Approximating Free-form Geometry with Height Fields for Manufacturing

Approximating Free-form Geometry with Height Fields for Manufacturing

We consider the problem of manufacturing free-form geometry with classical manufacturing techniques, such as mold casting or 3-axis milling. We determine a set of constraints that are necessary for manufacturability and then decompose and, if necessary, deform the shape to satisfy the constraints per segment. We show that many objects can be generated from a small number of (mold-)pieces if sli...

Free Form Incident Light Fields

This paper presents methods for photo-realistic rendering using strongly spatially variant illumination captured from real scenes. The illumination is captured along arbitrary paths in space using a high dynamic range, HDR, video camera system with position tracking. Light samples are rearranged into 4-D incident light fields (ILF) suitable for direct use as illumination in renderings. Analysis...

Information geometry of entanglement renormalization for free quantum fields

We provide an explicit connection between the differential generation of entanglement entropy in a tensor network representation of the ground states of two field theories, and a geometric description of these states based on the Fisher information metric. We show how the geometrical description remains invariant despite there is an irreducible gauge freedom in the definition of the tensor netw...

Elements with bounded height in number fields

We give a constructive proof of the fact that there exist only finitely many elements with bounded height in number fields. This provides an efficient method to enumerate all those elements. Such a method is helpful to compute bases on elliptic curves. Mathematics subject classification numbers, 11R33, 11G50, 14G05.

Approximating solution of fully fuzzy linear systems in dual form