Polygonal space carving with geometric anti-aliasing

This paper proposes an algorithm that solves the shape recovery problem from N arbitrary images. By introducing a polygonal carving technique, the proposed algorithm can reconstruct the image-consistent polygonal shape that is patched by input images. This algorithm eliminates the invalid vertices and polygons from the initial polygonal grid space according to the color variance that represents their image consistency. The carved shape is refined by moving the outlier vertices on the boundary of each image. The final reconstructed shape faithfully accounts for the input images, and its textured appearance reflects the similar color property of the target object.     

平面多边形域的快速约束Delaunay三角化

针对任意平面多边形域,采用增量思想和均匀网格,在局部范围内快速生成约束Delaunay三角形．该方法不会生成区域外的三角形;对存在折线、离散点以及含“洞”的情况不需要特殊处理．实验结果表明,该方法对于随机生成的简单多边形域三角化速度快,平均计算时间呈近似线性．另外,针对文字、工业图案等带状图像的边界多边形,充分利用其近似等宽性优化算法,将其应用于带状图像骨架的快速提取．     

一种基于最小搜索圆平面多边形域约束Delaunay三角剖分算法

给出一种新的基于边优先的二维多边形域任意散乱数据的约束Delaunay三角剖分算法.算法结合网格分块技术,提出基于最小搜索圆的点搜索思想,并证明了该思想的正确性,有效地提高了搜索第三点的速度.算法中散乱数据可以是任意复杂的折线、封闭多边形环及离散点.另外,在三角剖分过程中,实时地去掉封闭点和封闭边,极大地加快了构网速度,实现了平面多边形域散乱数据的快速约束Delaunay三角化.     

Approximate General Sweep Boundary of a 2D Curved Object

This paper presents an algorithm to compute an approximation to the general sweep boundary of a 2D curved moving object which changes its shape dynamically while traversing a trajectory. In effect, we make polygonal approximations to the trajectory and to the object shape at every appropriate instance along the trajectory so that the approximated polygonal sweep boundary is within a given error bound ϵ > 0 from the exact sweep boundary. The algorithm interpolates intermediate polygonal shapes between any two consecutive instances, and constructs polygons which approximate the sweep boundary of the object. Previous algorithms on sweep boundary computation have been mainly concerned about moving objects with fixed shapes; nevertheless, they have involved a fair amount of symbolic and/or numerical computations that have limited their practical uses in graphics modeling systems as well as in many other applications which require fast sweep boundary computation. Although the algorithm presented here does not generate the exact sweep boundaries of objects, it does yield quite reasonable polygonal approximations to them, and our experimental results show that its computation is reasonably fast to be of a practical use.     

一个通用的快速三角化算法

提出了一个适用于任意平面多边形区域及散乱点集的通用三角化算法。当算法应用于多边形区域时,首先对各个顶点和区域内部的散乱点按扫描方式排序,然后依次扫描各点,扩展生成新的三角形,从而获得局部已剖分区域,并最终完成整个区域的三角化。将上述过程作适当改动后,可被用于平面散乱点集的三角网格化,该通用算法除了具有快速三角化的特点之外,还采用局部域的优化组合来体现最优化准则,因此算法更具有可操作性和实用性。     

Polygonal representation of digital planar curves through dominant point detection—a nonparametric algorithm

We describe a new algorithm that detects a set of feature points on the boundary of an 8-connected shape that constitute the vertices of a polygonal approximation of the shape itself. The set of feature points (nodes) is a ranked subset of the original shape points whose connected left and right arm extents cover the entire shape. Nodes are ranked based on their strength (in terms of their importance to other boundary points), length of support region, and distance from the centroid. The polygon obtained by linking the detected nodes approximates the contour in an intuitive way. The proposed algorithm does not require an input parameter and works well for shapes with features of multiple sizes.     

