Intrinsic parametrization for approximation
Computer Aided Geometric Design
Fast construction of accurate quaternion splines
Proceedings of the 24th annual conference on Computer graphics and interactive techniques
Interpolating nets of curves by smooth subdivision surfaces
Proceedings of the 26th annual conference on Computer graphics and interactive techniques
A concept for parametric surface fitting which avoids the parametrization problem
Computer Aided Geometric Design
An improved Hoschek intrinsic parametrization
Computer Aided Geometric Design
Fitting B-spline curves to point clouds by curvature-based squared distance minimization
ACM Transactions on Graphics (TOG)
Interpolation by geometric algorithm
Computer-Aided Design
Curve interpolation with directional constraints for engineering design
Engineering with Computers
Point-tangent/point-normal B-spline curve interpolation by geometric algorithms
Computer-Aided Design
The convergence of the geometric interpolation algorithm
Computer-Aided Design
Progressive interpolation using loop subdivision surfaces
GMP'08 Proceedings of the 5th international conference on Advances in geometric modeling and processing
Curve interpolation based on the canonical arc length parametrization
Computer-Aided Design
Optimization of parameters for curve interpolation by cubic splines
Journal of Computational and Applied Mathematics
Convergence of Geometric Interpolation Using Uniform B-splines
CADGRAPHICS '11 Proceedings of the 2011 12th International Conference on Computer-Aided Design and Computer Graphics
Technical note: Progressive iteration approximation and the geometric algorithm
Computer-Aided Design
Efficient energies and algorithms for parametric snakes
IEEE Transactions on Image Processing
Editorial: Foreword to the special section on computer graphics in China
Computers and Graphics
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In this paper, we propose a sufficient condition for the convergence of a geometric algorithm for interpolating a given polygon using non-uniform cubic B-splines. Geometric interpolation uses the given polygon as the initial shape of the control polygon of the B-spline and reduces the approximate error by iteratively updating the control points with the deviations from the corresponding interpolated vertices to their nearest footpoints on the current B-spline curve. The convergence condition is derived by employing a spectral radius estimation technique. The primary goal is to find for each control point a parametric interval within which the nearest footpoint should be confined such that the spectral radius of the error iteration matrix is smaller than 1. A convergent condition for the geometric interpolation of uniform B-splines can be derived as a special case of the new scheme.