Positivity and convex-hull conjecture for converted matrix weighted rational Bézier curves

Let a matrix weighted rational Bézier curve be defined by Equation, with weight matrices given by Equation or Equation. Let the real weights be computed by Equation or Equation.

Positivity and convex-hull conjecture. The real weights are positive, and the convex hull of the original matrix weighted rational Bézier curve can be computed as the convex hull of the control points of the converted rational Bézier curve.

The conjecture would provide a sufficient positivity condition for computing the convex hull of the original curve from the control points of its converted rational Bézier curve. The authors report that all experiments support positivity, but state that a proof is not currently available.