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I settled on an ArcForm expression whose arguments are the list of ycoordinate values of the connection points, and lists of endpoint indices for the left and right arcs.

This simply involves finding the minimum and maximum xcoordinate and minimum and maximum ycoordinate of each pixel in a given component.

For each connected component, and for each xcoordinate in its box, determine the average ycoordinate, and put a black pixel in the new image at the (x, average y) point.

Obviously, initially this result will be the ycoordinate of the chosen pixel.

The ycoordinate is not transformed because we are only straightening the image based on the tilt of the left and right margins.

For every line, compute the topmost (smallest) ycoordinate (topY) and bottommost (largest) ycoordinate (botY).

Order the lines in the array by their first ycoordinate (lowest first).

Set up a new array of 30 yvalues, and initialize each element to the ycoordinate of the chosen pixel.

Then the length of the vertical side is simply the ycoordinate of its endpoint, A, and the length of the horizontal side is the xcoordinate of its endpoint, B.

Mathematicians attach a minus sign to the xcoordinates of all the points to the left of the yaxis (i.e., the “east side”), and to the ycoordinate of all points which lie below the xaxis (i.e., the “south side”).
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