> James H. wrote: > Multiplying this out you get: > > x(i)*y(i+1) - x(i+1)y(i) + [x(i+1)* y(i+1) - x(i)* y(i)] > > So THE SAME EXPRESSION as in the centroid method EXCEPT for the added term in > square brackets. So, WHY THE DIFFERENCE? > > In calculating this sum all of the intermediate terms in the sum cancel out, > leaving just the end terms: x(n)y(n) - x(1)* y(1) > But if the figure is closed, they too cancel each other.
Very clear explanation (it's in fact a proof) of the 'shoelace'-formula. > James H. wrote: > The center of mass bears no relation to the mass, and the centroid of a > closed curved bears no relation to the area. The connection between the centroid and the Area is purely 'scottish'. We need the terms of the area-sum for centroid's computation and have by that the area computed as a by-product. Because we are canny as the Scots (and the people from Southern Germany and Switzerland) we don't waste it, but return it too. If one takes a simple flat map (no relief), a centroid is good as a *first* approximation where to have a central storage that is the origin of catering goods for a certain region. Likewise one could use the centroid as an approximate good place for a time-and-cost sparing residence in a state or country. _______________________________________________ use-livecode mailing list use-livecode@lists.runrev.com Please visit this url to subscribe, unsubscribe and manage your subscription preferences: http://lists.runrev.com/mailman/listinfo/use-livecode
