Great deal, Heiner!
>The two stumps at the origin of the "claws"
are curves which can be used in a sweep or a cureve network for constructing the claws onto the base?
I believe so, any edge of any surface should have useable curves.
You could sweep those curves further, or even use Blend to create 'transitional' surface patches to existing claw shapes.
The best course may be to consider the whole object when forming the surfaces that make up the overall curved shape.
Maybe at least with the larger of the two claws, you would have carried the main top and bottom surfaces through the whole course, then worried about the smaller one later.
This way, the overall feel of the shape would be continuous.
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