Given a set of \(k\) points \(x_1, x_2, \dots x_k\), the convex combination of the points is a point of the form \(\theta_1 x_1 + \theta_2 x_2 + \dots + \theta_k x_k\) such that for \(i = 1 \dots k\), \(\theta_i \geq 0\) and \(\sum_{i=1}^{k} \theta_i = 1\).