نتایج جستجو برای: non convex polygon
تعداد نتایج: 1367003 فیلتر نتایج به سال:
A floodlight of size α is a light source that projects light in a cone of size α . In this paper we study the problem of illuminating a convex polygon using floodlights. We give an O(n 2 ) time algorithm to find an optimal pair of floodlights to illuminate a convex polygon P with n vertices; that is a pair of floodlights to illuminate a convex polygon in such a way that the sum of their sizes i...
A half-plane probe through a polygon measures the area of intersection between a half-plane and the polygon. We dev elop techniques based on xray probing to determine convex n-gons in 7n + 7 half-plane probes. We also show n + 1 half-plane probes are sufficient to verify a specified convex polygon and prove linear lower bounds for determination and verification.
The problem of cutting a convex polygon P out of a piece of planar material Q with minimum total cutting length is a well studied problem in computational geometry. Researchers studied several variations of the problem, such as P and Q are convex or non-convex polygons and the cuts are line cuts or ray cuts. In this paper we consider yet another variation of the problem where Q is a circle and ...
We present an exhaustive search of all families of convex pentagons which tile the plane. This research shows that there are no more than the already 15 known families. In particular, this implies that there is no convex polygon which allows only non-periodic tilings.
A convex hole (or empty convex polygon) of a point set P in the plane is a convex polygon with vertices in P , containing no points of P in its interior. Let R be a bounded convex region in the plane. We show that the expected number of vertices of the largest convex hole of a set of n random points chosen independently and uniformly over R is Θ(logn/(log log n)), regardless of the shape of R.
An n-gon is defined as a sequence P = (V0, . . . , Vn−1) of n points on the plane. An n-gon P is said to be convex if the boundary of the convex hull of the set {V0, . . . , Vn−1} of the vertices of P coincides with the union of the edges [V0, V1], . . . , [Vn−1, V0]; if at that no three vertices of P are collinear then P is called strictly convex. We prove that an n-gon P with n > 3 is strictl...
Viviani’s theorem states that the sum of distances from any point inside an equilateral triangle to its sides is constant. We consider extensions of the theorem and show that any convex polygon can be divided into parallel segments such that the sum of the distances of the points to the sides on each segment is constant. A polygon possesses the CVS property if the sum of the distances from any ...
We give a short proof of the following geometric inequality: for any two triangular meshes A and B of the same polygon C, if the number of vertices in A is at most the number of vertices in B, then the maximum length of an edge in A is at least the minimum distance between two vertices in B. Here the vertices in each triangular mesh include the vertices of the polygon and possibly additional St...
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