let e be the ellipse with major and minor radii a and b respectively, and pbe its perimeter, then p = lim 4 tan(p/n)(a + b + 2) σ a2 cos2 (2k-2)pi/n+ sin2 (2k-2)pi/n; where n = 2m. so without considering the limit, it gives a reasonable approxi-mation for p, it means that we can choose n large enough such that the amountof error be less than any given small number. on the other hand, the formul...

In the present study, an attempt was made to produce a precise 3D image of a tomato canopy using a portable high-resolution scanning lidar. The tomato canopy was scanned by the lidar from three positions surrounding it. Through the scanning, the point cloud data of the canopy were obtained and they were co-registered. Then, points corresponding to leaves were extracted and converted into polygo...

We are given a set S of n points in the Euclidean plane. assume that is general position. A simple polygon P an empty if each vertex point and every either outside or P. In this paper, we consider problem enumerating all polygons set. To design efficient enumeration algorithm, use reverse search by Avis Fukuda with child lists. propose algorithm enumerates O(n2 |ϵ(S) |)-time, where ϵ(S) S. More...

This paper presents how the image-based rendering technique of viewdependent texture-mapping (VDTM) can be efficiently implemented using projective texture mapping, a feature commonly available in polygon graphics hardware. VDTM is a technique for generating novel views of a scene with approximately known geometry making maximal use of a sparse set of original views. The original presentation o...

Some thoughts are presented on the inter-relation between beauty and truth in science in general and theoretical physics in particular. Some conjectural procedures that can be used to create new ideas, concepts and results are illustrated in both Boltzmann-Gibbs and nonextensive statistical mechanics. The sociological components of scientific progress and its unavoidable and benefic controversi...

Polygon clipping is an important operation that computers execute all the time. An algorithm that clips a polygon is rather complex. Each edge of the polygon must be tested against each edge of the clipping window, usually a rectangle. As a result, new edges may be added, and existing edges may be discarded, retained, or divided. Multiple polygons may result from clipping a single polygon. Afte...

We study a proper subset of polyominoes, called polygonal polyominoes, which are defined to be self-avoiding polygons containing any number of holes, each of which is a self-avoiding polygon. The staircase polygon subset, with staircase holes, is also discussed. The internal holes have no common vertices with each other, nor any common vertices with the surrounding polygon. There are no ‘holes-...

‎In this work‎, ‎a regular polygon with $n$ sides is described by a periodic (circular) sequence with period $n$‎. ‎Each element of the sequence represents a vertex of the polygon‎. ‎Each symmetry of the polygon is the rotation of the polygon around the center-point and/or flipping around a symmetry axis‎. ‎Here each symmetry is considered as a system that takes an input circular sequence and g...