技术领域technical field
本发明涉及空间距离校核仿真领域，具体涉及一种基于GIS的空间距离校核三维仿真方法。The invention relates to the field of space distance check simulation, in particular to a GIS-based three-dimensional simulation method for space distance check.
背景技术Background technique
输变电技术中的地理空间是物质、能量、信息的数量及行为在地理范畴中的广延性存在形式。特指形态、结构、过程、关系、功能的分布方式和分布格局同时在“暂时”时间的延续(抽象意义上的静止态)，讨论所表达出的“断片图景”。地理空间的研究是地理学的基本核心之一。而地表情况异常复杂，包含自然地物和人文地物，各种地物形状各异、关系复杂；因此对导线进行空间距离校核即为检验其是否运行正常的常用标准；而空间距离校核是指校核导线在40℃下运行或覆冰无风情况下导线最大弧垂对地面、建筑物、树木、铁路、道路、河流、管道、索道及各种架空线路的距离。所以地面及地物模型信息数字化是空间距离校核的基础。Geographic space in power transmission and transformation technology is the extensive existence form of the quantity and behavior of matter, energy and information in the geographical category. It refers specifically to the continuation of the form, structure, process, relationship, and function distribution mode and distribution pattern at the same time in the "temporary" time (static state in the abstract sense), and discusses the expressed "fragmentary picture". The study of geospatial is one of the fundamental cores of geography. However, the surface conditions are extremely complex, including natural features and cultural features, and various features have different shapes and complex relationships; therefore, the space distance check of the conductor is a common standard for checking whether it is operating normally; and the space distance check It refers to the distance of the maximum sag of the conductor to the ground, buildings, trees, railways, roads, rivers, pipelines, cableways and various overhead lines when the conductor is operated at 40°C or covered with ice and no wind. Therefore, the digitization of ground and surface object model information is the basis for spatial distance verification.
目前的空间距离校核仿真通常使用格网数据模型仿真，格网数据模型使用较多的空间和时间表示地表面；无法精确的表示异常复杂的地表面，因此，当地形包含有大量特征线如断裂线和构造线时，需要提供一种能够精确且使用较少空间及时间的仿真方法来对空间距离校核进行仿真。The current spatial distance calibration simulation usually uses a grid data model for simulation. The grid data model uses more space and time to represent the ground surface; it cannot accurately represent the extremely complex ground surface. Therefore, when the terrain contains a large number of feature lines such as For fault lines and construction lines, it is necessary to provide a simulation method that can accurately and use less space and time to simulate the spatial distance check.
发明内容Contents of the invention
有鉴于此，本发明提供的一种基于GIS的空间距离校核三维仿真方法，该方法充分利用了有序点子集的凸壳特性，避免了所有的交点测试，从而保证了对散乱点集生成Delaunay三角网的效率；能够快速地确定哪些点不可能再次参与构成新的三角形，大大的降低了搜索时间；提高了计算速度；保证了空间距离校核的准确性，进而为输变电技术地理空间的研究分析提供了有效且可靠的研究依据。In view of this, the present invention provides a GIS-based spatial distance check three-dimensional simulation method, which fully utilizes the convex hull characteristics of ordered point subsets, avoids all intersection tests, thereby ensuring the generation of scattered point sets The efficiency of the Delaunay triangulation; it can quickly determine which points are unlikely to participate in the formation of new triangles again, which greatly reduces the search time; improves the calculation speed; ensures the accuracy of the spatial distance check, and then provides technical geography for power transmission and transformation. The research and analysis of space provides an effective and reliable research basis.
本发明的目的是通过以下技术方案实现的：The purpose of the present invention is achieved through the following technical solutions:
一种基于GIS的空间距离校核三维仿真方法，所述方法包括如下步骤：A GIS-based three-dimensional simulation method for spatial distance checking, said method comprising the steps of:
步骤1.预处理GIS中的散乱点，确定点序列；Step 1. Preprocess the scattered points in the GIS to determine the point sequence;
步骤2.根据所述点序列，初始化凸壳链表、边链表及三角链表；Step 2. According to the point sequence, initialize the convex hull linked list, the edge linked list and the triangular linked list;
步骤3.将未处理的所述散乱点加入三角网；Step 3. adding the unprocessed described scattered points to the triangular network;
步骤4.优化所述三角网，得到Delaunay三角网；Step 4. optimize described triangulation, obtain Delaunay triangulation;
步骤5.根据所述Delaunay三角网，在GIS场景中进行空间距离计算并进行校验。Step 5. According to the Delaunay triangulation, calculate and check the spatial distance in the GIS scene.
优选的，所述步骤1包括：Preferably, said step 1 includes:
1-1.在散乱点的点集中，筛选出y坐标值最小的点，并判断其数量；1-1. In the point set of scattered points, filter out the point with the smallest y coordinate value, and judge its number;
若所述y坐标值最小的点只有1个，则该点为选点；If there is only one point with the smallest y coordinate value, then this point is the selected point;
若所述y坐标值最小的点大于1个，则选取其中x坐标最小的点为选点；If the point with the smallest y-coordinate value is more than 1, then select the point with the smallest x-coordinate value as the selected point;
1-2.连接所述选点与所述点集中其他各点，得到有向线段；1-2. Connect the selected point with other points in the point set to obtain a directed line segment;
1-3.分别计算各所述有向线段与正半轴的夹角值和长度；1-3. Calculate the angle value and length of each of the directed line segments and the positive semi-axis respectively;
1-4.按所述夹角值的递增以及长度递减进行词典式排序，得到点序列。1-4. Lexicographic sorting is performed according to the increasing value of the included angle and the decreasing length, to obtain a point sequence.
