Tomas Nally, P.E. on behalf of Tomas Nally, P.E. wrote:(snip)
> -- Now, going clockwise around the perimeter of the polygon,
> -- find the area of the virtual trapezoid under each line segment.
> -- A line segment is defined as the segment connecting
> -- the ith node and the (i + 1)th node. Do this inside a
> -- counted loop. In BASIC, a convenient loop for this is
> -- the For...Next loop.
>
> for i = 1 to (n - 1) -- note that I'm stopping at (n - 1)
> x1 = x(i)
> y1 = y(i)
> x2 = x(i + 1)
> y2 = y(i + 1)
> trapArea(i) = y1 * (x2 - x1) + (1/2) * (x2 - x1) * (y2 - y1)
> next i
>
> -- This doesn't quite "close the loop" around the perimeter
> -- of the polygon. In order to close the loop, we need to
> -- find the area under the line segment between the nth
> -- node and the very first node.
>
> x1 = x(n)
> y1 = y(n)
> x2 = x(1)
> y2 = y(1)
> trapArea(n) = y1 * (x2 - x1) + (1/2) * (x2 - x1) * (y2 - y1)
>
> -- Now, we have to add up all the areas of the elements
>
> TotalArea = 0
> for i = 1 to n
> TotalArea = TotalArea + trapArea(i)
> next i
>
For anyone interested, this BASIC program is equivalent to the Transcript program I posted last Tuesday:
on mouseUp
put field 1 into tList
put 0 into area
put line 1 of tList into pOld
repeat with i = 1 to the number of lines in tList
put line i of tList into pNew
add thisToArea(pNew,pOld) to area
put pNew into pOld
end repeat
put area
end mouseUpfunction thisToArea ptNew,ptOld put item 1 of ptNew into xNew put item 2 of ptNew into yNew put item 1 of ptOld into xOld put item 2 of ptOld into yOld return -(xNew - xOld)*(yNew + yOld)/2 end thisToArea
And it is also equivalent to the solution posted by Ray Griffith on the last installment of this list, although his is more efficient and nifty as hell.
If anyone is interested, this method, sometimes call Newton's approximation, may be extended to calculate the area under any curve by treating the curve as a sequence of straight line segments (open polygon--so to speak). In effect it performs an integration. (When you have a curve which closes on itself, the integral under the closed curve is the *positive* area under the upper portion of the curve, plus the *negative* area under the bottom portion of the curve. The difference is the area inside the curve.)
I'm sure that last parenthetical statement is incomprehensible. But sometimes it is wiser to simply abandon hopeless projects rather than attempt redemption.
Jim _______________________________________________ use-revolution mailing list [EMAIL PROTECTED] http://lists.runrev.com/mailman/listinfo/use-revolution
