the given curve and B-spline curve fitting to the polygon. Hausdorff distance is used as a criterion for approximation quality. The offset envelope of a line segment plays an important role in controlling the Hausdorff distance between the line segment and its corresponding curve segment. The method is simple in concept, provides reasonable accuracy control, and realizes efficient data reduction. Some experimental results demonstrate its usefulness and quality.