优选的，将所述散乱点的点集及预处理后的所述点序列保存在有序点表中。Preferably, the point set of the scattered points and the preprocessed point sequence are stored in an ordered point table.
优选的，所述步骤2包括：Preferably, said step 2 includes:
2-1.在所述点序列中，依次查找不在有向边上的点，将第一个所述有向边添加到凸壳链表和边链表中，令所述凸壳链表中凸壳边数及所述边链表中的有向边数均为i-1；其中，i为点序列总数；2-1. In the point sequence, find the points that are not on the directed edge in turn, and add the first directed edge to the convex hull linked list and the edge linked list, so that the convex hull edge in the convex hull linked list The number of directed edges in the number and the edge linked list is i-1; wherein, i is the total number of point sequences;
2-2.将第二个所述有向边添加到所述边链表中，令所述边链表中的有向边数为i-2；2-2. Adding the second directed edge to the edge list, so that the number of directed edges in the edge list is i-2;
2-3.将新产生的三角形添加到三角形链表中，并设置相关边的相邻三角形信息；令所述三角形链表中的三角形的数目为i-2；2-3. Add the newly generated triangles to the triangle list, and set the adjacent triangle information of the relevant side; make the number of triangles in the triangle list be i-2;
2-4.将所述选点添加到所述凸壳链表中；2-4. adding the selected point to the convex hull linked list;
2-5.输出所述凸壳链表、边链表及三角链表，结束初始化。2-5. Output the convex hull linked list, edge linked list and triangular linked list, and end the initialization.
优选的，所述步骤3包括：Preferably, said step 3 includes:
依次判断未处理的所述散乱点是否已经联结成三角网；Sequentially determine whether the unprocessed scattered points have been connected into a triangular network;
若是，并继续处理下一点；If so, proceed to the next point;
反之，则在所述凸壳链表中沿最后添加进去的所述有向边位置往前搜索直至所述凸壳链表结束，并修改相关边的相邻三角形信息，令凸壳链表中的凸壳边数+l，并继续处理下一点，直至所有所述散乱点都加入至三角网中。On the contrary, then search forward along the position of the directed edge added last in the convex hull linked list until the end of the convex hull linked list, and modify the adjacent triangle information of the relevant side, so that the convex hull in the convex hull linked list side number+1, and continue to process the next point until all the scattered points are added to the triangulation.
优选的，所述步骤4包括：Preferably, said step 4 includes:
在三角网的联结过程中不断对子三角网进行优化处理、或将点集联结成三角网后再统一对边链表的每条边进行一次局部优化处理；形成所述Delaunay三角网。During the connection process of the triangular network, the sub-triangular network is continuously optimized, or the point set is connected into a triangular network, and then each edge of the edge list is unified to perform a local optimization process; the Delaunay triangular network is formed.
优选的，所述步骤5包括：Preferably, said step 5 includes:
5-1.按下式(1)计算线路中任一点与地形地物间广义距离dij(q)：5-1. Calculate the generalized distance dij (q) between any point in the route and the terrain and features according to the formula (1):
其中，q为线路中任一点；xil为第l个点的第i维坐标；xjl为l个点的j维坐标；n为点的总数；l为1到n个点中的任意一点；Among them, q is any point in the line; xil is the i-th dimension coordinate of the l-th point; xjl is the j-dimensional coordinate of l points; n is the total number of points; l is any point from 1 to n points ;
当q＝2时，该值为欧氏距离；When q=2, the value is Euclidean distance;
当q＝1时，该值为绝对距离、即城市街坊距离dij(1)：When q=1, the value is the absolute distance, that is, the city neighborhood distance dij (1):
当q→∞时，该值为契比雪夫距离dij(∞)：When q→∞, the value is the Chebyshev distance dij (∞):
dij(∞)＝max{|xil-xjl|} l＝1,2,...,n (3)dij (∞)＝max{|xil -xjl |} l＝1,2,...,n (3)
根据所述契比雪夫距离求出固定点之间距离，并根据极限逼近的方法求解导线与地形地物间的最小距离；Find the distance between the fixed points according to the Chebyshev distance, and solve the minimum distance between the wire and the topography and features according to the method of limit approximation;
5-2.按下式(4)，根据点到直线段距离的计算来确定点到线的距离dPL：5-2. According to formula (4), the distance dPL from the point to the line is determined according to the calculation of the distance from the point to the line:
其中，L为线状物体；P为点状物体；dPx为点状物体P到线状物体L上任一点的距离；x为线状物体L上任一点；Among them, L is a linear object; P is a point object; dPx is the distance from the point object P to any point on the linear object L; x is any point on the linear object L;
5-3.根据两个线状物体L1，L2间的距离可以定义为L1中点P1(x1，y1)与L2中点P2(x2，y2)之间距离的极小值，且L1，L2均表现为折线；计算出线-线物体距离d：5-3. According to two linear objects L1, the distance between L2 can be defined as the minimum value of the distance between L1 midpoint P1(x1, y1) and L2 midpoint P2(x2, y2), and L1, L2 Both are shown as polylines; the line-line object distance d is calculated:
求得极大值，再计算方差曲线；Find the maximum value, and then calculate the variance curve;
5-4.设为角P1的度数；为角P2的度数；λ1为P1点的极角；λ2为P2点的极角；P为极点，球面三角形中点P1及P2中的以弧度计的两条边和一夹角已知：5-4. Set is the degree of angle P1; is the degree of angle P2; λ1 is the polar angle of P1 point; λ2 is the polar angle of P2 point; P is the pole, and the two sides and an included angle in radians of the midpoint P1 and P2 of the spherical triangle are known:
∠P＝λ1-λ2 (8)∠P＝λ1 -λ2 (8)
