A concept for parametric surface fitting which avoids the parametrization problem
Computer Aided Geometric Design
Gliding spline motions and applications
Computer Aided Geometric Design
Smooth constraints for spline variational modeling
Proceedings of the 2nd international conference on Computer graphics and interactive techniques in Australasia and South East Asia
Rational quadratic approximation to real algebraic curves
Computer Aided Geometric Design - Special issue: Geometric modeling and processing 2004
Fitting B-spline curves to point clouds by curvature-based squared distance minimization
ACM Transactions on Graphics (TOG)
Generating symbolic interpolants for scattered data with normal vectors
Journal of Computer Science and Technology
B-Spline curve smoothing under position constraints for line generalisation
GIS '06 Proceedings of the 14th annual ACM international symposium on Advances in geographic information systems
Optimal multi-degree reduction of Bézier curves with G2-continuity
Computer Aided Geometric Design
Evolution-based least-squares fitting using Pythagorean hodograph spline curves
Computer Aided Geometric Design
Moving parabolic approximation of point clouds
Computer-Aided Design
Dual evolution of planar parametric spline curves and T-spline level sets
Computer-Aided Design
B-spline surface fitting to random points with bounded boundary conditions
International Journal of Computer Applications in Technology
Cartographic generalisation of lines based on a B-spline snake model
International Journal of Geographical Information Science
Finding positively invariant sets of a class of nonlinear loops via curve fitting
Proceedings of the 2009 conference on Symbolic numeric computation
Rational quadratic approximation to real algebraic curves
Computer Aided Geometric Design
Weighted progressive iteration approximation and convergence analysis
Computer Aided Geometric Design
Fitting sharp features with loop subdivision surfaces
SGP '08 Proceedings of the Symposium on Geometry Processing
Sample-based polynomial approximation of rational Bézier curves
Journal of Computational and Applied Mathematics
A note of boundary geodesic problem on regular surfaces
ECC'11 Proceedings of the 5th European conference on European computing conference
The general orthogonal projection on a regular surface
ECC'11 Proceedings of the 5th European conference on European computing conference
Technical Section: An extended iterative format for the progressive-iteration approximation
Computers and Graphics
Information Sciences: an International Journal
Automatic reconstruction of B-spline surfaces with constrained boundaries
Computers and Industrial Engineering
Efficient parameterization of 3d point-sets using recursive dynamic base surfaces
PCI'05 Proceedings of the 10th Panhellenic conference on Advances in Informatics
Information Sciences: an International Journal
Least–squares approximation by pythagorean hodograph spline curves via an evolution process
GMP'06 Proceedings of the 4th international conference on Geometric Modeling and Processing
Surface creation on unstructured point sets using neural networks
Computer-Aided Design
Fast B-spline curve fitting by L-BFGS
Computer Aided Geometric Design
Certified approximation of parametric space curves with cubic B-spline curves
Computer Aided Geometric Design
Feature-aware partitions from the motorcycle graph
Computer-Aided Design
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An active contour model for parametric curve and surface approximation is presented. The active curve or surface adapts to the model shape to be approximated in an optimization algorithm. The quasi-Newton optimization procedure in each iteration step minimizes a quadratic function which is built up with help of local quadratic approximants of the squared distance function of the model shape and an internal energy which has a smoothing and regularization effect. The approach completely avoids the parametrization problem. We also show how to use a similar strategy for the solution of variational problems for curves on surfaces. Examples are the geodesic path connecting two points on a surface and interpolating or approximating spline curves on surfaces. Finally we indicate how the latter topic leads to the variational design of smooth motions which interpolate or approximate given positions.