Adaptive Representation of Large 3D Point Clouds for Shape Optimization

A numerical procedure for adaptive parameterization of changing 3D objects for knowledge representation, analysis and optimization is developed. The object is not a full CAD model since it involves many shape parameters and excessive details. Instead, optical 3D scanning of the actual object is used (stereo-photogrammetry, triangulation) which leads to the big-data territory with point clouds of size \(10^8\) and beyond. The total number of inherent surface parameters corresponds to the dimensionality of the shape optimization space. Parameterization must be highly compact and efficient while capable of representing sufficiently generic 3D shapes. The procedure must handle dynamically changing shapes in optimization quasi-time iterations. It must be flexible and autonomously adaptable as edges and peaks may disappear and new ones may arise. Adaptive re-allocation of the control points is based on feature recognition procedures (edges, peaks) operating on eigenvalue ratios and slope/ curvature estimators. The procedure involves identification of areas with significant change in geometry and formation of partitions.

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