其中，PP1为球面三角形中的一边；PP2为球面三角形中的另一边；∠P为球面三角形中的两边夹角；Wherein, PP1 is one side in the spherical triangle; PP2 is the other side in the spherical triangle; ∠P is the angle between two sides in the spherical triangle;
则根据球面三角形的余弦定理，有：Then according to the cosine theorem of spherical triangles, we have:
其中，P1P2为弧度，且P1P2实际长度为R×cos-1(P1P2)，R为球面三角形半径；Among them, P1 P2 is radian, and the actual length of P1 P2 is R×cos-1 (P1 P2 ), R is the radius of spherical triangle;
根据球面三角形的余弦定理，有：According to the law of cosines of spherical triangles, there are:
cosPP3＝cosPP1cosP1P3+sinPP1sinP1P3cosP1 (10)cosPP3 = cosPP1 cosP1 P3 + sinPP1 sinP1 P3 cosP1 (10)
其中，P3为由P、P1、P3所组成的球面三角形中的一点，；为P3点的极角；Among them, P3 is a point in the spherical triangle formed by P, P1 and P3 ; is the polar angle of point P3;
若先给定则求得再由球面三角正弦定理求出∠P3；其中，∠P3为由P、P1、P3所组成的球面三角形中的P3点的度数；If first given then obtain Then obtain ∠P3 by the law of sine of spherical triangle; Wherein, ∠P3 is the degree of P3 points in the spherical triangle formed by P, P1 , P3 ;
再由耐普尔公式求出P1P3：Then calculate P1 P3 by Napier's formula:
5-5.根据peano规则，对于平面上规则分布的正方形格网点，采用旋转函数进行排列次序。5-5. According to the peano rule, for the square grid points regularly distributed on the plane, the rotation function is used to arrange the order.
优选的，所述步骤5-5中的所述排列次序的方式包括：Preferably, the arrangement order in the step 5-5 includes:
a.按Morton次序和Pi次序将初始空间划分为用四叉树来表示的子空间；a. divide the initial space into subspaces represented by quadtrees according to Morton order and Pi order;
b.在Morton次序和Row次序中由空间坐标求得任何一个空间物体的顺序号和地址；b. Obtain the sequence number and address of any space object from the space coordinates in the Morton order and Row order;
c.在Pi次序和Row-Prime次序中，两者权值相等。c. In Pi order and Row-Prime order, the two weights are equal.
从上述的技术方案可以看出，本发明提供了一种基于GIS的空间距离校核三维仿真方法，首先对散乱点按有向角进行排序，以排序后的点顺序为基础，利用凸壳特性快速将散乱点联结成三角网，利用拓扑结构快速将其优化为Delaunay三角网；将地面及地物模型信息在GIS场景中数字化；对距离计算方法进行了有效改进。本发明提出的方法充分利用了有序点子集的凸壳特性，避免了所有的交点测试，从而保证了对散乱点集生成Delaunay三角网的效率；能够快速地确定哪些点不可能再次参与构成新的三角形，大大的降低了搜索时间；提高了计算速度；保证了空间距离校核的准确性，进而为输变电技术地理空间的研究分析提供了有效且可靠的研究依据。It can be seen from the above technical solution that the present invention provides a GIS-based three-dimensional simulation method for spatial distance checking. First, the scattered points are sorted according to the orientation angle, and based on the sorted point order, the convex hull characteristic is used. Quickly connect scattered points into a triangular network, and quickly optimize it into a Delaunay triangular network by using topology; digitize the ground and ground object model information in the GIS scene; effectively improve the distance calculation method. The method proposed by the present invention makes full use of the convex hull characteristics of ordered point subsets, avoids all intersection tests, thereby ensures the efficiency of generating Delaunay triangulation for scattered point sets; can quickly determine which points cannot participate in forming new The triangle greatly reduces the search time; improves the calculation speed; ensures the accuracy of the spatial distance check, and provides an effective and reliable research basis for the research and analysis of the geographical space of power transmission and transformation technology.
与最接近的现有技术比，本发明提供的技术方案具有以下优异效果：Compared with the closest prior art, the technical solution provided by the present invention has the following excellent effects:
1、本发明所提供的技术方案中，通过首先对散乱点按有向角进行排序，以排序后的点顺序为基础，利用凸壳特性快速将散乱点联结成三角网，利用拓扑结构快速将其优化为Delaunay三角网；将地面及地物模型信息在GIS场景中数字化；对距离计算方法进行了有效改进。本发明提出的方法充分利用了有序点子集的凸壳特性，避免了所有的交点测试，从而保证了对散乱点集生成Delaunay三角网的效率；能够快速地确定哪些点不可能再次参与构成新的三角形，大大的降低了搜索时间；提高了计算速度；保证了空间距离校核的准确性，进而为输变电技术地理空间的研究分析提供了有效且可靠的研究依据。1. In the technical solution provided by the present invention, by first sorting the scattered points according to the oriented angle, based on the sorted point order, the scattered points are quickly connected into a triangular network by using the convex hull characteristics, and the topological structure is used to quickly connect the scattered points. It is optimized as a Delaunay triangulation; the ground and surface object model information is digitized in the GIS scene; the distance calculation method is effectively improved. The method proposed by the present invention makes full use of the convex hull characteristics of ordered point subsets, avoids all intersection tests, thereby ensures the efficiency of generating Delaunay triangulation for scattered point sets; can quickly determine which points cannot participate in forming new The triangle greatly reduces the search time; improves the calculation speed; ensures the accuracy of the spatial distance check, and provides an effective and reliable research basis for the research and analysis of the geographical space of power transmission and transformation technology.
