PLOTTING DEPTH CONTOURS BASED ON GRID DATA IN IRREGULAR PLOTTING AREAS

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1 PLOTTING DEPTH CONTOURS BASED ON GRID DATA IN IRREGULAR PLOTTING AREAS Zhang, L., Li, S. and Li, Y. Department of Hydrography and Cartography,Dalian Naval Academy, 667, Jiefang Road, Dalian, Liaoning, 68, P.R.China. ABSTRACT Grid Contouring, which is a method based on regular grid data, can be used to plot depth contours by computers, but it is necessary for soundings to distribute over whole plotting area, and the border of the plotting area must be a regular rectangle. When areas of bathymetric survey are irregular, the method based on TIN (Triangular irregular network) is usually used to plot depth contours in the past. In China, grid soundings must be provided to the users after a bathymetric survey of port engineer, so the method of contouring from grid data is used to plot depth contours. However, Surveying areas are usually irregular, and it is possible to lack of depth data in some place of the surveying area. So the problem that depth contours is plotted based on grid data in irregular plotting areas should be solved. In this paper, the algorithm of grid contouring is introduced, including the interpolation of the values of the depth at specific grid node, calculating of positions of points of equal depth for each side and tracing of equal depth points. Plotting depth contours in irregular plotting areas is analyzed and studied, and a series of measures applied in the areas are put forward, such as special processes to the sounding interpolation, definition of border depths, determination of equal depth points and double-directions tracing of contours, etc. Especially the double-directions tracing method, which solves the difficult and complex problem determining beginning and end points of unclosed contours, is introduced in detail.. INTRODUCTION The depth contours are effective graphic means used to represent the features of the seabed and to describe the seafloor topography on the two-dimension plane. Regular Grid Contouring is one of common methods to plot contours, and the problem that how to apply it to plot depth contours automatically in hydrographical and marine engineering surveying is significant. In Grid Contouring, irregular discrete data are transforms into regular grid points data by interpolating at first, then nodes of contours and grid sides are calculated, and starting points of contours are searched for and other equal value points are traced, Contours are smoothed and plotted finally. Grid Contouring used in the regular plotting areas is introduced in detail in some books (e.g. Reference and ), but it has not been simply applied in the irregular areas. Grid Contouring used to draw depth contours in the past, the plotting area of which is always rectangle or square. In practice, it might be not such case. For example, first, in some place of an area including islands and rocks, it is impossible to be surveyed in some parts of the area, so there might be lack depth data in some parts. Second, when channels and harbors are surveyed, the surveyed area is likely to be irregular. Third, some areas might not have data because of the omission in bathymetric surveying. Therefore, we must deal with these irregular areas especially in order to plot right depth contours in Grid Contouring. In this paper, the method of Grid Contouring is improved so that it can be used plot depth contours in the irregular areas, and good results are achieved by practical applications. Figure. Interpolation of equal value points in grid sides Proceedings of the st International Cartographic Conference (ICC) Durban, South Africa, 6 August Cartographic Renaissance Hosted by The International Cartographic Association (ICA) ISBN: Produced by: Document Transformation Technologies

