Conical Combination
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Conical Combination

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The conical hull of a set S is a convex set. In fact, it is the intersection of all convex cones containing S plus the origin. If S is a compact set (in particular, when it is a finite set of points), then the condition "plus the origin" is unnecessary. If we discard the origin, we can divide all coefficients by their sum to see that a conical combination is a convex combination scaled by a positive factor. In the plane, the conical hull of a circle passing through the origin is the open half-plane defined by the tangent line to the circle at the origin. Therefore, the "conical combination" an...