2、本发明所提供的技术方案，相对于三角网生长算法来说，最大的优点是:在三角网生长过程中，能够快速地确定哪些点不可能再次参与构成新的三角形，因为当一个点位于己形成的凸壳之内时，此点已不可能再次构成新的三角形。通过将点按一定的顺序排序后，动态修改排在当前点前的点所形成的凸壳，很容易确定出哪些点不会再次参与其他新插入的点形成新的三角网。因此，相对于三角网生长算法来说大大的降低了搜索时间。并且凸壳内部的三角网的边绝对不可能再次参与三角网的生成。从而提高了计算速度。2, the technical solution provided by the present invention, with respect to the triangular network growth algorithm, the biggest advantage is: in the triangular network growth process, it can be determined quickly which points cannot participate in forming new triangles again, because when a point When it is inside the convex hull already formed, it is impossible for this point to form a new triangle again. By sorting the points in a certain order and dynamically modifying the convex hull formed by the points before the current point, it is easy to determine which points will not participate in other newly inserted points to form a new triangular network. Therefore, the search time is greatly reduced compared with the triangulation growing algorithm. And it is absolutely impossible for the edges of the triangulation inside the convex hull to participate in the generation of the triangulation again. Thus, the calculation speed is improved.
3、本发明提供的技术方案，在输变电技术领域应用广泛，具有显著的社会效益和经济效益。3. The technical solution provided by the present invention is widely used in the field of power transmission and transformation technology, and has significant social and economic benefits.
附图说明Description of drawings
图1是本发明的一种基于GIS的空间距离校核三维仿真方法的流程图；Fig. 1 is a kind of flow chart of the three-dimensional simulation method of space distance checking based on GIS of the present invention;
图2是本发明的实施例的仿真方法的步骤1的流程图；Fig. 2 is the flowchart of step 1 of the emulation method of the embodiment of the present invention;
图3是本发明的应用例的仿真方法的步骤2的流程图；Fig. 3 is the flowchart of step 2 of the emulation method of the application example of the present invention;
图4是本发明的一种基于GIS的空间距离校核三维仿真方法的具体应用例中的旋转函数度量最短距离方法示意图。FIG. 4 is a schematic diagram of a method for measuring the shortest distance with a rotation function in a specific application example of a GIS-based three-dimensional simulation method for space distance checking according to the present invention.
具体实施方式detailed description
下面将结合本发明实施例中的附图，对本发明实施例中的技术方案进行清楚、完整地描述，显然，所描述的实施例仅仅是本发明一部分实施例，而不是全部的实施例。基于本发明的实施例，本领域普通技术人员在没有做出创造性劳动前提下所获得的所有其他实施例，都属于本发明保护的范围。The following will clearly and completely describe the technical solutions in the embodiments of the present invention with reference to the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only some, not all, embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by persons of ordinary skill in the art without making creative efforts fall within the protection scope of the present invention.
如图1所示，本发明提供一种基于GIS的空间距离校核三维仿真方法，其中，GIS为地理信息系统(Geographic Information System，GIS)；Delaunay三角网用于对点集进行三角剖分，对数值分析(比如有限元分析)以及图形学来说，都是极为重要的一项预处理技术；peano规则是数学家皮亚诺(皮阿罗)提出的关于自然数的五条公理系统。根据这五条公理可以建立起一阶算术系统，也称皮亚诺算术系统；Morton次序、Row次序、Row-Prime次序、Hilbert-Peano次序为完全栅格结构的四种扫描顺序；Pi次序为栅格结构的扫描顺序；As shown in Figure 1, the present invention provides a kind of three-dimensional simulation method of spatial distance checking based on GIS, wherein, GIS is Geographic Information System (Geographic Information System, GIS); Delaunay triangulation is used for triangulating point set, It is an extremely important preprocessing technique for numerical analysis (such as finite element analysis) and graphics; the peano rule is a system of five axioms for natural numbers proposed by the mathematician Peano (Piaro). According to these five axioms, a first-order arithmetic system can be established, also known as Peano arithmetic system; Morton order, Row order, Row-Prime order, and Hilbert-Peano order are the four scanning orders of the complete grid structure; Pi order is grid The scanning order of the lattice structure;
方法包括如下步骤：The method includes the following steps:
步骤1.预处理GIS中的散乱点，得到点序列；Step 1. Preprocess the scattered points in the GIS to obtain a point sequence;
步骤2.根据点序列，初始化凸壳链表、边链表及三角链表；Step 2. According to the point sequence, initialize the convex hull linked list, edge linked list and triangular linked list;
步骤3.将未处理的散乱点加入三角网；Step 3. Add unprocessed scattered points to the triangular network;
步骤4.优化三角网，得到Delaunay三角网；Step 4. optimize triangular network, obtain Delaunay triangular network;
步骤5.根据Delaunay三角网，在GIS场景中进行空间距离计算并进行校验。Step 5. According to the Delaunay triangulation, calculate and verify the spatial distance in the GIS scene.