Base station placement on boundary of a convex polygon

Let P be a polygonal region which is forbidden for placing a base station in the context of mobile communication. Our objective is to place one base station at any point on the boundary of P and assign a range such that every point in the region is covered by that base station and the range assigned to that base station for covering the region is minimum among all such possible choices of base stations. Here we consider the forbidden region P as convex and base station can be placed on the boundary of the region. We present optimum linear time algorithm for that problem. In addition, we propose a linear time algorithm for placing a pair of base stations on a specified side of the boundary such that the range assigned to those base stations in order to cover the region is minimum among all such possible choices of a pair of base stations on that side.     

Prager's layout theory: a nonnumeric computer method for generating optimal structural configurations and weight-influence surfaces

After illustrating the versatility of the proposed computer method on an introductory example, the basic principles of Prager's layout theory and its applications to least-weight grillages and space frames are briefly reviewed. Then a computer algorithm for generating analytically the optimal layout for both grillages and space frames is described in detail. The algorithm can handle a broad class of boundary conditions of unusual complexity and also furnishes a weight-influence surface for evaluating directly the minimum weight of the considered structure.In the case of grillages, the present computer program can derive optimal layouts for any polygonal domain with simply supported and/or clamped edges and internal point supports and the solution is valid for any nonnegative (downward) loading. Layouts for optimal space frames are restricted to ‘Prager-structures’ (i.e. frames with all members in pure tension or all members in pure compression) with polygonal support and a single point-load in any arbitrary location.     

Polygonal Boundary Evaluation of Minkowski Sums and Swept Volumes

We present a novel technique for the efficient boundary evaluation of sweep operations applied to objects in polygonal boundary representation. These sweep operations include Minkowski addition, offsetting, and sweeping along a discrete rigid motion trajectory. Many previous methods focus on the construction of a polygonal superset (containing self‐intersections and spurious internal geometry) of the boundary of the volumes which are swept. Only few are able to determine a clean representation of the actual boundary, most of them in a discrete volumetric setting. We unify such superset constructions into a succinct common formulation and present a technique for the robust extraction of a polygonal mesh representing the outer boundary, i.e. it makes no general position assumptions and always yields a manifold, watertight mesh. It is exact for Minkowski sums and approximates swept volumes polygonally. By using plane‐based geometry in conjunction with hierarchical arrangement computations we avoid the necessity of arbitrary precision arithmetics and extensive special case handling. By restricting operations to regions containing pieces of the boundary, we significantly enhance the performance of the algorithm.     

任意多边形区域交的有效算法

为有效进行任意多边形区域的交运算,采用接缝技术消除多边形区域内部的孔洞,化复连通域为单连通域,通过单连通域的交集得到复连通域的交.改写Weiler-Atherton裁减算法的交点遍历方法,以便在跟踪时跳过接缝,同时借助队列保存这些接缝的节点,确保能正确得到交集区域的每条边界.算法无须包容性测试就能自然得到交集的外边界与孔洞的包容关系.与已有算法相比,该算法具有更高的稳定性和健壮性,特别适合计算带有孔洞区域的交、并、差运算.     

Polygon reduction of 3D objects using Stokes' theorem

Surface over volume rendering can be useful for many applications. However, the tremendously large number of polygons composing the surface primitives should be reduced to a manageable size so as to utilize the capability of low cost hardware and software rendering engines, a standard Internet protocol and VRML format. In this paper, we propose a novel algorithm that deletes several vertices simultaneously by forming a closed arbitrary shaped boundary. The Stokes' theorem, used in electro-magnetic field analysis, was newly adapted to extract the arbitrary shaped boundary. The simultaneous deletion procedure provides a computational gain and increases the reduction ratio without sacrificing the topological distortion of the original mesh. Numerically synthesized polygonal objects and real CT data were tested to evaluate the performance of the new algorithm and to demonstrate the possibility of a medical rendering application. The new algorithm outperforms the conventional decimation algorithm in both computational and reduction efficiency.     

