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Digital representations targeting design and simulation for Additive Manufacturing (AM) are addressed from the perspective of Computer Aided Geometric Design. We discuss the feasibility for multi-material AM for Brep based CAD, STL, sculptured triangles as well as trimmed and blockstructured trivariate locally refined spline representations. The trivariate spline representations support Isogeometric Analysis (IGA), and topology structures supporting these for CAD, IGA and AM are outlined. The ideas of (Truncated) Hierarchical B-splines, T-splines and LR B-splines are outlined and the approaches are compared. An example from the EC H2020 Factories of the Future Research and Innovation Actions CAxMan illustrates both trimmed and block-structured spline representations for IGA and AM.

Locally refined B-spline (LRB) surfaces provide a representation that is well suited to scattered data approximation. When a data set has local details in some areas and is largely smooth elsewhere, LR B-splines allow the spatial distribution of degrees of freedom to follow the variations of the data set. An LRB surface approximating a data set is refined in areas where the accuracy does not meet a required tolerance. In this paper we address, in a systematic study, different LRB refinement strategies and polynomial degrees for surface approximation. We study their influence on the resulting data volume and accuracy when applied to geospatial data sets with different structural behaviour. The relative performance of the refinement strategies is reasonably coherent for the different data sets and this paper concludes with some recommendations. An overall evaluation indicates that bi-quadratic LRB are preferable for the use cases tested, and that the strategies we denote as “full span" have the overall best performance.

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