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1、基于数字地面模型的土方计算软件的开发与应用李为民(厦门市测量队361003)【摘要】本文阐述了基于三角网数字地面模型计算土方的基本原理，描述了以此为基础的DTM-VOL土方计算软件的基本算法、程序结构和主要功能。一、引言测绘信息网突飞猛进发展的计算机技术、空间技术和现代通讯技术推动了以3S为代表的现代数字测绘技术的研究和应用，数据采集和数据处理手段的多样化、自动化、智能化程度日益提高。然而，也存在这样的问题：实际生产对现代测绘成果的应用并不充分，土方测算就是一例。全站仪、计算机和数字测图软件等先进软硬件设备的普遍应用与传统方格网法和断面法土方测算等落后手段的普遍采用并不协调，生产单位对土方测算
2、依然“忧喜参半”。喜在土方测算效益显著，忧在测算过程繁琐且精度差，纠纷难免。为此，笔者经过努力，利用数字测图软件自动建立的数字地面模型，开发了DTM-VOL土方计算软件，实现了土方测算内外业一体化的全自动过程。二、基本原理和设计目标1. 基本原理测绘信息网土方计算的目的主要是计算同一地块开挖(或填充)前后的填方量(或挖方量)，实际上就是计算体积。无论采用什么方法进行体积计算，都必须已知的两个基本条件是：(1) 开挖(或填充)前地面的起伏状况；(2) 开挖(或填充)后地面的起伏状况。地面起伏状况在计算机中的准确描述就是通常所说的数字地面模型(DTM)。其描述方法有三种：曲面方程、三角网或方格网、
3、横(纵、水平)断面。用曲面方程准确描述地面的起伏状况十分困难，通常采用后两种方法，其实质分别是：(1) 用大量相互连接的三角形面或矩形面拟合地面的起伏状况；(2) 用平行截取的横(纵、水平)断面拟合地面的起伏状况。三角形面、矩形面或横(纵、水平)断面数量越多，对实际地面起伏的描述越准确。由于断面对地面的描述不连续，因此，通常所说的DTM指三角网或方格网，就是把若干三角形或矩形顶点的三维坐标(E，N，H)以及它们之间的邻接关系输入计算机而建立起来的。据此，计算机便可以准确无误地识别地面的高低起伏情况。如果将DTM视为空间的曲面，填挖前后的两个DTM即为两个空间曲面，那么计算机便可以自动计算两个曲
4、面的交线，也可以用一条铅垂线同时对两个曲面任意切割，并计算夹在两个切割下来的曲面间的空间的体积，实际上就是土方计算中的填挖交界线、填方量和挖方量。2. 设计目标测绘信息网土方测算中，外业的工作内容就是地形测量。充分利用全站仪坐标存储和数据传输功能测量地形特征点是最自由、简便的地形测量作业方式，这样既准确刻画了地形的整体面貌和局部细节特征，又最大限度地减少了冗余高程点，为外业生产提供了无约束的工作空间，同时具有较高的作业效率。计算机智能化辅助数据处理则是内业追求的工作境界。因此，支持上述作业方式，实现内外业一体化、自动化成为设计DTM-VOL土方计算软件的目标。三、DTM的建立测绘信息网目前，国
5、产数字测图软件已日趋成熟，它们均具备用离散的碎部高程点建立三角网DTM，并自动生成等高线的功能。EPSW 97数字测图软件在建立三角网数字地面模型方面具有可靠的分析能力和良好的编辑功能，为快速准确构造一般地形甚至破碎地形的三角网DTM提供了一个有力的工具。DTM-VOL软件识别的基础数据就是来自EPSW 97的三角网DTM。采用三角网DTM的原因有三：(1) 三角网DTM对地形的描述准确，且数据冗余量小；(2) 直接利用了数字测图软件的图形功能和DTM数据成果。通过数字测图软件生成的等高线走向可以十分直观地判断三角网DTM本身是否准确描述了实际的地形情况，尤其是对陡坎、斜坡等特殊地形的描述。如
6、果DTM对地形细节描述不准确或不正确，可方便地进行修正，从而保证建立的DTM准确无误，使计算机“看”到的地形与实地一致；(3) 方便判断有效计算区域和准确计算出填挖交界线。EPSW建立的三角网DTM数据包括以PN1为扩展名的点坐标文件和以TR1为扩展名的三角网拓扑关系文件。二者均为ASCII文本文件，格式如下：测绘信息网PN1文件：n9999minE minN maxE maxN0：E0N0H01：E1N1H12：E2N2H2n-1-1:En-1Nn-1Hn-1其中，n为总点数；9999为常数；minE、minN、maxE、maxN分别为最小东坐标、最小北坐标、最大东坐标、最大北坐标；0n-1
7、为点号；(E,N,H)0(E,N,H)n-1为各点的三维坐标。TR1文件：n0：013655351655351：12365535655350n-1:p1 p2 p3 t1 t2 t3其中，n为三角形总数；0n-1为三角形号；p1、p2、p3为顶点点号；t1、t2、t3分别为p1p2、p1p3、p2p3边的邻接三角形号，当值为65535时表示无邻接三角形。测绘信息网四、程序结构DTM-VOL软件的总体框图如图1所示。1. DTM数据重组EPSW97建立的三角网的拓扑关系信息比较含蓄，点、线、面三者的邻接关系必须通过分析间接获取，为了提高计算速度，有必要重建DTM的拓扑关系，并建立平面分析缓冲区。
8、新建拓扑关系模型如图2所示。该模型直接体现了点、线和三角形在平面上的拓扑关系，利用空间代替大量的重复分析，以此换取速度。结果表明，效果是不错的。平面分析缓冲区采用栅格模型，如图3所示。任何在栅格内或穿过栅格的点、线、三角形均成为该栅格的一个对象，栅格内的对象彼此为近邻，不同栅格中的对象为远邻。2. DTM的加密测绘信息网DTM1和DTM2以不同的三角网形和密度表征不同的地形特征，为了避免计算体积过程中DTM1和DTM2的失真，必须进行DTM三角网加密求两个三角网平面投影的并，然后分解求并后产生的多边形为三角形，如图4所示。图1图 2图 3图 43. 体积计算DTM加密的结果：DTM1和DTM2
9、具有形状和大小完全相同的三角网。至此土方计算归结为若干三棱柱体积计算。三棱柱的形状有图5所示的几种情况。测绘信息网图 54. 成果输出DTM-VOL可以直接打印“土方计算成果表”和“土方计算成果明细表”，同时生成EPSW格式的图形文件，利用EPSW 97灵活的绘图功能绘制自定义比例尺的三角网图、地形图等图件。结合图件和“土方计算成果明细表”可以检验任意单三角形内土方计算结果的正确性，为用户提供充分的验证资料。五、算例以下是一个土方计算的算例，为了节省图面，此例的面积较小。图6是施工前工地的地形状况，图中各高程即为实地测量的地形特征点，三角网为依据地形建立的数字地面模型。图7是设计(或者说施工后
10、形成)的地形状况。图8是经过三角网加密后的填挖前的数字地面模型，图9是经过三角网加密后的填挖后的数字地面模型，图中的虚线为填挖交界线。根据图8和图9进行的土方计算结果见表1，表2列出了面积大于10 m2的三角形土方计算明细表，与图8和图9对照可以检核计算结果的正确性。测绘信息网图6施工前工地的地形状况(1300)图7设计的地形状况(1300)图8填挖前的数字地面模型(三角网加密，1300)表1计算结果总表填方区平面面积/m2192.0总填方量/m3428.9挖方区平面面积/m270.9总挖方量/m378.1表2计算明细表三角形号挖方面积/m2挖方量/m3填方面积/m2填方量/m300213.7