2 . THE BASIC PRINCIPLES OF GRID CONTOURING Grid Contouring, which is based on regular grid data. If the data is irregular initial soundings, they must be transferred into regular grid data by interpolation. Suppose all grids are marked j =,,, n along X axis and i =,,, n along Y in a plotting area, it exists m n grid data points. The depth of each grid can be expressed with S i,, and there are ( m ) n vertical sides and ( n ) m horizontal sides in the area, as Figure shows.. Interpolation of equal value points When prepare to plot a group of contours, we need to use depth data of grid points mentioned above and work out the position of every equal value point of a depth contour by linear interpolating. Given the value of a depth contour plotted is W, only if W is between the depth values of two neighboring grid points, there is an equivalent depth point in the grid side which contains the two points. The criteria for judgment are as follows: () If ( S ) ( S j + ) ), there is an equivalent depth t in the horizontal side; () If S ) ( S ( i +, ), there is an equivalent depth in the vertical side. In Figure, the position of the equivalent depth point is S in the horizontal side, as well as H in the vertical side. The depth value of grid points A, B, C and D are S (, i, S(, i j+ ), S( i+, j+ ) and S ( i+, respectively.. Equal value points trace and coordinates calculation The plane positions( S and H ) of all equal value points in a depth contour are calculated, in turn, these equal value points are arranged to orderly sets in unclosed or closed contours. Because there might be two or more equivalent points in a grid cell, S and H must be analyzed and method of connecting the points must be determined, which avoids intersection of traced contours... Determination of trace direction As Figure shows, two equal value points a and a are found out in two arbitrary neighboring grid unit I and II, there is a in the neighboring side of grid cell I and II, and a in other sides of grid cell II. If No. of grid I is represented with ( i,, No. of grid II might be ( i +,, ( i, j + ), ( i, and ( i, j )... Specific judgment for tracing equal value points To a contour, if two equal value points such as a and a have been found Figure. Determination of trace direction out, we can trace the third equal value point a following certain rules. The details are abbreviated... Coordinates calculation of equal value points Once find the equal value point a, we can calculate absolute coordinates of point a by corresponding formula...4 Searching for starting points of depth contours To the closed curve, wherever start to trace the equal value points from, we will be back to the starting point after a complete tracing, and a closed curve will be formed. Thus, we can do this job from every point of the curve. However, to the unclosed curve, we usually trace from the starting point in order not to break up the depth contours and to form an integral one. To the unclosed curve, we search the starting point in four sides of map border at first. If a point are found out, that is a point represented a. Suppose a point a based on the rule of determination of trace direction, we can continue to search a point a. Then a is regarded as new a, and a is regarded as new a, new a will be found out. When all contours that start from the border have been searched, the remains are closed contours. For more details, see reference I and II.

3 . SPECIAL TREATMENTS WITH IRREGULAR AREAS When plot depth contours in irregular plotting areas, instead of drawing with general algorithm simply, we should do a series of special treatments such as data interpolation and calculating positions of the equivalent depth points.. Data interpolation Although soundings of bathymetric surveying distribute over irregular area, we still interpolate depth in all grid points as on some regular area. Given a distance r, if a area, which based on a grid point as circle center and r as radius, doesn t exist initial depth points, the grid point is regarded as a blank point and specially marked, and the point doesn t display when output grid depths. By such method, regular grid depth coming from irregular point, which distribute over irregular plotting area, and there are specially marked as blank points in the area.. Border depth of the area As far as the chart of regular areas with entire depth records is concerned, the boundary of it is rectangle. However, the case is more complicated in irregular areas. After data Interpolated, if some depth, which is not continuous with ambient depth, namely is that a neighboring point might be blank point at least. The depth is named as depth of border of the area in this paper. Figure. Border depth of the area Since the depth contour is a continuous planar curve, it will only be broken up on the border of the bathymetric surveying area on the chart. To the depth of the border of the area, it is not only the points that need to be hunted in searching starting points of unclosed depth contours, but also effective control points, which prevent the deep contour from extending to the blank area without sounding points.. Calculation of equivalent depths interpolated It is necessary to work out all S and H in the process of calculating equal value points on in the plotting area. In the same time, < S < and < H < are thought of as conditions whether a grid side exists a equal value point or not. After judgment, grid sides which threaded by the contour are marked with -, namely is S =- or H =-. Thus, the grid sides, which exist equal value points, can be distinguished from those do not. The same method is used in grid sides that exist border depth of the area..4 Decision of the starting point of unclosed depth contours and the two-directions tracing of equal value points Grid Contouring used in a regular area, the area of discrete points data is larger than the plotting one in order to calculate all grid nodes of regular grid contour. Grid Contouring in regular area was mainly discussed in the past, the starting points of unclosed depth contours must be in the 4 borders because the plotting area was square or rectangle. Then, if we started from the 4 borders, the problem of tracing on unclosed depth contours would be solved naturally. However, the plotting area is usually irregular in the bathymetric surveying, and data can t suffuse all the area in the actual case. Therefore, the decision on the starting points of unclosed depth contours differs from in the regular plotting area, and the past tracing algorithm of equal value points in regular areas is not suit for irregular ones. The following is the algorithm of decision on starting points of unclosed depth contours, which is defined as the two-direction tracing of equal value points.

