Bottle neck- cap problem

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this is not exactly our MATLAB project problem, but it puts our situation in a simpler way. suppose we have two 3d surfaces- i. bottle neck ii. bottle cap. If we have to design a bottle cap that fits in bottle neck Obviously, bottle cap exterior (whatever it is) is not issue. But bottle cap interior surfaces should exactly be negative space of bottle neck positive space (also considering some offsets in bottle cap interior so that it won't be tight fit, that is not much issue in this discussion ) what would be the better way to render bottle cap interior surface?
we have been researching on surface intersection, iso2mesh etc.

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Image Analyst
Image Analyst 2015-6-9
Maybe you could take a look at the code for klein1
>> edit klein1.m

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