11、12.20.00.000311.316.50.00.000412.76.81.30.20050.00.021.468.20060.00.014.441.20070.00.017.056.3其他小三角形之和33.142.7137.9263.0表中三角形号与图8和图9中的三角形号对应。图9填挖后的数字地面模型(三角网加密，1300)六、结束语测绘信息网DTM-VOL土方计算软件开发过程较长，其间经历了上百次模拟数据检验，开发成功后，至今已完成了数十件土方测算工程，从外业测量到成果输出，作业效率提高几十倍，成果准确可靠。虽然软件某些部分采用的基本算法并非十分优化，但从实际生产来看，软件的计算速度和方
12、便程度完全可以接受，而且具备较完善的功能：(1) 分期填挖工程中，只要实测并保留每期DTM(包括起始DTM)，建立设计面DTM，可以计算出任意两期间完成的土方量，或任意一期完成和尚未完成的土方量以及填挖交界线坐标；(2) 实际测量区域与计算土方区域大小不一致，软件可以自动识别重叠区；设计填挖区域与实际填挖区域不一致，软件允许指定边界确定有效区，并只计算有效区内重叠区的土方量；(3) 具备大型土方计算的数据容量；(4) 能提供美观的成果报表和充分的检验资料计算细表和图件，从而透视其计算过程，检验其计算结果；(5) 具备公开的数据格式，为用户提供方便灵活的使用空间。参考文献1 清华山维新技术开发公
13、司.EPSW 97电子平板测图系统使用手册，1997测绘信息网2 马日杰编著.Foxpro for Windows实用程序设计.北京：学苑出版社，1994Editors note: Judson Jones is a meteorologist, journalist and photographer. He has freelanced with CNN for four years, covering severe weather from tornadoes to typhoons. Follow him on Twitter: jnjonesjr (CNN) - I will alwa
14、ys wonder what it was like to huddle around a shortwave radio and through the crackling static from space hear the faint beeps of the worlds first satellite - Sputnik. I also missed watching Neil Armstrong step foot on the moon and the first space shuttle take off for the stars. Those events were wa
15、y before my time.As a kid, I was fascinated with what goes on in the sky, and when NASA pulled the plug on the shuttle program I was heartbroken. Yet the privatized space race has renewed my childhood dreams to reach for the stars.As a meteorologist, Ive still seen many important weather and space e
16、vents, but right now, if you were sitting next to me, youd hear my foot tapping rapidly under my desk. Im anxious for the next one: a space capsule hanging from a crane in the New Mexico desert.Its like the set for a George Lucas movie floating to the edge of space.You and I will have the chance to
17、watch a man take a leap into an unimaginable free fall from the edge of space - live.The (lack of) air up there Watch man jump from 96,000 feet Tuesday, I sat at work glued to the live stream of the Red Bull Stratos Mission. I watched the balloons positioned at different altitudes in the sky to test
18、 the winds, knowing that if they would just line up in a vertical straight line we would be go for launch.I feel this mission was created for me because I am also a journalist and a photographer, but above all I live for taking a leap of faith - the feeling of pushing the envelope into uncharted ter
19、ritory.The guy who is going to do this, Felix Baumgartner, must have that same feeling, at a level I will never reach. However, it did not stop me from feeling his pain when a gust of swirling wind kicked up and twisted the partially filled balloon that would take him to the upper end of our atmosph
