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Computing Contour Areas

Once each contour is defined by a set of coordinate pairs, the areas can be computed by numerically integrating around each contour. Computing area by the Trapezoid Rule is:

A = Sum { 1/2(xi + xi-1) * (yi - yi-1) }

Prior to the use of digitizing tablets and planimetering software, the two methods for computing contour areas were counting squares and the use of a mechanical planimeter. In counting squares, a square grid is overlaid over the maps, the number of squares in each contour is counted and then multiplied by the square area. Not only is this method very time consuming to count the squares, but accuracy is lost counting squares along the contour boundaries.

Using a digitizing tablet with the PLAN 2002 software is very similar to a mechanical planimeter with a few very important differences. In terms of accuracy, the two methods are identical. A mechanical planimeter integrates the areas along the contour. Digitized contours integrated along (x,y) coordinates which if they are closely spaced and sufficiently accurate will greatly exceed the error introduced by tracing the curve. In terms of speed, the two methods are similar in regard to tracing curves. However, the computer is faster in computing areas and volumes because all calculations are handled by computer software. Mechanical planimeters require much work and time by the analysts to compute areas. Computer software is more dependable because these is less chance for error in the area calculations. As mentioned above, quality control is enhanced by the ability to print or plot the map. Another benefit of the computer is that the digitized maps are saved, when future changes are made to the map, only those contours that have been changed need to be redigitized. Thus computer planimetering software holds many advantages over mechanical planimeters.

 

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Further      Information &  Examples

Planimeter Software

Plan 2002, p1

Plan 2002, p2

Plan Plus 2002

 

First Example

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Digitizing Maps

Contour Areas

Pitfalls

Computing Volumes