Implicit Functionally Graded Conforming Microstructures

The tensor product parametric representations are the most commonly used representation in geometric modeling. Yet, other representations have advantages in certain aspects, and in this work, we focus on employing implicit representations in the construction of microstructures. An implicit function, either functionally precise, or spline trivariate-based, is used to populate a macro-shape trivariate parametric form, and construct a conforming microstructure. Either the implicit tile or the macro-shape can be functionally graded or be heterogeneous, carrying graded properties such as material, translucency, or color alongside the geometry. Further, the implicit tiles can be parametrized and hence their geometry can vary across the macro-shape. The representation is locally precise and we demonstrate that in a slicing process that employs no (piecewise-linear) approximation. Finally, we demonstrate this framework on several 3D printed heterogeneous models.