基于局部中心度量的边界点划分密度聚类算法

针对聚类算法在检测任意簇时精确度不高、迭代次数多及效果不佳等缺点,提出了基于局部中心度量的边界点划分密度聚类算法——DBLCM.在局部中心度量的限制下,数据点被划分到核心区域或边界区域.核心区域的点按照互近邻优先成簇的分配方式形成初始簇,边界区域的点参考互近邻中距离最近点所在簇进行分配,从而得到最终簇.为验证算法的有效性,将DBLCM与3个经典算法和3个近几年新提出的优秀算法,在包含任意形状、任意密度的二维数据集和任意维度的多维数据集上进行测试.另外,为了验证DBLCM算法中参数k的敏感性,在所用的数据集上做了k值与簇质量的相关性测试.实验结果表明,DBLCM算法具有识别精度高,检测任意簇效果好和无需迭代等优点,综合性能优于6个对比算法.     

任意多边形内带特征约束的散列数据的最优三角剖分

给出了一种新的基于Ｄｅｌａｕｎａｙ三角形化的任意多边形边界内散列数据的优化三角剖分算法，该算法可允许散列数据任意复杂的折线及封闭多边形环的特征约束。算法用统一的数据结构来记录散列数据、约束特征和三角剖分信息，并且引入了辅助窗的概念，从而使优化剖分和加入约束容易实现。     

一个笔划填充算法及其在计算机书法中的应用

笔划填充是对任意多边形围成区域的一种填充方式，要求填充的视觉效果象人用毛笔摹帖一样。本文描述了一个实现笔划填充的算法，说明了这个算法在表现计算机书法中的应用情况。     

Six degree-of-freedom haptic rendering using spatialized normal cone search

This paper describes a haptic rendering algorithm for arbitrary polygonal models using a six degree-of-freedom haptic interface. The algorithm supports activities such as virtual prototyping of complex polygonal models and adding haptic interaction to virtual environments. The underlying collision system computes local extrema in distance between the model controlled by the haptic device and the rest of the scene. The haptic rendering computes forces and torques on the moving model based on these local extrema. The system is demonstrated on models with tens of thousands of triangles and developed in an accessibility application for finding collision-free paths.     

一种新的基于链码的填充算法

将计算机图形学的栅栏填充算法移植到链码的填充算法中，发展出了一种新的基于链码的填充算法。利用边界Freeman链码，定义了一种新的边界点分类方法，通过对边界上的左右端点到栅栏间的像素取补填充该区域，算法能填充任意复杂图像区域，不需要辅助内存空间和标记边界色。与现有的算法进行了对比实验，实验表明该文提供的算法对于图像具有填充速度快、效率高等优点。     

Polygonal approximation of digital planar curves through break point suppression

This paper presents a new algorithm that detects a set of dominant points on the boundary of an eight-connected shape to obtain a polygonal approximation of the shape itself. The set of dominant points is obtained from the original break points of the initial boundary, where the integral square is zero. For this goal, most of the original break points are deleted by suppressing those whose perpendicular distance to an approximating straight line is lower than a variable threshold value. The proposed algorithm iteratively deletes redundant break points until the required approximation, which relies on a decrease in the length of the contour and the highest error, is achieved. A comparative experiment with another commonly used algorithm showed that the proposed method produced efficient and effective polygonal approximations for digital planar curves with features of several sizes.     

基于多边形边界约简的启发式在线时间序列表示算法

提出了一种新颖的可在线计算的时间序列启发式算法。算法具有多边形约简算法相同的优良的近似质量,并可在固定数据缓冲区空间内在线运算。用启发式搜索方法自动获取最佳分段数。在随机时间序列上仿真试验证明算法有很高的逼近质量和较低的计算复杂性。     

噪声边界的保形平滑

本文给出了数字图象边界的多边形逼进的算法和步骤，讨论了边界噪声的去除，边界形状控制点的获取，提出了改进运算速度的递推算法以及保持尖点不变的拟合原理。