In the world of medical computing, 3D reconstruction of slice data is a common topic. A slice is a single cross-section image obtained by CT or MRI devices, and can be processed to obtain polygonal data describing the material to be analyzed. For example, if images are taken of a heart, contours around the cross sections might be found and saved as point data for further processing. An example ...

Analytical solutions are presented for laminar fully developed flow in micro-/ minichannels of hyperelliptical and regular polygonal cross sections in the form of compact relationships. The considered geometries cover a wide range of common simply connected shapes including circle, ellipse, rectangle, rectangle-with-round-corners, rhombus, star-shape, equilateral triangle, square, pentagon, and...

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This paper addresses the issue of trap design for sensor-less automated assembly. First, we present a simple algorithm that determines in O(nmm(nm) log(nm)) time whether an n-sided polygonal part will fall through an m-sided polygonal trap. We then introduce the notion of a minimal trap for a polygonal part, and develop an O(n 4+") algorithm that designs a family of minimal feeders built from t...

We describe Veech groups of flat surfaces arising from irrational angled polygonal billiards or irreducible stable abelian differentials. For irrational polygonal billiards, we prove that these groups are non-discrete subgroups of SO(2,R) and we calculate their rank.