六角网格系统下的多边形填充算法

针对六角网格系统下图形、图像处理及显示时像素之间相邻的唯一性,挺出六角网格系统下的多边形填充算法,其中包括边界填充算法和扫描线填充算法,采用图示与伪代码的方法描述箅法。与矩形网格上的图像处理算法相比,六角网格系统上的图像处理算法具有更好的唯一性和简便性。     

六角网格中三维物体模式识别算法

提出一些算法,这些算法预期成为在六角网格中实现对三维物体快速、并行的模式识别的整体方案的一部分。这些算法包括在7-像素六角邻域之内基于灰度差值的边缘检测、局部边缘减薄和基于7-点六角掩模的特征提取。通过串行计算机模拟,这些算法对诸如方体等一些简单物体的真实六角网格数字图像的实验性验证已经显示了在快速识别三维物体轮廓的关键性特征方面的成功。     

六角网格上的图象算法及几何量定义

很多研究已经证明,将网格点排列成六角网格的形式是一种最佳排列。文中首先描述六角网格相对于方形网格的优点,给出在六角网格上进行图象处理时所用到的一些几何量的定义。提出二个六角网格上的图象算法。     

分层六角网格中物体边缘检测的算法

本文提出了在分层六角网格中基于像素灰度实现边缘检测的边缘点确定算法和边缘构造算法。文中首先介绍了六角网格结构的优势和1：3面积比、1：4面积比两类六角网格金字塔,而后给出了相应的实验论证。实验结果显示应用六角网格金字塔的算法对图像数据中的缝隙与噪声具有鲁棒性,1：4面积比六角金字塔在边缘检测中优于1：3面积比金字塔。     

基于分层六角网格对简单三维物体的快速识别

提出了一种利用目前的CRS系统摄取六角网格数字图像的方法,并对获取的图像提出了基于金字塔处理的、从边缘检测等低层处理到模式识别等高层处理的算法.借助串行计算机模拟,利用六角几何和并行处理构架来识别六角网格数字图像中的物体.实验结果表明,该算法能够快速地识别一些简单的三维物体.最后提出了一个2层的六角网格视网膜的设计方案.文中论证了用于图像分析的六角像素网格的鲁棒性.     

六角网格上的图象处理算法的研究

经研究表明,屏幕上的点最佳分布是按六角网格形式分布的,文中首先讨论了六角网格的特点,屏幕用正六边形覆盖,即每个象素对应着一个正六边形,而将正六边形的中心点做为网格点;并从图形图象处理的角度分析了它的优点,如显示的直线（或曲线）没有“断开”的感觉,每个象素与所有相邻象素之间只有一种相邻关系,这就为许多图象处理提供了简便的实现途径,然后提出了在六角网格上进行图象处理的数字化过程以及在图象恢复时几何失真校正的算法,可以看出,在达到同样精度时计算量比方型网格上有明显减少。     

六角网格上的直线生成算法

经研究表明,屏幕上的点最佳分布是按六角网格形式分布的,文中首先讨论了六角网格的特点,并从图形图象处理的角度分析了它伯优点,然后提出了在六角网格上的直线生成算法,此算法仅用了整数运算。     

兵棋推演中地形量化算法研究与实现

传统手工兵棋推演计算机化的一个重要方面是实现兵棋棋盘的计算机化.需要借助于计算机实现兵棋棋盘的数字化并对兵棋地图进行地形量化.兵棋推演系统采用不同大小的六角网格量化地形,将兵棋推演系统与地理信息系统组件MapX结合.在MapX中显示兵棋推演区域的Maplnfo格式地图数据,并提出了一种基于MapX的六角网格绘制算法,算法充分利用MapX中图元与组合图元的思想,可以根据推演需求实时生成不同比例尺的六角网格覆盖整个或部分作战区域,降低了手工兵棋地形量化的工作量,对提高兵棋推演效率有一定的意义.     

六角网格系统下图形几何变换的方法研究

屏幕上的点最佳分布是按六角网格形式分布的,因此,对六角网格系统下的图形生成和操作方法的研究是十分有意义的.在六角网格下的对称坐标系统上对平移变换、对称变换和缩放变换的变换矩阵及实现方法进行了研究,使六角网格系统下的图形变换成为可能.由于采用变换矩阵的方法进行旋转变换较为复杂,提出了基于像素的旋转变换方法,此方法计算量少、运算效率高.     