如图2所示，步骤1包括：As shown in Figure 2, step 1 includes:
1-1.在散乱点的点集中，筛选出y坐标值最小的点，并判断点的数量；1-1. In the point set of scattered points, filter out the point with the smallest y coordinate value, and judge the number of points;
若y坐标值最小的点只有1个，则该点为选点；If there is only one point with the smallest y coordinate value, then this point is the selected point;
若y坐标值最小的点大于1个，则选取其中x坐标最小的点为选点；If there are more than one point with the smallest y-coordinate value, select the point with the smallest x-coordinate value as the selected point;
1-2.连接选点与点集中其他各点，得到有向线段；1-2. Connect the selected point with other points in the point set to obtain a directed line segment;
1-3.分别计算各有向线段与正半轴的夹角值和长度；1-3. Calculate the angle value and length between each directed line segment and the positive semi-axis;
1-4.按夹角值的递增以及长度递减进行词典式排序，得到点序列。1-4. Perform dictionary sorting according to the increasing value of the included angle and the decreasing length to obtain the point sequence.
其中，散乱点的点集及预处理后的点序列均保存在有序点表中。Among them, the point set of scattered points and the preprocessed point sequence are stored in the ordered point table.
如图3所示，步骤2包括：As shown in Figure 3, step 2 includes:
2-1.在点序列中，依次查找不在有向边上的点，将第一个有向边添加到凸壳链表和边链表中，令凸壳链表中凸壳边数及边链表中的有向边数均为i-1；其中，i为点序列总数；2-1. In the point sequence, find the points that are not on the directed edge in turn, and add the first directed edge to the convex hull linked list and the edge linked list, so that the number of convex hull edges in the convex hull linked list and the number of edges in the edge linked list The number of directed edges is i-1; where i is the total number of point sequences;
2-2.将第二个有向边添加到边链表中，令边链表中的有向边数为i-2；2-2. Add the second directed edge to the edge list, so that the number of directed edges in the edge list is i-2;
2-3.将新产生的三角形添加到三角形链表中，并设置相关边的相邻三角形信息；令三角形链表中的三角形的数目为i-2；2-3. Add the newly generated triangle to the triangle list, and set the adjacent triangle information of the relevant side; let the number of triangles in the triangle list be i-2;
2-4.将选点添加到凸壳链表中；2-4. Add the selected points to the convex hull linked list;
2-5.输出凸壳链表、边链表及三角链表，初始化结束。2-5. Output the convex hull linked list, edge linked list and triangular linked list, and the initialization is completed.
其中，步骤3包括：Among them, step 3 includes:
依次判断未处理的散乱点是否已经联结成三角网；Determine whether the unprocessed scattered points have been connected into a triangular network in turn;
若是，并继续处理下一点；If so, proceed to the next point;
若否，则在凸壳链表中沿最后添加进去的有向边位置往前搜索直至凸壳链表结束，并修改相关边的相邻三角形信息，令凸壳链表中的凸壳边数+l，并继续处理下一点，直至所有散乱点都加入至三角网中。If not, search forward along the last added directed edge position in the convex hull linked list until the end of the convex hull linked list, and modify the adjacent triangle information of the relevant edge, so that the number of convex hull edges in the convex hull linked list+l, And continue to process the next point until all scattered points are added to the triangulation.
其中，步骤4包括：Among them, step 4 includes:
在三角网的联结过程中不断对子三角网进行优化处理、或将点集联结成三角网后再统一对边链表的每条边进行一次局部优化处理；形成Delaunay三角网。During the connection process of the triangular network, the sub-triangular network is continuously optimized, or the point set is connected into a triangular network, and then a local optimization is performed on each edge of the edge list to form a Delaunay triangular network.
其中，步骤5包括：Among them, step 5 includes:
5-1.计算线路中任一点与地形地物间广义距离dij(q)：5-1. Calculate the generalized distance dij (q) between any point in the line and the terrain and features:
其中，q为线路中任一点；xil为第l个点的第i维坐标；xjl为l个点的j维坐标；n为点的总数；l为1到n个点中的任意一点；Among them, q is any point in the line; xil is the i-th dimension coordinate of the l-th point; xjl is the j-dimensional coordinate of the l point; n is the total number of points;l is any point from 1 to n points ;
当q＝2时，该值为欧氏距离；When q=2, the value is Euclidean distance;
当q＝1时，该值为绝对距离、即城市街坊距离dij(1)：When q=1, the value is the absolute distance, that is, the city neighborhood distance dij (1):
当q→∞时，该值为契比雪夫距离dij(∞)：When q→∞, the value is the Chebyshev distance dij (∞):
dij(∞)＝max{|xil-xjl|} l＝1,2,...,n (3)dij (∞)＝max{|xil -xjl |} l＝1,2,...,n (3)
根据契比雪夫距离求出固定点之间距离，并根据极限逼近的方法求解导线与地形地物间最小距离；Calculate the distance between fixed points according to the Chebyshev distance, and solve the minimum distance between the wire and the terrain and features according to the method of limit approximation;
5-2.根据点到直线段距离的计算来确定点到线的距离dPL：5-2. Determine the distance dPL from the point to the line according to the calculation of the distance from the point to the straight line:
