Trivariate Spline Representations for Computer Aided Design and Additive Manufacturing

TL;DR

This paper explores advanced trivariate spline representations for CAD and Additive Manufacturing, emphasizing multi-material capabilities, integration with Isogeometric Analysis, and comparison of hierarchical spline methods.

Contribution

It introduces and compares various trivariate spline techniques for CAD and AM, highlighting their feasibility and advantages in multi-material additive manufacturing.

Findings

Trivariate spline representations support multi-material AM.

Hierarchical B-splines, T-splines, and LR B-splines are compared.

Example demonstrates application in IGA and AM processes.

Abstract

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 B-rep based CAD, STL, sculptured triangles as well as trimmed and block-structured 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.