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2002
IEEE

Approximation with Active B-Spline Curves and Surfaces

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Approximation with Active B-Spline Curves and Surfaces
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.
Helmut Pottmann, Stefan Leopoldseder, Michael Hofe
Added 15 Jul 2010
Updated 15 Jul 2010
Type Conference
Year 2002
Where PG
Authors Helmut Pottmann, Stefan Leopoldseder, Michael Hofer
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