基于QTM的线状图形自动化简算法探讨

全球网格是由形成地球表面剖分的一系列区域所组成,八面体四分三角网(QTM)是其中一种具有层次性的网格。本文依据数据点在规则网格中的分布规律,提出了一种在QTM数据结构支持下的线状图形化简算法。该算法以经过每级QTM网格的数据点的平均值为标准,能自动地对比较平缓的线段进行较粗选点,而对相对复杂的线段进行较密选点。本文以及Dutton算法都能克服DouglasPeucker算法中难以客观和合理确定阈值的困难,但是本算法比Dutton算法简单,且具有更高的化简率,能更好地保留了线状图形的弯曲特征。     

Evaluating Alternative Line Simplification Strategies for Multiple Representations of Cartographic Lines

Two basic strategies have been identified for handling multiple representations of line features in digital databases. Either a finite number of scale-dependent representations of cartographic lines can be explicitly stored, or a scale-independent database is generated from which subsequent scale representations can be extracted as needed. These two strategies parallel differences in hierarchical and non-hierarchical line simplification operators. Non-hierarchical line-simplification can produce the most geometrically accurate simplification at any scale, while hierarchical operators are often associated with scale-independent databases. In this research, hierarchical and non-hierarchical line simplification operators are evaluated by comparing both the points retained by these different algorithms and the overall quality of the graphic portrayal for sample lines of different complexity and at different scales. Visual inspection of the results did not reveal any discernable difference at any scale for any line. Subsequent numerical analyses shows some differences but overall little geometric quality is lost by using a hierarchical operator as opposed to a non-hierarchical one and given the greater flexibility of scale representations that is possible, hierarchical methods appear to be more satisfactory.     

Contour line simplification method based on the two‐level Bellman–Ford algorithm

The contour line is one of the basic elements of a topographic map. Existing contour line simplification methods are generally applied to maps without topological errors. However, contour lines acquired from a digital elevation model (DEM) may contain topological errors before simplification. Targeted at contour lines with topological errors, a progressive simplification method based on the two‐level Bellman–Ford algorithm is proposed in this study. Simplified contour lines and elevation error bands were extracted from the DEM. The contour lines of the elevation error bands were initially simplified with the Bellman–Ford (BF) algorithm. The contour lines were then segmented using the vertices of the initial simplification result and connected curves with the same bending direction were merged into a new curve. Subsequently, various directed graphs of the merged curves were constructed and a second simplification was made using the BF algorithm. Finally, the simplification result was selected based on the similarity between several simplification results and adjacent contour lines. The experimental results indicate that the main shapes of the contour groups can be maintained with this method and original topological errors are resolved.     

一种顾及多重约束的三维地形简化方法

三维模型在许多领域内均有着越来越深入的应用,为保证三维模型在不同存储空间、不同图形绘制能力、不同显示分辨率的终端电子设备上显示的统一性和一致性,在很多情况下需要对三维模型进行适度的简化。对于三维地形而言,纹理颜色、地形区域边界和重要顶点是其非常重要的视觉特征,本文将这三项特征作为约束因子引入到三维地形的简化过程中,并根据这三项特征对现有的二次误差测度算法和边折叠代价的计算方法进行了改进,使其在三维地形简化过程中不会出现明显退化。本文还将改进后的算法与原来算法进行了实验对比,结果表明,改进后的简化算法不仅能够在不同精度上保持三维地形视觉上的一致性,而且产生的几何误差也相对较小。     

The use of cartographic control points in the harmonization and revision of MRDBs

The main purpose of the research is to achieve fully automated approach for supplying multi-resolution databases with linear objects in each scale. Moreover, the proposed solutions maintain the repeatability and accuracy of output data wherever possible according to the input scale. These properties are achieved by keeping the minimal object dimensions as well as the appropriate data pre-processing, based on the classification of source points. The classification distinguishes three classes of points: constant (unchangeable), temporary, and inherited. These classes build a structure of cartographic control points. Based on these solutions, the authors proposed an algorithm for linear object simplification based on minimal object dimensions and cartographic control points. It was also confirmed that the simplification between constant points does not cause geometry discrepancies in relation to the global simplification of the whole line.     

