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object

I only care about the sphere and its design, not the bird on top.

This kind of curvy iron design shows up on many Victorian designs and other examples of old-fashioned smithing. How can I efficiently produce a sphere like this? (Also feel free to comment/edit if you know a more precise term for this than just "curvy Victorian ironwork.")

My first idea was to make a wireframe UV sphere, then model the curvy bits separately. Then, if I could somehow snap the curvy bits to the sphere in a way that makes the bits follow the curve of the sphere, I could do something with an Array modifier. However, I don't know how to snap objects that way.

Another example of the "curvy bits" I'm talking about:

more curvy bits
(source: rackcdn.com)

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Looking at what you're wanting to achieve, I think using the decimate modifier >un-subdivide with 1 iteration should work well to get you started, and keep a uniform pattern across the model. Hope that helps get you started.enter image description here

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This is no shortcut. But you will have detailed control over your model.

I would start with a highres UVsphere and then add geometry with snap and shrinkwrap to follow the spheres surface.

geometry along sphere surface

Then add a solidify modifier followed by a subsurface modifier:

with modifiers

You can apply the solidify modifier and fiddle with the geometry if you want to make it beveled or such.

fiddle with the geometry

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    $\begingroup$ Unfortunately, I can't accept multiple answers, or else I would have accepted this one too! $\endgroup$ – Somatic Jan 6 '16 at 2:40
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enter image description here

Some assorted ideas.

  • Left to Right.
  • Start with sphere or cylinder. Place Ends. Push Pull. Loop Cuts.
  • Proportional Editing.
  • Curve Modifier. Example Curve in Red.
  • Sizing to Curve. More proportional editing
  • Modify Twist on Curve. Consider Shrink Wrap Modifier to sphere for curve only. Not Mesh.
  • You can be more artistic than shown above
  • Arrange to sphere not shown
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