Computational geometry: curve and surface modeling
Computational geometry: curve and surface modeling
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
Data point selection for piecewise linear curve approximation
Computer Aided Geometric Design
A New Method of Interpolation and Smooth Curve Fitting Based on Local Procedures
Journal of the ACM (JACM)
Modern Differential Geometry of Curves and Surfaces with Mathematica
Modern Differential Geometry of Curves and Surfaces with Mathematica
Computational Geometry for Design and Manufacture
Computational Geometry for Design and Manufacture
Interactive Data Interpolation by Rational Bezier Curves
IEEE Computer Graphics and Applications
Curvature and torsion estimators based on parametric curve fitting
Computers and Graphics
Constructing 3D motions from curvature and torsion profiles
Computer-Aided Design
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Given a string of discrete planar points, the estimation of principal curvature vectors using circle fitting and Richardson's extrapolation principle has been considered by several authors. However, these methods can not be directly applied to end points, due to symmetry. This article extends these methods to cope with end points. The method is based on the construction of interpolating circles using the first (or last) four data points. Error analysis suggests that the accuracy of curvature estimation using circle fitting is determined by arc-lengths and derivatives of curvature with respect to arc-length. A comparison is made between the proposed four-point method and the well established threepoint method.