Line generalisation by repeated elimination of points

Abstract

This paper presents a new approach to line generalisation which uses the concept of 'effective area' for progressive simplification of a line by point elimination. Two coastlines are used to compare the performance of this, with that of the widely used Douglas-Peucker, algorithm. The results from the area-based algorithm compare favourably with manual generalisation of the same lines. It is capable of achieving both imperceptible minimal simplifications and caricatural generalisations. By careful selection of cut-off values, it is possible to use the same algorithm for scale-dependent and scale-independent generalisations. More importantly, it offers scope for modelling cartographic lines as consisting of features within features so that their geometric manipulation may be modified by application- and/or user-defined rules and weights. The paper examines the merits and limitations of the algorithm and the opportunities it offers for further research and progress in the field of line generalisation.     

采用斜拉式弯曲划分的曲线化简方法

线要素化简一直是自动制图综合中的重要研究内容。分析已有线化简算法在线弯曲形态保持和单调弧段划分时只考虑一侧等不足,提出线要素的斜拉式弯曲划分和化简新方法。该方法对线要素采用斜剖方式划分弧段,兼顾线要素两侧的弯曲形态;识别出每个划分的单调弧段是U型弧段还是V型弧段,是大弧段还是小弧段,从而分别对其进行不同的处理;在处理过程中,每化简完一个单调弧段,重新对线要素进行弧段划分,然后再次对每个单调弧段进行化简,以此类推,因此该算法是一种动态化简过程。实例显示,本算法在线要素特征点保持、u型弧段和V型弧段保持、大弯曲的保持、整体形态保持等方面非常有效,且化简率非常高,充分证明本算法的科学性和优越性。     

利用质心Voronoi图对地形自适应简化的算法

地形简化算法利用少量有效的地形信息表达整体地形,能很好地解决海量地形数据与计算机硬件之间的矛盾,同时满足多尺度地形应用需求。针对现有地形简化算法难以兼顾局部地形起伏与地形整体特征的问题,提出一种基于质心Voronoi图的地形自适应简化算法。首先,利用质心Voronoi图的特点,以地形起伏度作为密度函数生成质心Voronoi图;然后,利用分布在地形起伏较大区域的质心Voronoi图种子点及大多分布在地形特征线上的Voronoi区域顶点重构地形;最后,通过原始地形与重构地形的特征线验证地形简化的效果,并与三维道格拉斯-普克（3D DouglasPeucker,3D DP）算法进行精度对比。实验结果表明,从简化地形中提取的山脊线、山谷线、等高线等地形特征线与原始地形的重叠度均较高,算法能较好地保持地形整体特征;且在相同的简化级别下,算法的简化误差小于3D DP算法,具有较高的地形简化精度。     

线要素多尺度表达的一种新方法

本文依据多比例尺条件下矢量数据的绘制原理,提出了多尺度线化简与线选取方法。多尺度线化简算法依比例尺将空间坐标转换为像素坐标,根据像素坐标删除曲线中重合点与共线点,综合后的曲线与原始曲线在各比例尺下绘制结果相同;多尺度线选取算法利用仿射变换结果快速计算线要素之间的连通关系,然后渐进删除长度小于阈值的悬线与孤立弧段,保持了线要素的连通性。对不同类型数据的实验验证了本文算法的有效性和可行性。     

