Is there some purpose for this endeavor? I once wrote a program that was used to compute highway construction fill quantities. I don't remember what method I used, probably Green's theorem, as the shoelace doesn't ring any bells. One important note: the origin chosen should lie close to the center of the area one wishes to measure, for the most accurate results.
On Fri, Mar 8, 2019 at 2:24 AM Ralph Boland rpboland@gmail.com wrote:
In Squeak should the vertices of a polygon be listed in clockwise or counter-clockwise order? Note that I am not concerned about which is best, just which Squeak uses. I need to make a choice in order to compute the areas of polygons and the algorithms that do this negate the area if you process the vertices in the opposite order.
Note that it is not sufficient to just take the absolute value of the result of computing the area because I have to deal with a polygon being cut into two parts by a line seqment (a chord). Which of the two parts of the polygon I want the area of is determined by the ordering of the vertices of the polygon and also the ordering of the the vertices of the line segment. Reversing the ordering of the vertices of either switches the subpolygon chosen. Reversing both has no affect because the two switches cancel.
So I have to make a choice and live with it. I want my choice to be consistent with any similar choice made in Squeak code.
If none of the Squeak code depends on polygon vertices ordering then I would like to hear opinions on the matter so at least I can a decision that is at least better then arbitrary.
Note that mathematics doesn't seem to help much here. The shoelace algorithm for computing the area of a polygon and Green's theorem both use a counter-clockwise orientation. However simple integration to determine the area under a curve implies a clockwise orientation (adding areas under each edge of the polygon when going left to right and subtracting when going right to left implied a clockwise orientation).
Thanks
Ralph Boland _______________________________________________ Beginners mailing list Beginners@lists.squeakfoundation.org http://lists.squeakfoundation.org/mailman/listinfo/beginners