When the lines are close together the magnitude of the gradient is large: the variation is steep. The gradient of the function is always perpendicular to the contour lines. The contour interval of a contour map is the difference in elevation between successive contour lines. ![]() A contour map is a map illustrated with contour lines, for example a topographic map, which thus shows valleys and hills, and the steepness or gentleness of slopes. In cartography, a contour line (often just called a "contour") joins points of equal elevation (height) above a given level, such as mean sea level. More generally, a contour line for a function of two variables is a curve connecting points where the function has the same particular value. It is a plane section of the three-dimensional graph of the function f ( x, y ) -plane. Retaining wall heights for proposed routes AB and EF would be moderate compared to CD.A two-dimensional contour graph of the three-dimensional surface in the above picture.Ī contour line (also isoline, isopleth, or isarithm) of a function of two variables is a curve along which the function has a constant value, so that the curve joins points of equal value. This indicates steep slopes and costly and high retaining walls. Contours for the most part are tightly packed along CD. A large retaining wall is needed in this section. Contours 120 and 130 are locate just north of the road CD. The northwestern end of route CD goes through contour 110. The drainage infrastructure build up costs would be less for CD. Drainage to route EF would be higher than route AB, therefore drainage costs for the route EF would be higher than AB. ![]() Since on site cut material could be used, the cost could be cheaper.Īs per contours given, the hills to the north would drain to the proposed routes AB and EF. It can be argued that the cut from the northwestern end can be utilized for the fill in the southeast end of the road. EF route needs more fill than AB route.ĬD-The CD route has plenty of cut (the northwestern end) while the southeast requires fill. The proposed route requires a large amount of fill that needs to be brought in from outside.ĮF-Proposed road EF goes mostly through 60 and 70. When the proposed road passes through 80 and 70 contours, fill is needed to bring it to 90 ft. ![]() Perimeter-Area RelationshipĪB-The proposed road elevation is at 90 ft, AB passes mostly through contours 80 and 70. The average value of the map is then taken to be the fractal dimension of the surface. This method improves the accuracy of computing the fractal dimension of a surface by computing the fractal dimension of the vertical slices in the x- and y-directions plus 1, and generating a new map of the fractal dimensions created where each point is defined by the average fractal dimensions of the two profiles intersecting at that position. Another choice can be made with regard to the 1D algorithm used to compute the fractal dimensions. ![]() To add flexibility, this technique can be implemented with the possibility of computing either or both directions (rows and/or columns) and to consider only a limited number of slices. This approach considers the fractal dimension of the surface to be the normal average of all the vertical slices in the x- and y-directions plus 1. The results are generally close to those computed using the box counting method for fractal dimensions between 2.1 and 2.4.
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