Pasting a Logo or Seal to a cylinder
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With 96 sectors the disortion effect is no longer recognizable.

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Although for our eyes, SU seems to use single faces for unlimited number of polygons, I suspect that in the background it in fact triangulates those faces. And when you intersect some curved surfaces, you have no control over the direction of that triangulation/autofold function - thus the ugly effect.
This can also be suspected when you try to close the face of some definitely coplanar but rather complex structure and often SU only lets you do it by manual triangulation and then keeps the face even after you delete those coplanar, dividing edges.
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Is there a plugin that will take rectangular faces and triangulate them?
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Here you can find one.
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