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Institute
Knot placement for curve approximation is a well known and yet open problem in geometric modeling. Selecting knot values that yield good approximations is a challenging task, based largely on heuristics and user experience. More advanced approaches range from parametric averaging to genetic algorithms.
In this paper, we propose to use Support Vector Machines (SVMs) to determine suitable knot vectors for B-spline curve approximation. The SVMs are trained to identify locations in a sequential point cloud where knot placement will improve the approximation error. After the training phase, the SVM can assign, to each point set location, a so-called score. This score is based on geometric and differential geometric features of points. It measures the quality of each location to be used as knots in the subsequent approximation. From these scores, the final knot vector can be constructed exploring the topography of the score-vector without the need for iteration or optimization in the approximation process. Knot vectors computed with our approach outperform state of the art methods and yield tighter approximations.
Deep 3D
(2017)
Vortrag
In the reverse engineering process one has to classify parts of point clouds with the correct type of geometric primitive. Features based on different geometric properties like point relations, normals, and curvature information can be used, to train classifiers like Support Vector Machines (SVM). These geometric features are estimated in the local neighborhood of a point of the point cloud. The multitude of different features makes an in-depth comparison necessary. In this work we evaluate 23 features for the classification of geometric primitives in point clouds. Their performance is evaluated on SVMs when used to classify geometric primitives in simulated and real laser scanned point clouds. We also introduce a normalization of point cloud density to improve classification generalization.
Creating cages that enclose a 3D-model of some sort is part of many preprocessing pipelines in computational geometry. Creating a cage of preferably lower resolution than the original model is of special interest when performing an operation on the original model might be to costly. The desired operation can be applied to the cage first and then transferred to the enclosed model. With this paper the authors present a short survey of recent and well known methods for cage computation.
The authors would like to give the reader an insight in common methods and their differences.