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snip a slab surface into bezier patches

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I want to snip a slab surface into 2 bezier patches.

 

Image.png


Shown below is the desired result. The main concern is the smaller patch, which should be of G2 to the larger patch.

 

Image.png


I can think of two workflows to the fix the small patch:

 

1. using Match Edge

 

Image.png


The problem is that one edge deviates from the cutting curve greatly.

 

Image.png


2. using Studio Surface

 

The problem is that, I don't know how to fit the projected curve to get an approximate spline of G2 to the left half surface.

 

Image.png


Hope to have your help on both workflows. Thanks!


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