Surface algorithms using bounds on derivatives
Computer Aided Geometric Design
Approximate conversion of spline curves
Computer Aided Geometric Design - Special issue: Topics in CAGD
Knot removal for parametric B-spline curves and surfaces
Computer Aided Geometric Design
Approximate conversion of rational splines
Computer Aided Geometric Design
Computational geometry: curve and surface modeling
Computational geometry: curve and surface modeling
The NURBS book
Knot removal for B-spline curves
Computer Aided Geometric Design
Curve fitting with Be´zier cubics
Graphical Models and Image Processing
Shape preserving least-squares approximation by polynomial parametric spline curves
Computer Aided Geometric Design
Numerical parameterization of curves and surfaces
Computer Aided Geometric Design
Rasterizing Algebraic Curves and Surfaces
IEEE Computer Graphics and Applications
An error-bounded approximate method for representing planar curves in B-splines
Computer Aided Geometric Design
Target curvature driven fairing algorithm for planar cubic B-spline curves
Computer Aided Geometric Design
Normal based subdivision scheme for curve design
Computer Aided Geometric Design
B-spline curve fitting based on adaptive curve refinement using dominant points
Computer-Aided Design
Adaptive knot placement in B-spline curve approximation
Computer-Aided Design
An improved parameterization method for B-spline curve and surface interpolation
Computer-Aided Design
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In this paper we present a local fitting algorithm for converting smooth planar curves to B-splines. For a smooth planar curve a set of points together with their tangent vectors are first sampled from the curve such that the connected polygon approximates the curve with high accuracy and inflexions are detected by the sampled data efficiently. Then, a G^1 continuous Bezier spline curve is obtained by fitting the sampled data with shape preservation as well as within a prescribed accuracy. Finally, the Bezier spline is merged into a C^2 continuous B-spline curve by subdivision and control points adjustment. The merging is guaranteed to be within another error bound and with no more inflexions than the Bezier spline. In addition to shape preserving and error control, this conversion algorithm also benefits that the knots are selected automatically and adaptively according to local shape and error bound. A few experimental results are included to demonstrate the validity and efficiency of the algorithm.