Fakhruddin has proved that for two lattice polygons P and Q any lattice point in their Minkowski sum can be written as a sum of a lattice point in P and one in Q, provided P is smooth and the normal fan of P is a subdivision of the normal fan of Q. We give a shorter combinatorial proof of this fact that does not need the smoothness assumption on P .

Under the extra assumption that the boundary is of class C this was proven by S. Nakajima (= A. Matsumura) in 1926 Theorem 1 solves this problem. For convex bodies with C boundaries and positive curvature Nakajima’s result was generalized by Chakerian [?] in 1967 to “relative geometry” where the width and brightness are measured with with respect to some convex body K0 symmetric about the origi...

background: poisoning is one of the main causes of visits to emergency departments and hospitals in iran. drug and poison information centers (dpic) are reliable sources to guide poisoned patients and provide information about pharmaceutical agents. this study was designed to analyze recorded phone calls to iran dpics during 2011-2012. methods: this was a retrospective study on phone calls to d...

Vacuum.-By creating a vacuum the process of decalcification can be characterized as follows: Insoluble calciurn-salts+acid o-soluble calciumsalts+CO2. The carbon dioxide, rapidly extracted, will disturb the balance of the chemical equilibrium, and, according to Le Chatelier, result in an acceleration of the reaction. Waerhaug (1949), however, points out that there will be a more intensive conta...

TheMinkowski sum of two setsA,B ∈ IR, denotedA⊕B, is defined as {a+ b | a ∈ A, b ∈ B}. We describe an efficient and robust implementation for the construction of Minkowski sums of polygons in IR using the convolution of the polygon boundaries. This method allows for faster computation of the sum of non-convex polygons in comparison to the widely-used methods for Minkowski-sum computation that d...

This paper presents a new algorithm for computing the hit point and normal of a ray and a general convex object. The algorithm is loosely based on the the Gilbert-Johnson-Keerthi algorithm for computing the distance between convex objects in the sense that it is applicable to the same family of convex objects and uses the same subalgorithm for computing the closest point of a simplex. Since thi...