Mesh problem

Hi! May I get some guidance on the following problem please?

I have mesh circle of 8 points, and their center-point.
1 I need to turn it into mesh of 4 quads, which share the center-point as one of their vertices
2 Then, I need to extrude it (see picture below)
3 sometimes, the 8 points are not all part of the convex hull (see second picture below). How can I make it so that the quad-making is always ‘good’ (convex shape, like the quadding on the right), not ‘bad’ (concave, like the quaking on the left) (in other words, how can I make all the quads convex hull of the 4 points they use?)
mesh (5.0 KB)

What I already tried:
1 I use the MakeQuad function, but it gives me ‘Face’, which is not actually quad?
Then found that the faces are in the form Q(list of indices of points), but the points (like in the internalized data in attached gh file) already have some random indices, so when I plug in the ‘Face’ to the Construct Mesh function, the function thinks I have 100 indices (because these points have such huge index numbers), and won’t run
2 use brep first, then convert to quad. The problem is, a BREP ‘quad’ turns into 6-vertex mesh (extra line cutting through it) that I can’t get rid of, and I want to avoid that (it’s unnecessary geometry I really want to avoid)

Thanks so much!

Sort the verts along curve, dispatch them and connect them to the center point.
Rebuild the mesh.

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Thanks for your reply! I don’t understand the following:
1 what should the sort keys be? Is the sorting just to give them new indices?
Also, 8 of the 9 points are part of the contour, but the point inside is not on the curve
2 how does ‘connect them to the center point’ work?
As in using Make Quad to construct mesh?

Show your gh with points

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I think I found a rough solution. Thanks for your help!