4 As to the equal value points tracing of Grid Contouring, the unclosed contours and closed are distinguished in the methods discussed in the past. To the unclosed depth contours, first the starting points are found out, then trace from it in sequence until to the end point. To the closed, trace from an equal value point of it until back to the starting point. Considering the difference of irregular areas, the following method of towdirections tracing, treats unclosed and closed depth contours in the same means, which can be used. The basic theory is, to a depth contour, scan each horizontal side of and see if there is an equal value points threading through; if there are an equal value point in some side, the side is regarded as the starting side. Then trace equal value points from the side and remain the value of the points until which the contour has been traced. If the depth contour is closed, it is bound to back to this side. As Figure 4 shows, a contour is found to pass through the side AB in the scanning, the side is regarded as the starting side, the searching start from No., and trace No., No.,No.4,No.5,No.6,No.7,No.8,No9 successively, then go back to the side AB, which is process of searching of a close contour. If a contour is unclosed, the searching must be trace to border of the area, then should go back to the starting point, and trace from opposite direction. If the tracing cannot continue, the starting side is a border, or traces the other half of the contour. After all traced points of the other half of the contour are sorted in opposite order, an unclosed contour come by combining and the two half. From Figure 4, we find a contour pass through side CD in the scanning. The side is look on as starting side and No. is found, No., No., No.4, No.5, No.6 and No.7 can also be found in sequence until border is arrived. Because of not going back to starting point, it is an unclosed contour. The searching should go back to side CD and tracing should be continued in opposite direction, No.8, No.9 and No. are found until other border are arrived. Thus, all equal value points of a whole contour have been traced. Then the traced points of the last half should be sorted in opposite order, namely is No. No.9 No.8 No.. The two half are combined and a whole contour comes at last. The closed and unclosed curve can be traced at same time in the method. 4. CONCLUSION Because Surveying areas are usually irregular and it is possible to lack of depth data in some place of the surveying area, the problem that depth contours is plotted based on grid data in irregular plotting areas are studied in the paper. Especially the double-directions tracing method, which solves the difficult and complex problem determining beginning and end points of unclosed contours, is introduced in detail. 5. REFERENCES Figure 4. Two-directions tracing of equal value points [] Hu you-yuan, Huang xing-yuan et al. Computer Mapping.BeiJing: Surveying and Mapping press(987) [] Wang Lai-Sheng et al. computer Algorithm and programmes of larger-scale topographical map: Surveying and Mapping press(99) [] ZHANG Li-hua, YIN Xiao-dong. Digital Hydrographical Surveying and Mapping. Da Lian: Da Lian Naval Academy Press( ) [4] Wang Lai-Sheng et al. Computer Algorithm and Programmes of Larger-scale Topographical Map. BeiJing: Surveying and Mapping press(99.) [5] H.S.B MAT ZIN, J.McMANUS and R.W DUCK. Methods of Gridding Bathymetric Data for the Study of Seafloor Topographic Changes. The 9 th Internatoal Symposium of the Hydrographic Society.

5 PLOTTING DEPTH CONTOURS BASED ON GRID DATA IN IRREGULAR PLOTTING AREAS Zhang, L., Li, S. and Li, Y. Department of Hydrography and Cartography,Dalian Naval Academy, 667, Jiefang Road, Dalian, Liaoning, 68, P.R.China. Biography: Zhang Lihua(97-), male, engineer, master, major research direction: automatic data process of hydrographic survey and visualization techniques of seafloor terrain. He has published over papers. His representative achievement is digital bathymetric surveying and mapping.

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