Improving Conformal Flattening

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Improving Conformal Flattening
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The Problem

• Conformal transformations preserve angle but not
  scale
• Flattening a triangulated surface conformally can
  lead to undesirable results

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Why flattening?

• Graphics texture mapping, remeshing, level of
  detail, analytic surface fitting
• Industry developable surfaces (ship hulls,
  shoes, clothing), metal fabrication
• Cartography world maps, navigation
• Astronomy sky maps, cosmic background imaging

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Our solution

• Do a least-squares optimization on the
  already-flattened surface
• This minimizes the error between the perfect and
  actual conformal transformation of each triangle

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Results

• Least Squares Conformal Maps (LSCM)
• Scaling problems
• Angles preserved

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Results

• Our method
• Scale evenly distributed
• Angles preserved