Exchangeable Integral and Partitioned Parameterization in 3D Shape Modeling

Early-stage design and modeling of shape require sufficient generality and global and local shape control which the corresponding numerical tools, typically based on parametric surfaces, must offer. However, these requirements typically materialize into a large number of shape parameters. If numerical shape optimization is to be applied, this maps to excessively high-dimensional search spaces, sometimes prohibitively complex in terms of numerical effort. This paper presents an approach which involves reparameterization into a different set of shape variables based on partitioning of the overall geometry and applying simpler geometric primitives at partitions where it is adequate. Depending on the case, this may lead to short-cutting many iterations of evolutionary shape optimization involving also re-structuring of the genotypes. The transition from partitioned to integral representation is implemented by B-spline surface fitting and the inverse process from integral surfaces to partitioned models is based on feature detection, data-set decomposition and elementary surface fitting. Basic primitives are applied here with more complex ones to be demonstrated in future work.