Finding the Center of a Spherical Surface

http://www.geocities.com/wwswimming/center_of_spherical_surface2.jpg

i stuck this image up. it's a Solidworks screen image of a solid whose
spherical surface is a map of Antarctica.

now my challenge is finding the center of the spherical surface.

i think that if i could place lines normal to the "inside" of the
spherical surface, at the intersection of just 2 lines i would find the
center of the sphere. i think.

how to do that in Solidworks i am not yet sure of.

the lines highlighted green in the image show the original direction of
extrusion of the solid.

anybody that could help me with this analytic geometry/ Solidworks kind
of question i'd really appreciate it.

 

Use a 3D sketch to place two points anywhere on the spherical surface
(use coincident constraint between point and surface). Create axes
through the points and normal to the surface. The intersection of two
axes will give you the spere center.

 

Assuming the map is projected onto a sphere and not on an Elipsoid
(since the earth is not a true sphere). Another way to tackle this may
be to:

1. Copy the spherical surface (surface offset at zero)
2. Use a surface untrim on that surface. You may need to up the
percentage.
3. A couple options: You can repeat step 2 with high percentages
until the surface turns into a sphere, but it may not be neccessary:
Notice that the surface untrim should create two (of the four) edges
that are planar to the center of the sphere. Create a plane using the
end points and midpoint of one of those edges. This will create a
plane running through the center of the sphere. Open a sketch on that
plane and convert the edge into a arc. This should locate the center.


I mocked this up and imported similar data into solidworks and it
worked.

Hope it works for you.

Dan S.

 

Try this,

Create a plane intersecting the spherical surface, then select that
palne and use Tools/Sketch Tools/Intersection Curve. That gives you a
planar scetch with an intersection curve. The center of that curve is
the center of the sphere.

 

How can you be sure the plane intersects the center?

 

You're right, you have to make sure that a normal vector to the surface
is on that plane. Easy way to check that is to try to dimension the
intersection curve. If SW recognizes it as an ark (not as an ellipse) it
means you're sectioning thru the center.

 

Your approach (3d sketch & 2 axes) works faster. I just tried it.

 

Here's an example based from the responses.. (I actually did it last
night but did not have time to send it)

http://zxys.com/misc/centerofsphere.zip

...