How to construct a sphere in enclosed surface.

Hello all ,
in my project , i need to develop a sphere inside the closed surface, i have a tessellated points on surface , in each point i need to calculate thickness on particular point by using sphere.

if any one have a idea regarding about this please do a needful help.

Thanks in advance
"to develop a sphere"? Like "to put a sphere inside"?

"thickness on point"? What does that mean?


Would geometric center of the points of the surface be a decent guess for the center for a sphere?

When you have chosen the center for the sphere, distance from center to nearest point sets a upper limit for the size of the sphere.
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