Progressive Visualization of Complex 3D Models Over the Internet

The online transmission and real‐time rendering of complex 3D models have always been a bottleneck which limits the performance of Web 3D simulation systems. To improve the efficiency of data transmission and mesh reconstruction, this article proposes a novel progressive mesh structure. In the first stage of progressive visualization, the base data and the base index generated by vertex clustering simplification are transmitted to the client for the fundamental rendering. Then the incremental data and corresponding indexes at higher levels are transmitted, as the viewpoint approaches the simulation object. The multi‐scale incremental data organization benefits the performance and efficiency of the Web 3D simulation system by separately transmitting and reconstructing the corresponding level of mesh details. To demonstrate the adaptability and reliability of this algorithm, we developed an experimental prototype system to conduct a series of experiments. The results of experiments show that the improved progressive mesh structure described in this article takes good advantage of the vertex clustering simplification scheme to increase the efficiency of online transmission and mesh reconstruction, and the average frame rate of the progressive visualization has been increased to some extent, especially for massive data in large scale scenes.     

线状地图要素的自相似性分析及其自动综合

通过线状地图要素的自相似性分析和分维估值，研究了线状地图要素的形状结构特征随量测尺度和比例尺变化的规律，并在此基础上，提出了旨在使综合过程自适应进行和保持图形形状特征的线状要素自动综合的方法。     

等高线图形综合策略的研究

利用Arc/Info的功能研究了等高线图形综合方法,其一是通过地形结构线控制的渐进式等高线综合,其二是利用Douglas方法得到更抽象的TIN间接来完成等高线图形综合。     

Estimation of the Positional Uncertainty in Line Simplification in GIS

Abstract

This paper presents a new model for handling positional uncertainty in the process of line simplification. It considers that positional uncertainty in a simplified line is caused by (a) positional uncertainty in an initial line propagated through the process and (b) a deviation of the simplified line from the initial line. In order to describe the uncertainty in the simplified line, the maximum distance is defined as a measure. This measure is further adopted to determine parameters to a line simplification algorithm. Therefore, this model makes a step forward in the implementation of an uncertainty indicator for the line simplification. As compared existing models, the proposed uncertainty model in this paper is more comprehensive in uncertainty assessment for line simplification.     

An appearance‐preserving simplification method for complex 3D building models

The simplification of 3D building models to effectively reduce model complexity and improve rendering efficiency is an important component of 3D GIS. To reduce the data volume while preserving the model appearance, this article proposes a novel simplification method for complex 3D building models. Texture discontinuities are addressed by developing a new data model that records the mapping relation between the texture coordinates of each vertex and its neighboring triangles. The surface mesh of the building model is then segmented into regions, guided by topology and appearance. Finally, the mesh segmentation information is used to derive an improved error metric that considers both geometric and texture errors, and the texture coordinates are adjusted after each simplification operation. A series of comparative experiments alongside traditional methods demonstrates that our approach achieves a good balance between geometric fidelity and texture preservation, and produces simplified 3D building models with better visual quality.     

基于可见性预处理的地形模型视相关简化算法

提出了一种基于可见性预处理的点删除简化算法。该算法针对海量地形数据,首先建立了高效的空间索引系统,利用这一索引系统快速完成了视锥截取、背面剔除和隐藏面消除等可见性测试,再对预处理后的网格模型依据顶点曲率大小进行点删除简化。实验表明,采用可见性预处理可大大提高绘制速度,并且绘制帧速率基本独立于模型的复杂度。     

Area‐preservation Simplification of Polygonal Boundaries by the Use of the Structured Total Least Squares Method with Constraints

