VectorD PrincipalOrientationCenter(out PointD center) // The principle orientation is one of the eigenvectors of the covariance matrix { double meanX, meanY; double[,] covariance = CovarianceMatrix(out meanX, out meanY); center = new PointD(meanX, meanY); // double a = covariance[0,0], b = covariance[0,1]; double c = covariance[1,0], d = covariance[1,1]; // double r = Math.Sqrt(a*a + 4*b*c - 2*a*d + d*d); double n = (a - d + r); Debug.Assert(n >= 0); double x = n / (2 * c); // if (!x.IsFinite()) { // Y does not vary with X: all X's look the same so far as Y is concerned // double width = this.Vertices.Max(v => v.Location.X) - this.Vertices.Min(v => v.Location.X); double height = this.Vertices.Max(v => v.Location.Y) - this.Vertices.Min(v => v.Location.Y); if (width > height) return new VectorD(1, 0); else return new VectorD(0, 1); } else { VectorD eigenVector = new VectorD(x, 1) * Math.Sign(c); return eigenVector.Unit(); } }