Constrained B-spline curve and surface fitting
Computer-Aided Design
Geometric Hermite interpolation with Tschirnhausen cubics
Journal of Computational and Applied Mathematics
Global reparametrization for curve approximation
Computer Aided Geometric Design
Fast computation of generalized Voronoi diagrams using graphics hardware
Proceedings of the 26th annual conference on Computer graphics and interactive techniques
Construction and shape analysis of PH Hermite interpolants
Computer Aided Geometric Design
Hermite interpolation by pythagorean hodograph curves of degree seven
Mathematics of Computation
Approximation with Active B-Spline Curves and Surfaces
PG '02 Proceedings of the 10th Pacific Conference on Computer Graphics and Applications
A concept for parametric surface fitting which avoids the parametrization problem
Computer Aided Geometric Design
Fitting B-spline curves to point clouds by curvature-based squared distance minimization
ACM Transactions on Graphics (TOG)
Computing - Special issue on Geometric Modeling (Dagstuhl 2005)
Industrial geometry: recent advances and applications in CAD
Computer-Aided Design
Approximating curves and their offsets using biarcs and Pythagorean hodograph quintics
Computer-Aided Design
Circular spline fitting using an evolution process
Journal of Computational and Applied Mathematics
Distance regression by Gauss–Newton-type methods and iteratively re-weighted least-squares
Computing - Geometric Modelling, Dagstuhl 2008
Cubic B-spline curve approximation by curve unclamping
Computer-Aided Design
Parallel manipulators and Borel-Bricard problem
Computer Aided Geometric Design
Low degree euclidean and minkowski pythagorean hodograph curves
MMCS'08 Proceedings of the 7th international conference on Mathematical Methods for Curves and Surfaces
Certified approximation of parametric space curves with cubic B-spline curves
Computer Aided Geometric Design
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The problem of approximating a given set of data points by splines composed of Pythagorean hodograph (PH) curves is addressed. We discuss this problem in a framework that is not only restricted to PH spline curves, but can be applied to more general representations of shapes. In order to solve the highly non-linear curve fitting problem, we formulate an evolution process within the family of PH spline curves. This process generates a family of curves which depends on a time-like variable t. The best approximant is shown to be a stationary point of this evolution process, which is described by a differential equation. Solving it numerically by Euler's method is shown to be related to Gauss-Newton iterations. Different ways of constructing suitable initial positions for the evolution are suggested.