其中，L为线状物体；P为点状物体；dPx为点状物体P到线状物体L上任一点的距离；x为线状物体L上任一点；Among them, L is a linear object; P is a point object; dPx is the distance from the point object P to any point on the linear object L; x is any point on the linear object L;
5-3.根据两个线状物体L1，L2间的距离可以定义为L1中点P1(x1，y1)与L2中点P2(x2，y2)之间距离的极小值，且L1，L2均表现为折线；计算出线-线物体距离d：5-3. According to two linear objects L1, the distance between L2 can be defined as the minimum value of the distance between L1 midpoint P1(x1, y1) and L2 midpoint P2(x2, y2), and L1, L2 Both are shown as polylines; the line-line object distance d is calculated:
求得极大值，再计算方差曲线；Find the maximum value, and then calculate the variance curve;
5-4.设为角P1的度数；为角P2的度数；λ1为P1点的极角；λ2为P2点的极角；P为极点，球面三角形中点P1及P2中的以弧度计的两条边和一夹角已知：5-4. Set is the degree of angle P1; is the degree of angle P2; λ1 is the polar angle of P1 point; λ2 is the polar angle of P2 point; P is the pole, and the two sides and an included angle in radians of the midpoint P1 and P2 of the spherical triangle are known:
∠P＝λ1-λ2 (8)∠P＝λ1 -λ2 (8)
其中，PP1为球面三角形中的一边；PP2为球面三角形中的另一边；∠P为球面三角形中的两边夹角；Wherein, PP1 is one side in the spherical triangle; PP2 is the other side in the spherical triangle; ∠P is the angle between two sides in the spherical triangle;
则根据球面三角形的余弦定理，有：Then according to the cosine theorem of spherical triangles, we have:
其中，P1P2为弧度，且P1P2实际长度为R×cos-1(P1P2)，R为球面三角形半径；Among them, P1 P2 is radian, and the actual length of P1 P2 is R×cos-1 (P1 P2 ), R is the radius of spherical triangle;
根据球面三角形的余弦定理，有：According to the law of cosines of spherical triangles, there are:
cosPP3＝cosPP1cosP1P3+sinPP1sinP1P3cosP1 (10)cosPP3 = cosPP1 cosP1 P3 + sinPP1 sinP1 P3 cosP1 (10)
其中，P3为由P、P1、P3所组成的球面三角形中的一点，；为P3点的极角；Among them, P3 is a point in the spherical triangle formed by P, P1 and P3 ; is the polar angle of point P3;
若先给定则求得再由球面三角正弦定理求出∠P3；其中，∠P3为由P、P1、P3所组成的球面三角形中的P3点的度数；If first given then obtain Then obtain ∠P3 by the law of sine of spherical triangle; Wherein, ∠P3 is the degree of P3 points in the spherical triangle formed by P, P1 , P3 ;
再由耐普尔公式求出P1P3：Then calculate P1 P3 by Napier's formula:
5-5.根据peano规则，对于平面上规则分布的正方形格网点，采用旋转函数进行排列次序。5-5. According to the peano rule, for the square grid points regularly distributed on the plane, the rotation function is used to arrange the order.
其中，步骤5-5中的排列次序的方式包括：Wherein, the manner of ordering in step 5-5 comprises:
a.Morton次序和Pi次序将初始空间划分为用四叉树来表示的子空间；a. The Morton order and the Pi order divide the initial space into subspaces represented by quadtrees;
b.在Morton次序和Row次序中由空间坐标求得任何一个空间物体的顺序号和地址；b. Obtain the sequence number and address of any space object from the space coordinates in the Morton order and Row order;
c.在Pi次序和Row-Prime次序中，两者权值相等。c. In Pi order and Row-Prime order, the two weights are equal.
本发明提供一种基于GIS的空间距离校核三维仿真方法的具体应用例，具体包括：The present invention provides a specific application example of a GIS-based spatial distance check three-dimensional simulation method, which specifically includes:
首先对散乱点按有向角进行排序；First sort the scattered points according to the oriented angle;
以排序后的点顺序为基础，利用凸壳特性快速将散乱点联结成三角网；Based on the sorted point order, use the convex hull feature to quickly connect the scattered points into a triangular network;
最后利用拓扑结构快速将其优化为Delaunay三角网。Finally, it is quickly optimized into a Delaunay triangulation by using the topological structure.
在联网过程中，充分利用了有序点子集的凸壳特性，避免了所有的交点测试，从而保证了对散乱点集生成Delaunay三角网的效率。In the process of networking, the convex hull property of ordered point subsets is fully utilized, and all intersection tests are avoided, thereby ensuring the efficiency of generating Delaunay triangulation for scattered point sets.
算法的执行效率与数据结构之间存在密切的关系，为了提高优化处理的效率，本算法在数据结构方面，借鉴了拓扑原理，采用了简化的GIS多变性拓扑结构，该结构可以实现优化过程中点、边、三角形之间的快速相互索引，同时也作为TIN的输出数据结构，以便于GIS的应用，数据格式有如下四种:There is a close relationship between the execution efficiency of the algorithm and the data structure. In order to improve the efficiency of optimization processing, this algorithm uses the principle of topology for reference in terms of data structure, and adopts a simplified GIS variability topology structure, which can realize the optimization process. The fast mutual index between points, edges, and triangles is also used as the output data structure of TIN to facilitate the application of GIS. There are four data formats as follows:
(1)有序点表。该表保存散乱点集和预处理后的点序列。(1) Ordered point table. This table holds scattered point sets and preprocessed point sequences.
(2)有向边表。该表保存三角形的边以及与该边相邻的三角形信息，其中三角形信息用于局部优化计算。(2) Directed edge table. The table saves the side of the triangle and the information of the triangles adjacent to the side, where the triangle information is used for local optimization calculation.
