Date: Mon, 13 Aug 2001 13:08:47 +0200 To: efg2@efg2.com From: Frank vhV Subject: ComputerLab Feedback Dear Earl, First of all I want to thank you for your information on your EFG page. It has already helped me through some graphical problems (graphical problems are not my normal type of problems as I am a chemical engineer). I refer to your example of polygon and centroid lab report : Area and centroid of a Non-Convex Polygon. Your example uses Green's theorem where a is calculated as a subtraction of two products (X1*Y2 - X2*Y1) (Forgive me that I do not use subscripts as Eudora does not allow me to do so but you'll understand anyway ;-) This is nice for X and Y values lower than say 1.0E6 (like pixel coordinates). However when this theorem is used to calculate the area of polygons that have vertices that represent "real" data (e.g. map absolute coordinate points that represent a gas cloud contour) that exceed 1.0E6, the error will quickly increase because the product of both terms in Green's formula are getting so big (1.0E12 or larger) that subtraction of these two large terms may result in unexpected deviations when using Delphi's Double type of variable. A double variable has 15 or 16 significant digits. Try this example: Area := 3/4 - 2/3 ; Area := (1.0E12+3/4) - (1.0E12+2/3) ; Both answers will differ. Maybe you could put some extra information on your Internet page that explains about this behavior when people apply this theorem on data points that have a large absolute values. Regards, Frank.