基于六角网格的椭圆快速生成算法

大多数图形生成算法均是针对方形网格系统,即直角坐标系,而研究表明,屏幕上的网格点最佳分布是按六角网格分布的,本文就椭圆在六角网格的生成,提出了一个快速有效的并行算法。算法中全部采用了整数型运算。     

Hexagonal grid methods with applications to partial differential equations

We consider in this work hexagonal grids for two-dimensional applications. A finite volume-based finite difference approach to solving Laplacian-related differential equations on hexagonal grids is developed. Both ordinary and compact hexagonal seven-point schemes are investigated. Theoretical properties of the associated linear algebraic systems are determined. These methods are applied to solve PDEs on both regular and curved domains, successfully exhibiting linear and spiral wave propagations in regular domains and curved wave in a reversed C-type domain.     

The Generation of Straight Lines on Hexagonal Grids

The best disposition of a discrete set of points on the plane can be reached if the points are on a hexagonal grid. This paper describes an algorithm for the generation of straight lines on hexagonal grids. It uses only integer arithmetic.     

The Generation of Circular Arcs on Hexagonal Grids

The best disposition of a discrete set of points on the plane can be reached if the points are on a hexagonal grid. This paper describes two algorithms for circular arc mesh point selection on hexagonal grids. They find the closest integer coordinates to the actual circular arc using only integer arithmetic. Error criteria are explicitly specified.     

Alternative Tilings for Improved Surface Area Estimates by Local Counting Algorithms

In this paper, we first review local counting methods for perimeter estimation of piecewise smooth binary figures on square, hexagonal, and triangular grids. We verify that better perimeter estimates, using local counting algorithms, can be obtained using hexagonal or triangular grids. We then compare surface area estimates using local counting techniques for binary three-dimensional volumes under the three semi-regular polyhedral tilings: the cubic, truncated octahedral, and rhombic dodecahedral tilings. It is shown that for surfaces of random orientation with a uniform distribution, the expected error of surface area estimates is smaller for the truncated octahedral and rhombic dodecahedral tilings than for the standard cubic or rectangular prism tilings of space. Additional properties of these tessellations are reviewed and potential applications of better surface area estimates are discussed.     

Invariant image reconstruction from irregular samples and hexagonal grid splines

We present an algorithm for the reconstruction of images from irregularly placed samples, using linear splines with control points on a hexagonal grid. Several spline approximations are computed for different transformations of the control point grid (e.g. translations and rotations). These approximations are then merged together after compensation of the transformations, yielding a high-quality invariant image reconstruction. Evaluations show that the use of hexagonal grids of the “invariance by integration” principle improves reconstruction quality. An application to image coding is also presented.     

Resampling on a Pseudohexagonal Grid

This paper investigates resampling techniques on a pseudohexagonal grid. Hexagonal grids are known to be advantageous in many respects for sampling and representing digital images in various computer vision and graphics applications. Currently, a real hexagonal grid device is still difficult to find. A good alternative for obtaining the advantages of a hexagonal grid is to construct a pseudohexagonal grid on a regular rectangular grid device. In this paper we first describe the options and procedures for constructing such a pseudo-hexagonal grid and then demonstrate techniques of resampling digital images on the pseudohexagonal grid. Four distinct resampling kernels are tested, and their results are illustrated and compared.     

Dynamic monopolies and feedback vertex sets in hexagonal grids

In a majority conversion process, the vertices of a graph can be in one of the two states, colored or uncolored, and these states are dynamically updated so that a vertex becomes colored at a certain time period if at least half of its neighbors were in the colored state in the previous time period. A dynamic monopoly is a set of vertices in a graph that when initially colored will eventually cause all vertices in the graph to become colored. This paper establishes a connection between dynamic monopolies and the well-known feedback vertex sets which are sets of vertices whose removal results in an acyclic graph. More specifically, we show that dynamic monopolies and feedback vertex sets are equivalent in graphs wherein all vertices have degree 2 or 3. We use this equivalence to provide exact values for the minimum size of dynamic monopolies of planar hexagonal grids, as well as upper and lower bounds on the minimum size of dynamic monopolies of cylindrical and toroidal hexagonal grids. For these last two topologies, the respective upper and lower bounds differ by at most one.     

Hierarchical grid conversion

Hierarchical grids appear in various applications in computer graphics such as subdivision and multiresolution surfaces, and terrain models. Since the different grid types perform better at different tasks, it is desired to switch between regular grids to take advantages of these grids. Based on a 2D domain obtained from the connectivity information of a mesh, we can define simple conversions to switch between regular grids. In this paper, we introduce a general framework that can be used to convert a given grid to another and we discuss the properties of these refinements such as their transformations. This framework is hierarchical meaning that it provides conversions between meshes at different level of refinement. To describe the use of this framework, we define new regular and near-regular refinements with good properties such as small factors. We also describe how grid conversion enables us to use patch-based data structures for hexagonal cells and near-regular refinements. To do so, meshes are converted to a set of quadrilateral patches that can be stored in simple structures. Near-regular refinements are also supported by defining two sets of neighborhood vectors that connect a vertex to its neighbors and are useful to address connectivity queries.