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# Euclidean Distances on the Raster

Distance is measured between two points. The two points used when measuring distance on a raster (or grid) are the centers of two specific cells. That is, in the case of the raster, the measurements are made from cell center to cell center. See Figure 8-9.

FIGURE 8-9 Distance is measured from cell center to cell center If the cell size is 50, the distance shown would be 200, spanning all or parts of five cells.

For another example, if you had a raster that had cells of size 10 and 1000 columns, the longest east-west distance measurement would be 9990.

The most fundamental “distance raster” is one in which there is a single “source” cell and all other cells indicate the distance from that cell.

Measurements are made from cell center to cell center, regardless of intervening cells or the angle of the line connecting the two cells of interest. The distance is calculated by the law of Pythagoras, who, despite having lived 200 years before Euclid, determined that the hypotenuse of a right triangle is the square root of the sums of the squares of the other two sides.

As illustrated in Figure 8-10, the area of the square on the hypotenuse is the sum of the areas of the squares on the other two sides.

FIGURE 8-10 The law of Pythagoras (the Pythagorean theorem)

When you put the law of Pythagoras (also known as the Pythagorean theorem) together with ...

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