Computed Geometries

Computed Axial Lithography (CAL): Toward Single Step 3D Printing of Arbitrary Geometries

Most additive manufacturing processes today operate by printing voxels (3D pixels) serially point-by-point to build up a 3D part. In some more recently-developed techniques, for example optical printing methods such as projection stereolithography [Zheng et al. 2012], [Tumbleston et al. 2015], parts are printed layer-by-layer by curing full 2d (very thin in one dimension) layers of the 3d part ...

Homogeneous Geometries

For the purposes of this paper, a geometry will consist of a set together with a closure operation on that set, satisfying the exchange condition, and under which singletons are closed (for more precise definitions, see §2.1). The geometry is homogeneous if in the automorphism group of the geometry, the pointwise stabilizer of any finitedimensional closed subset of the geometry is transitive on...

Spacetime Geometries

Injection geometries

In this paper a new concept, injection geometries, is considered. This provides a common generalization of matroids and permutation geometries. Different systems of axioms and various examples are given. Theorem 5.1 provides an extremal set theoretic characterization of injection designs. 0 1984 Academic Press, Inc.

Imbrex geometries

We introduce an axiom on strong parapolar spaces of diameter 2, which arises naturally in the framework of Hjelmslev geometries. This way, we characterize the Hjelmslev-Moufang plane and its relatives (line Grassmannians, certain half-spin geometries and Segre geometries). At the same time we provide a more general framework for a lemma of Cohen, which is widely used to study parapolar spaces. ...