STEP 2: Potentially reverse the normals of each tangent plane to achieve consistent orientation

• Construct a graph with one node per tangent plane.
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
• Add edges to the graph between close centers (within k-neighborhoods), to create a Riemannian Graph, encoding geometric proximities of the tangent plane centers
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
• Assign a cost to each edge depending on the angle between the normals (if two normals are nearly parallel, they better be oriented the same way!)
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
• Select the orientations for the tangent planes so as to maximize the total cost of the graph (NP-complete by reduction to MAXCUT)
  
  
  
  
• Approximate the best solution by traversing the MST of the Riemannian graph and "propagate" orientation (solves areas of low curvature first).