20、ere. As soon as the 40-acre balloon, with skin no thicker than a dry cleaning bag, scraped the ground I knew it was over.How claustrophobia almost grounded supersonic skydiverWith each twist, you could see the wrinkles of disappointment on the face of the current record holder and capcom (capsule co
21、mmunications), Col. Joe Kittinger. He hung his head low in mission control as he told Baumgartner the disappointing news: Mission aborted.The supersonic descent could happen as early as Sunday.The weather plays an important role in this mission. Starting at the ground, conditions have to be very cal
22、m - winds less than 2 mph, with no precipitation or humidity and limited cloud cover. The balloon, with capsule attached, will move through the lower level of the atmosphere (the troposphere) where our day-to-day weather lives. It will climb higher than the tip of Mount Everest (5.5 miles/8.85 kilom
23、eters), drifting even higher than the cruising altitude of commercial airliners (5.6 miles/9.17 kilometers) and into the stratosphere. As he crosses the boundary layer (called the tropopause), he can expect a lot of turbulence.The balloon will slowly drift to the edge of space at 120,000 feet (22.7
24、miles/36.53 kilometers). Here, Fearless Felix will unclip. He will roll back the door.Then, I would assume, he will slowly step out onto something resembling an Olympic diving platform.Below, the Earth becomes the concrete bottom of a swimming pool that he wants to land on, but not too hard. Still,
25、hell be traveling fast, so despite the distance, it will not be like diving into the deep end of a pool. It will be like he is diving into the shallow end.Skydiver preps for the big jumpWhen he jumps, he is expected to reach the speed of sound - 690 mph (1,110 kph) - in less than 40 seconds. Like hi
26、tting the top of the water, he will begin to slow as he approaches the more dense air closer to Earth. But this will not be enough to stop him completely.If he goes too fast or spins out of control, he has a stabilization parachute that can be deployed to slow him down. His team hopes its not needed
27、. Instead, he plans to deploy his 270-square-foot (25-square-meter) main chute at an altitude of around 5,000 feet (1,524 meters).In order to deploy this chute successfully, he will have to slow to 172 mph (277 kph). He will have a reserve parachute that will open automatically if he loses conscious
28、ness at mach speeds.Even if everything goes as planned, it wont. Baumgartner still will free fall at a speed that would cause you and me to pass out, and no parachute is guaranteed to work higher than 25,000 feet (7,620 meters).It might not be the moon, but Kittinger free fell from 102,800 feet in 1960 - at the dawn of an infamous space race that captured the hearts of many. Baumgartner will attempt to break that record, a feat that boggles the mind. This is one of those monumental moments I will always remember, because there is no way Id miss this.
