Question

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?

Answer 1

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?