We present a novel shape deformation method for its use in design optimization tasks. Our space deformation technique based on moving least squares approximation improves upon existing approaches in crucial aspects: It offers the same level of modeling flexibility as surface-based deformations, but it is independent of the underlying geometry representation and therefore highly robust against defects in the input data. It overcomes the scalability limitations of existing space deformation techniques based on globally supported triharmonic radial basis functions while providing the same high level of deformation quality. Finally, unlike existing space deformation approaches, our technique directly incorporates geometric constraints-such as preservation of critical feature lines, circular couplings, or planar construction parts-into the deformation, thereby fostering the exploration of more favorable and producible shape variations during the design optimization process.
Sieger, D., Menzel, S., & Botsch, M. (2014). Constrained space deformation for design optimization. In Procedia Engineering (Vol. 82, pp. 114–126). Elsevier Ltd. https://doi.org/10.1016/j.proeng.2014.10.377