Constrained deformation for evolutionary optimization

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This thesis investigates shape deformation techniques for their use in design optimization tasks. In the first part, we introduce state-of-the-art deformation methods and evaluate them in a set of representative benchmarks. Based on these benchmarking results, we derive essential criteria and features a deformation technique should satisfy in order to be successfully applicable within design optimization. In the second part, we concentrate on the application and improvement of deformation techniques based on radial basis functions. We present and evaluate a unified framework for surface and volume mesh deformation and investigate questions of performance and scalability. In the final third part, we concentrate on the integration of additional constraints into the deformation, thereby improving the overall effectiveness of the design optimization process and fostering the creation of more feasible and producible design variations. We present a novel shape deformation technique that effectively maintains different types of geometric constraints such as planarity, circularity, or characteristic feature lines during deformation. At the same time, our method provides a unique level of modeling flexibility, quality, robustness, and scalability. Finally, we integrate techniques for automatic constraint detection directly into our deformation framework, thereby making our method more easily applicable within complex design optimization scenarios.

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