Remesh

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Local-Remesh without Parameterization
Tingfang Zhou
2005 -3 -31
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Background (I)

• Optimize mesh quality

Poor quality
Good quality
3
Background (II)

• Prepare for B-spline fitting

Often Lead to poor b-spline surface
Nice for fitting
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What is a good gridding ?

• Arc length uniformity
• The grid spacing along a particular gird line
  should be uniform
• Aspect ratio uniformity
• The grid spacing along u grid line should be the
  same as v
• Parametric fairness
• Every gird line should be of the minimal possible
  length given the first two

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Overview algorithm

• Select patch and perform a seed fill of the patch
• Compute an initial guess for the uv grid lines
  using Dijkstra algorithm
• Refine the mesh with the arc length and fairness
  constrains
• Subdivide the mesh
• Iterate between step 3 and 4

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Select Patch

• Select four corners in turn
• Compute the dijkstra shortest path
• Select seed point
• Compute select patch

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Initialization of remesh points

• Initial mesh points are computed as intersections
  of initial uv grid lines

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Refining using force vector
Iterative
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Subdivide

• Failure case
• Solution subdivision
• Get initial position from polygon model
• Refine with Force(P1,P) and Force(P2,P)

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Gridding algorithm
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Improvement

• Applied to points?
• Generalize to global remesh?