Support-Free Hollowing for 3D Printing via Voronoi Diagram of Ellipses

Abstract: Recent work has demonstrated that the interior material layout of a 3D model can be designed to make a fabricated replica satisfy application-specific demands on its physical properties such as resistance to external loads. A widely used practice to fabricate such models is by layer-based additive manufacturing (AM) or 3D printing, which however suffers from the problem of adding and removing interior supporting structures. In this paper, we present a novel method for generating support-free elliptic hollowing for 3D shapes which can entirely avoid additional supporting structures. To achieve this, we perform the ellipse hollowing in the polygons on parallel section planes and protrude the ellipses of one plane to its neighboring planes. To pack the ellipses in a polygon, we construct the Voronoi diagram of ellipses to efficiently reason the free-space around the ellipses and other geometric features by taking advantage of the available algorithm for the efficient and robust construction of the Voronoi diagram of circles. We demonstrate the effectiveness and feasibility of our proposed method by generating interior designs for and printing various 3D shapes.