convex combination

A blend of points, each weighted nonnegatively, with the weights summing to exactly 1.

A convex combination of points $x_1,\dots,x_k\in\mathbb R^n$ is a point $\theta_1x_1+\cdots+\theta_kx_k$ with $\theta_i\ge0$ for every $i$ and $\sum_i\theta_i=1$ . For $k=2$ this traces exactly the straight segment between $x_1$ and $x_2$ as $\theta_1$ sweeps from $0$ to $1$ ; a set is convex exactly when it contains every convex combination of its own points.