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I have zero 3D modeling skills and this is a very, very basic question - please bear with me.

I have a 2D drawing (I made it in Omnigraffle so I can export all sorts of formats - SVG seems most helpful, but I am naive).

What I want to do is to spin the drawing around a center line to make a 3D "top hat" like object. The result is to be given to Shapeways.

This seems super, super basic, but I lack the vocabulary to even formulate a reasonable google search to learn how this can be done.

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You can import the drawing via the File menu : File/Import/Scalable Vector Graphic (.svg)

Make sure the Origin of the object (the orange dot) is located along the axis you want to spin around. If you need to move it, the easiest way is to enter Edit Mode (Tab), select everything (A) and grab it (G). You can now leave Edit Mode (Tab).

Add a Screw Modifier, and select the good axis (X,Y or Z). You may want to increase the Steps setting, if the object looks too angular.

Before sending it to Shapeways, it would probably be a good idea to convert it to a Mesh (for now, your object is a Curve with a modifier) : Alt+C / Convert to Mesh from Curve.

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Thibsert's answer is fine, but if you're using mesh already you can use the Spin tool from the Tool tab in Edit Mode. The number of degrees (Angle) needs to be set to 360 and you need to find the right axis and enter 1 there instead of the default 0

enter image description here

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