Adaptive direct slicing of volumetric attribute data represented by trivariate B-spline functions

We introduce a framework for modeling of heterogeneous objects in terms of trivariate B-spline functions and a method for slicing them directly for additive manufacturing. We first fit volumetric attribute data associated with the geometry in terms of trivariate B-spline functions under the assumption that the geometric volume is already defined by the trivariate B-spline functions. Then, the B-spline volume and the associated attribute data are directly sliced without converting them to stereo-lithography format, resulting in a tool path with fewer errors. Furthermore, adaptive ray shooting is introduced in the slicing plane so that the zigzag tool path passes through all the tangential intersection points of the heterogeneous objects to represent all the feature points in the fabricated model. Complex examples illustrate the effectiveness of our method.