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This paper analyzes the convex hull of the parametric curve $\left(t, t^2,\cdots, t^N\right)$, where $t$ is in a closed interval. It finds that everypoint in the convex hull is representable as a convex combination of$\frac{N+1}{2}$ points on the curve. It also finds that the evaluation of theconvex combination is a homeomorphism from the convex combinations of$\frac{N+1}{2}$ points on the curve to the convex hull of the curve, as long asthe points are listed in increasing order, and as long as two representationsthat are reachable from each other by removing terms with coefficient zero,combining terms with the same point, the inverses of these operations, or asequence of these operations in any order, are considered to be equivalent.

Convex Hull of $\left(t, t^2, \cdots, t^N\right)$