A Bound on a Convexity Measure for Point Sets

A planar point set is in convex position precisely when it has a convex polygonization, that is, a polygonization with maximum interior angle measure at most [Formula: see text]. We can thus talk about the convexity of a set of points in terms of its min-max interior angle measure. The main result presented here is a nontrivial upper bound of the min-max value in terms of the number of points in the set. Motivated by a particular construction, we also pose a natural conjecture for the best upper bound.

The sum of the interior angles in geodesic and translation triangles of Sl2(R)~ geometry

We study the interior angle sums of translation and geodesic triangles in the universal cover of real 2 x 2 matrices with unit determinant, as, a Thurston geometry denoted by P of SL2(R)~ geometry. We prove that the angle sum ?3i =1(?i) ? ? for translation triangles and for geodesic triangles the angle sum can be larger, equal or less than ?.

AN INVARIANT SHAPE REPRESENTATION: INTERIOR ANGLE CHAIN

This paper proposes a novel shape representation scheme — Interior Angle Chain (IAC) — which is invariant to translation, rotation and scaling. The proposed method first approximates the contour of a planar shape with an equilateral polygon and then makes a representation using the polygon's interior angle chain. The difference between two shapes is measured by the distance between their IAC's. An algorithm to obtain equilateral polygon approximation and its associated IAC is proposed in this paper. The proposed shape representation scheme has been tested on two benchmarks and applied to lake recognition in SAR (Synthetic Aperture Radar) images. The results show that IAC is an effective shape representation scheme.

Analysis of the Effects of Interior Aperture Angle on Print Quality in Solder Paste Stenciling

ABSTRACTStencil apertures of various interior angle, i.e. angle between two sides of a polygon, are analyzed for print performance. Aperture size and sidewall taper are also examined for their individual and combined effects on printing. The results show no effect of interior angle within the bounds of the experiment. Sidewall taper becomes relevant when aperture geometry is nearly square.