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Curved Surface through control points.

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Hey there,

1)First of all I want to create a curved 3d-surface through specific 3D-points.
Up to now I checked the Bezier patches and NURBS, but as far as I understand
you can only define control points such that the curve is getting near to them,
but not through them with C2 continuity.

2)Secondly I would not want to use a texture but merely smooth color shading, between some control points of this surface (not all of the control points. actually very few of it). That the colors are smoothly interpolated across this surface. Is that possible?

Could you give me hint how I should procede?

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