Intrinsic parametrization for approximation
Computer Aided Geometric Design
Constrained B-spline curve and surface fitting
Computer-Aided Design
Curve and surface fitting with splines
Curve and surface fitting with splines
Minimization, constraints and composite Be´zier curves
Computer Aided Geometric Design
Grouping and parameterizing irregularly spaced points for curve fitting
ACM Transactions on Graphics (TOG)
Advanced surface fitting techniques
Computer Aided Geometric Design
Rapid and accurate computation of the distance function using grids
Journal of Computational Physics
Constrained fitting in reverse engineering
Computer Aided Geometric Design
Curve-fitting with piecewise parametric cubics
SIGGRAPH '83 Proceedings of the 10th annual conference on Computer graphics and interactive techniques
Interval B-Spline Curve Evaluation Bounding Point Cloud
PG '02 Proceedings of the 10th Pacific Conference on Computer Graphics and Applications
Constrained interpolation with rational cubics
Computer Aided Geometric Design
An improved Hoschek intrinsic parametrization
Computer Aided Geometric Design
A second order algorithm for orthogonal projection onto curves and surfaces
Computer Aided Geometric Design
A Bayesian method for probable surface reconstruction and decimation
ACM Transactions on Graphics (TOG)
Fitting B-spline curves to point clouds by curvature-based squared distance minimization
ACM Transactions on Graphics (TOG)
Reassembling fractured objects by geometric matching
ACM SIGGRAPH 2006 Papers
Newton-KKT interior-point methods for indefinite quadratic programming
Computational Optimization and Applications
Constrained curve fitting on manifolds
Computer-Aided Design
Computer Aided Geometric Design
Recovering geometric detail by octree normal maps
Transactions on Edutainment VII
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We consider the problem of fitting B-spline curves and surfaces to point clouds in the presence of obstacles constraining this approximation at the same time. Therefore, we describe the fitting problem as optimization problem and employ an iterative procedure to solve it-the presence of obstacles poses constraints on this minimization process. We examine two families of obstacles: first, the point cloud itself is interpreted as obstacle, e.g. to reconstruct any apparent boundaries of the data set. Second, we define arbitrary regions the fitting must not penetrate. We discuss several numerical aspects of this constrained optimization and present experimental results for B-spline curve and surface fittings in the presence of obstacles.