This article presents an area‐preservation approach for polygonal boundary simplification by the use of structured total least squares adjustment with constraints (STLSC), with the aim being to maintain the area of the original polygons after the simplification. Traditionally, a simplified line is represented by critical points selected from the original one. However, this study focuses on maintaining the areas of the polygons in the process of simplification of polygonal boundaries. Therefore, the proposed method in this article is a supplement to the existing line simplification methods, and it improves the quality of the simplification of polygonal boundaries in terms of positional and area errors. Based on the sub‐divisions of the original polyline, using the critical points detected from the polyline by the use of line simplification methods, the framework of the proposed method includes three main components, as follows: (1) establishment of the straight‐line‐segment fitting model based on both the critical and intermediate points on the sub‐polyline; (2) introduction of both area and end‐point constraints to reduce the geometric distortions due to the line simplification; and (3) derivation of the solution of boundary simplification by the use of STLSC. An empirical example was conducted to test the applicability of the proposed method. The results showed that: (1) by imposing the linear fitting model on both the critical and intermediate points on the sub‐polylines in the proposed STLSC method, the positional differences between the original points and the simplified line are approximately in a normal distribution; and (2) by introducing both end‐point and area constraints in the proposed STLSC method, the areas of the simplified polygons are the same as those of the original ones at different scales, and the two neighboring fitted lines are connected to each other at the optimized position.     

Multi-Scale Representation of a Digital Line

A scheme for multi-scale geometrical representation of a digital line is proposed. A digital line is represented as a structured object in which lines at different levels of resolution are represented as lists, quadcodes are used as control mechanism for guiding line simplification at multiple scales of a pyramid, and operators for simplification and smoothing are used to generate lines at different levels of resolution. In this scheme, lines at different levels of an image pyramid can be automatically generated without specifying the so-called tolerance value. Experimental results show that up to a certain level of resolution, the simplified lines retain important information content and recognizable characteristics. Also, the image pyramid assures a legible representation at any level of representation. Future research should improve the current line simplification operator and address the correspondence between lines at different levels of an image pyramid and the lines at different map scales.     

基于多比例尺地图数据的线状要素综合方法

提出了一种基于多比例尺地图数据的线状要素综合方法,若一个顶点在两个不同比例尺的对应线状要素上都存在,则它在中间比例尺线状要素上也应该得到保留。首先,利用不同比例尺线状要素进行同名点识别,并在较大比例尺线状要素上进行标记;然后,以标记的同名点为断点,将大比例尺线状要素分割成多个线段;最后,对分割后的各线段结合Douglas-Peucker算法进行综合。通过实验分析论证了该方法的可行性及有效性。     

带线约束的摄影测量网格变分精化算法

针对城市场景三维重建模型在有线特征的边缘区域过于平滑的问题,提出一种带线约束的摄影测量网格变分精化方法。算法以初始重建网格模型为基础,引入3个能量项,将网格精化问题转化成能量下降问题。首先结合所有的影像信息构建影像一致性约束项,然后对网格表面顶点附加正则化约束,最后引入三维线特征约束,将3个能量项加权相加后离散化到每个顶点,得到梯度变化值。采用梯度下降法,使顶点沿着梯度方向移动,当能量不再下降或迭代一定次数时,即得到了精化后的网格模型。试验结果表明,本文算法能较好地保持边缘特征,与现有的泊松重建算法相比,网格的质量更高,视觉效果更好。     

A method for assessing generalized data accuracy with linear object resolution verification

The article is composed of two sections. In the first section, the authors describe the application of minimum line dimensions which are dependent on line shape, width and the operational scale of the map. The proposed solutions are based on the Euclidean metric space, for which the minimum dimensions of Saliszczew’s elementary triangle (Elementary triangle – is the term pertaining to model, standard triangle of least dimensions securing recognizability of a line. Its dimensions depend on scale of the map and width of the line representing it. The use of a triangle in the simplification process is as follows: triangles with sides (sections) on an arbitrary line and bases (completing the sides) are compared with lengths of the shorter side and the base of the elementary triangle.) were adapted. The second part of the article describes an application of minimum line dimensions for verifying and assessing generalized data. The authors also propose a method for determining drawing line resolution to evaluate the accuracy of algorithm simplification. Taking advantage of the proposed method, well-known simplification algorithms were compared on the basis of qualitative and quantitative evaluation. Moreover, corresponding with the methods of simplified data accuracy assessment the authors have extended these solutions with the rejected data. This procedure has allowed the identification of map areas where graphic conflicts occurred.