Constructive heterogeneous object modeling using signed approximate real distance functions

We introduce a smooth approximation of the min / max operations, called SARDF (Signed Approximate Real Distance Function), for maintaining an approximate signed distance function in constructive shape modeling. We apply constructive distance-based shape modeling to design objects with heterogeneous material distribution in the constructive hypervolume model framework. The introduced distance approximation helps intuitively model material distributions parameterized by distances to so-called material features. The smoothness of the material functions, provided here by the smoothness of the defining function for the shape, helps to avoid undesirable singularities in the material distribution, like stress or concentrations. We illustrate application of the SARDF operations by twoand three-dimensional heterogeneous object modeling case studies.