The layered depth-normal images (LDNIs) is an implicit representation of solid models that sparsely encodes the shape boundary in three orthogonal directions. We present a LDNIbased geometric modeling method for applications with high accuracy requirements. In our method, we first construct LDNIs models from input polygonal models. The accuracy of the generated LDNIs models can be controlled by...

1. Abelson and diSessa, Turtle Geometry, MIT Press, 1992 2. Erdely,D.http://www.bridgesmathart.org/art exhibits/bridges2007/erdely.html. 3. Gangopadhyay, T. On an alternate construction method for generating spidrons and new tiling patterns generated by them, International journal of Computer Applications, /volume160/number3/27054-2017913010 4. Jacques, F. http://polyspidrons.over-blog.com/arti...

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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...

By a dihedral folding tiling (f-tiling, for short) of the sphere S whose prototiles are spherical right triangles, T1 and T2, we mean a polygonal subdivision τ of S such that each cell (tile) of τ is congruent to T1 or T2 and the vertices of τ satisfy the angle-folding relation, i.e., each vertex of τ is of even valency and the sums of alternating angles around each vertex are π. In fact, the c...

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.

A wallpaper map is a conformal projection of a spherical earth onto regular polygons with which the plane can be tiled continuously. A complete set of distinct wallpaper maps that satisfy certain natural symmetry conditions is derived and illustrated. Though all of the projections have been published before, the family had not been characterized as a whole. Some wallpaper maps generalize to one...