Reduced-Order Shape Optimization Using Offset Surfaces

摘要

Given the 2-manifold surface of a 3d object, we propose a novelrnmethod for the computation of an offset surface with varying thicknessrnsuch that the solid volume between the surface and its offsetrnsatisfies a set of prescribed constraints and at the same time minimizesrna given objective functional. Since the constraints as wellrnas the objective functional can easily be adjusted to specific applicationrnrequirements, our method provides a flexible and powerfulrntool for shape optimization. We use manifold harmonics to deriverna reduced-order formulation of the optimization problem, whichrnguarantees a smooth offset surface and speeds up the computationrnindependently from the input mesh resolution without affecting thernquality of the result. The constrained optimization problem canrnbe solved in a numerically robust manner with commodity solvers.rnFurthermore, the method allows simultaneously optimizing an innerrnand an outer offset in order to increase the degrees of freedom.rnWe demonstrate our method in a number of examples where werncontrol the physical mass properties of rigid objects for the purposernof 3d printing.