(3)三角形表。该表保存生成的各个三角形的边信息和顶点信息。基于上述拓扑数据结构，由三角形可以查找构成这个三角形的有向边的点，以及此边被哪一个或两个三角形所使用，而三角形的优化处理往往是以边为着眼点的，因此这种数据结构非常适合三角网的优化处理。另外为了三角形网的快速联结，还需要下面的凸壳链表。(3) Triangle table. This table holds the edge information and vertex information of each generated triangle. Based on the above topological data structure, the triangle can find the point of the directed edge that constitutes the triangle, and which one or two triangles use this edge, and the optimization of the triangle usually focuses on the edge, so this kind of The data structure is very suitable for the optimized processing of triangulation. In addition, for the fast connection of the triangular network, the following convex hull linked list is also needed.
(4)凸壳边表。该表保存点集凸壳的边在边集中的位置。(4) Convex hull edge table. This table holds the position of the edges of the convex hull of the point set in the edge set.
利用上述四种数据结构，经过预处理、初始化、连结三角形、三角形优化四步，即可形成Delaunay三角网。Using the above four data structures, the Delaunay triangulation can be formed through four steps of preprocessing, initialization, triangle connection and triangle optimization.
(1)预处理：寻找出点集中y坐标最小的点p，如果这样的点不唯一，则选取其中x坐标最小的点。连接该点与点集中其他各点得到有向线段，计算线段与正半轴的夹角和长度，然后按夹角值的递增以及长度递减进行词典式排序。得到序列，根据凸壳的定义可以得知有向边一定是点集的凸壳上的一条边，即点p一定落在点序列的凸壳之外或在有向边形成的凸壳的外。(1) Preprocessing: Find the point p with the smallest y-coordinate in the out-point set. If such a point is not unique, select the point with the smallest x-coordinate. Connect this point with other points in the point set to obtain a directed line segment, calculate the angle and length between the line segment and the positive semi-axis, and then perform dictionary sorting according to the increasing value of the included angle and decreasing length. According to the definition of the convex hull, it can be known that the directed edge must be an edge on the convex hull of the point set, that is, the point p must fall outside the convex hull of the point sequence or outside the convex hull formed by the directed edge .
(2)初始化：用conv表示凸壳链表CList中凸壳边的数目，edge表示边链表EList中有向边的数目，triangle表示三角形链表TList中三角形的数目，与点集S的三角剖分计算相关的凸壳链CLISt、边链表EList和三角链表TList的初始化步骤如下:首先按照预处理后所得到的点序列，顺序查找第一个不在有向边上的点，将有向边添加到凸壳链表cList和边链表EList中，令convex＝i-1，edge＝i-1；将有向边添加到边链表EList。令edge＝i-2；将新产生的三角形添加到三角形链表TList中，设置相关边的相邻三角形信息。令triangle＝i-2；将p添加到凸壳链表CList，输出CList、EList和TList，初始化结束。(2) Initialization: use conv to represent the number of convex hull edges in the convex hull list CList, edge to represent the number of directed edges in the edge list EList, triangle to represent the number of triangles in the triangle list TList, and the triangulation calculation of the point set S The initialization steps of the related convex hull chain CLISt, edge list EList and triangular list TList are as follows: First, according to the point sequence obtained after preprocessing, the first point that is not on the directed edge is sequentially searched, and the directed edge is added to the convex hull chain. In the shell list cList and the edge list EList, let convex=i-1, edge=i-1; add the directed edge to the edge list EList. Set edge=i-2; add the newly generated triangle to the triangle list TList, and set the adjacent triangle information of the relevant edge. Let triangle=i-2; add p to the convex hull linked list CList, output CList, EList and TList, and the initialization ends.
(3)联结三角形：联结三角形是为了将未处理的散乱点加入到三角网，使得所有的点构成一个三角网。假设当前处理的点为p且已经联结成三角网，凸壳链表中最后添加进去的有向边位置往前搜索直至链表结束，修改相关边的相邻三角形信息，令triangle＝triangle+l，继续处理下一点，直至所有散乱点都处理完毕。(3) Connecting triangles: Connecting triangles is to add unprocessed scattered points to the triangular network, so that all points form a triangular network. Assuming that the currently processed point is p and has been connected into a triangular network, the position of the directed edge added last in the convex hull linked list is searched forward until the end of the linked list, and the adjacent triangle information of the relevant edge is modified, set triangle=triangle+l, continue Process the next point until all scattered points are processed.
根据上述可以得知，加入点联结合理三角形所需要的判断次数等于其产生的合理三According to the above, it can be known that the number of judgments required to join a point-connected rational triangle is equal to the reasonable three triangles generated by it.
角形个数加1，且凸壳链表极易维护，大大减少联结三角网所需时间。The number of angles is increased by 1, and the convex hull linked list is very easy to maintain, which greatly reduces the time required to connect the triangular network.
(4)三角形优化：由于按以上技术所联结的三角形不符合Delaunay三角网的条件，因此需要采用局部优化处理。优化过程可以在三角网联结的过程中不断对子三角网进行优化处理，也可以将点集联结成三角网后再统一对边链表的每条边进行一次局部优化处理。(4) Triangle optimization: Since the triangles connected by the above techniques do not meet the conditions of the Delaunay triangulation, local optimization is required. The optimization process can continuously optimize the sub-triangulation in the process of triangulation connection, and can also perform local optimization on each edge of the edge list after connecting the point sets into a triangulation.
形成Delaunay三角网后，地形地物信息已经完成了矢量化、数字化，可以直接提取各三角表面坐标，使用三维距离计算公式即可求出导线最大弧垂点到地形地物距离并进行校验。After the formation of the Delaunay triangulation, the terrain and features information has been vectorized and digitized, and the surface coordinates of each triangle can be directly extracted. Using the three-dimensional distance calculation formula, the distance from the maximum sag point of the wire to the terrain and features can be calculated and verified.
