Igor Pehnec

Computational procedure for optimum shape design based on chained Bezier surfaces parameterization

Optimum design introduces strong emphasis on compact geometry parameterization in order to reduce the dimensionality of the search space and consequently optimization run-time. This paper develops a decision support system for optimum shape which integrates geometric knowledge acquisition using 3D scanning and evolutionary shape re-engineering by applying genetic-algorithm based optimum search within a distributed computing workflow. A shape knowledge representation and compaction method is developed by creating 2D and 3D parameterizations based on adaptive chaining of piecewise Bezier curves and surfaces. Low-degree patches are used with adaptive subdivision of the target domain, thereby preserving locality. C^1 inter-segment continuity is accomplished by generating additional control points without increasing the number of design variables. The control points positions are redistributed and compressed towards the sharp edges contained in the data-set for better representation of areas with sharp change in slopes and curvatures. The optimal decomposition of the points cloud or target surface into patches is based on the requested modeling accuracy, which works as lossy geometric data-set compression. The proposed method has advantages in non-recursive evaluation, possibility of chaining patches of different degrees, options of prescribing fixed values at selected intermediate points while maintaining C^1 continuity, and uncoupled processing of individual patches. The developed procedure executes external application nodes using mutual communication via native data files and data mining. This adaptive interdisciplinary workflow integrates different algorithms and programs (3D shape acquisition, representation of geometry with data-set compaction using parametric surfaces, geometric modeling, distributed evolutionary optimization) such that optimized shape solutions are synthesized. 2D and 3D test cases encompassing holes and sharp edges are provided to prove the capacity and respective performance of the developed parameterizations, and the resulting optimized shapes for different load cases demonstrate the functionality of the overall distributed workflow.

Reverse Shape Synthesis of the Hydropump Volute Using Stereo-Photogrammetry, Parameterization, and Geometric Modeling

An automatic procedure for reverse 3D shape synthesis is proposed. Shape acquisition of an existing object involving stereo-photogrammetry, triangulation, and 3D reconstruction is applied to obtain the point clouds. Subsequent parameterization of the acquired geometry using mathematical surfaces yields a compact set of parameters as shape variables to be used in diagnostics. The developed procedure and several specific computational geometry operators are applied with a hydro-pump casing whose complex shape is processed and related to the volute design and flow theory.