On convex lattice polygons
نویسندگان
چکیده
منابع مشابه
On convex lattice polygons
Let II be a convex lattice polygon with b boundary points and c (5 1) interior points. We show that for any given a , the number b satisfies b 5 2e + 7 , and identify the polygons for which equality holds. A lattice polygon II is a simple polygon whose vertices are points of the integral lattice. We let A = 4(11) denote the area of II , b{U) the number of lattice points on the boundary of II , ...
متن کاملConvex Lattice Polygons
Let n ≥ 3 be an integer. A convex lattice n-gon is a polygon whose n vertices are points on the integer lattice Z 2 and whose interior angles are strictly less than π. Let a n denote the least possible area enclosed by a convex lattice n-gon, then [1, 2, 3] {a n } ∞ n=3 = n 1 2
متن کاملOn the Number of Convex Lattice Polygons
We prove that there are at most exp{cA 1 ^} different lattice polygons of area A. This improves a result of V. I. Arnol'd.
متن کاملMinkowski decomposition of convex lattice polygons
A relatively recent area of study in geometric modelling concerns toric Bézier patches. In this line of work, several questions reduce to testing whether a given convex lattice polygon can be decomposed into a Minkowski sum of two such polygons and, if so, to finding one or all such decompositions. Other motivations for this problem include sparse resultant computation, especially for the impli...
متن کاملOn k-convex polygons
We introduce a notion of k-convexity and explore polygons in the plane that have this property. Polygons which are k-convex can be triangulated with fast yet simple algorithms. However, recognizing them in general is a 3SUM-hard problem. We give a characterization of 2-convex polygons, a particularly interesting class, and show how to recognize them in O(n log n) time. A description of their sh...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Bulletin of the Australian Mathematical Society
سال: 1976
ISSN: 0004-9727,1755-1633
DOI: 10.1017/s0004972700022826