普通的距离计算采用三维空间欧式距离公式Ordinary distance calculations use the three-dimensional space Euclidean distance formula
D(AB)为两三角形间最短距离；D(AB) is the shortest distance between two triangles;
对该方法进行改进，首先计算线路中任一点与地形地物间广义距离To improve this method, first calculate the generalized distance between any point in the line and the terrain and features
当q＝2时，该值为欧氏距离；当q＝1时，该值为绝对距离(城市街坊距离)When q=2, the value is the Euclidean distance; when q=1, the value is the absolute distance (city neighborhood distance)
当q→∞时，称为契比雪夫距离When q→∞, it is called the Chebyshev distance
dij(∞)＝max{|xil-xjl|} l＝1,2,...,ndij (∞)＝max{|xil -xjl |} l＝1,2,...,n
利用契比雪夫距离可求出固定点之间距离，求解导线与地形地物间最小距离可使用极限逼近的方法。The distance between fixed points can be obtained by using the Chebyshev distance, and the method of limit approximation can be used to solve the minimum distance between the wire and the terrain and features.
点-线物体定义为点状物体(P)与线状物体(L)上的点之间的距离的最小值。在GIS中，线状物体一般是由折线来表示的，具有有限个数值点，因此可以通过点到直线段距离的计算来确定点到线的距离。A point-line object is defined as the minimum value of the distance between a point object (P) and a point on a line object (L). In GIS, linear objects are generally represented by polylines and have a limited number of numerical points. Therefore, the distance from a point to a line can be determined by calculating the distance from a point to a straight line.
两个线状物体L1，L2间的距离可以定义为L1中点P1(x1，y1)与L2中点P2(x2，y2)之间距离的极小值。因为L1，L2均表现为折线，因此对d的计算可以是先计算出L1，L2中折线线段对之间的距离，然后再从中挑出最小值。The distance between two linear objects L1, L2 can be defined as the minimum value of the distance between the midpoint P1(x1, y1) of L1 and the midpoint P2(x2, y2) of L2. Because both L1 and L2 are polylines, the calculation of d can be to calculate the distance between the polyline segment pairs in L1 and L2 first, and then pick out the minimum value.
同理可求出极大值，然后计算方差曲线。In the same way, the maximum value can be obtained, and then the variance curve can be calculated.
设P为极点，球面三角形P1、P2中两条边(以弧度计)和一夹角已知：Assume P is the pole, and the two sides (in radians) and an included angle in spherical triangles P1 and P2 are known:
∠P＝λ1-λ2∠P＝λ1 -λ2
根据球面三角形的余弦定理，有According to the law of cosines of spherical triangles, we have
球面三角形计算原理中P1P2为弧度，实际长度为R×cos-1(P1P2)；In the calculation principle of spherical triangle, P1 P2 is radian, and the actual length is R×cos-1 (P1 P2 );
cosPP3＝cosPP1cosP1P3+sinPP1sinP1P3cosP1cosPP3 ＝cosPP1 cosP1 P3 +sinPP1 sinP1 P3 cosP1
如先给定则可先求出再由球面三角正弦定理求出∠P3as given can be obtained first Then calculate ∠P3 by the sine theorem of spherical trigonometry
再由下式(耐普尔公式)求出P1P3:Then P1 P3 is obtained by the following formula (Nippur's formula):
根据peano规则，即对于平面上规则分布的正方形格网点，可以有多种变换(排列)次序。According to the Peano rule, that is, for the square grid points regularly distributed on the plane, there can be multiple transformation (arrangement) orders.
(1)Morton次序和Pi次序将初始空间划分成可以用四叉树来表示的子空间；(1) Morton order and Pi order divide the initial space into subspaces that can be represented by quadtrees;
(2)在Morton次序和Row次序中很容易由空间坐标求得任何一个空间物体的顺序号和地址；(2) In the Morton order and Row order, it is easy to obtain the sequence number and address of any space object from the space coordinates;
(3)在Pi次序和Row-Prime次序中，两者权值相等。(3) In the Pi order and the Row-Prime order, the two weights are equal.
根据此规则采用旋转函数进行变化，保证旋转函数不会随曲线的平移而发生变化。According to this rule, the rotation function is used to make changes to ensure that the rotation function will not change with the translation of the curve.
根据旋转函数变换多义线的方法进行变换后即可度量两曲线间最短距离；The shortest distance between two curves can be measured after transformation by the method of transforming the polyline according to the rotation function;
如图4所示，根据旋转函数度量最短距离的方法，沿虚线方向纵坐标差值即为所求距离。As shown in Figure 4, according to the method of measuring the shortest distance by the rotation function, the difference in the ordinate along the dotted line is the desired distance.
以上实施例仅用以说明本发明的技术方案而非对其限制，尽管参照上述实施例对本发明进行了详细的说明，所属领域的普通技术人员依然可以对本发明的具体实施方式进行修改或者等同替换，而这些未脱离本发明精神和范围的任何修改或者等同替换，其均在申请待批的本发明的权利要求保护范围之内。The above embodiments are only used to illustrate the technical solutions of the present invention and not to limit them. Although the present invention has been described in detail with reference to the above embodiments, those of ordinary skill in the art can still modify or equivalently replace the specific embodiments of the present invention. , and any modifications or equivalent replacements that do not deviate from the spirit and scope of the present invention are all within the protection scope of the claims of the pending application of the present invention.
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| CN201510639472.6ACN106557602B (en) | 2015-09-30 | 2015-09-30 | Spatial distance checking three-dimensional simulation method based on GIS |
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