Given a sequence of (integer, integer) points, say (p1, ..., pn), which define the lines (p_i, p_i+1) for 1 <= i < n, plus the line (p_n, p_1). The resulting lines have the additional property that they don't intersect pairwise. What would be the best way to calculate the resulting volume?
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Sergey Kalinichenko
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Jo So
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1Just to clarify: You are asking for an algorithm to calculate the area of a 2D polygon, right? Have you looked at the relevant [Wikipedia article](http://en.wikipedia.org/wiki/Polygon#Area_and_centroid)? – thiton Dec 05 '11 at 15:13
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Duplicate of http://stackoverflow.com/questions/451426/how-do-i-calculate-the-surface-area-of-a-2d-polygon. – Per Dec 05 '11 at 15:32
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@thiton thanks for pointing to the right direction. – Jo So Dec 05 '11 at 16:22
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Here is a nice code blurb with explanations as to why it works: http://alienryderflex.com/polygon_area/
// Public-domain function by Darel Rex Finley, 2006.
double polygonArea(double *X, double *Y, int points) {
double area=0. ;
int i, j=points-1 ;
for (i=0; i<points; i++) {
area+=(X[j]+X[i])*(Y[j]-Y[i]); j=i; }
return area*.5; }
You should also read the previous incarnation of this question: How do I calculate the area of a 2d polygon?
