  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.
