The method should be aware geometric properties of the mesh (for example: edges, normals, curvature,..) . It means that the method will makes dense sampling or sparse sampling depending on the sampling region. I appreciate for any suggestions.
Thanks in advance.
The majority of data visualization software systems use some mesh reduction algorithms, particularly effective in the case of Amira and Paraview. Personally, I have implemented an algorithm based on optimization/mesh size ratio based on the following observation:
1. Error of a linear interpolation of a function f on a triangle T can be estimated by square of the diameter of T times maximum of the norm of the second derivative of f over T. Thus, optimum coarsening of a mesh M should have triangles of the size ~1/sqrt(norm(D^2f)). Similar estimation can be obtained with the respect to the line and surface curvature. This leads to the following algorithm:
1. create a hierarchy of points like
"smooth" points
"surface edge" - segments where triangles meet at the angle < e.g. 120 deg
"singular edges" where surface crosses itself or has a contour
"edge vertices" where edge segments rapidly change directions
"vertices" where 3 or more contours meet, contour ends etc.
2. leave "vertices",
downsample vertices at the singular edges and surface edges according to the rule stated above
downsample smooth vertices
3. re-triangulate.
It is usually possible so obtain simplification ratio of 1:100 ... 1:1000.
Hi Krzysztof Nowiński,
Do you have any publication or code regarding the method mentioned ?
Thank you.
It depends on the software you use. We normally decimate 3D models from laser scanner with Rapidform, but you can find the "decimate" option in most of 3D software, modelling or reverse engineering (Blender, MeshLab -open source- or Rhino, Rapidform and many others -commercial-). Most of them use specific algorithms to preserve the shape (so you will have stronger decimation on flat surfaces).
Yepp, I'm also using Meshlab at work and Blender at home, and both have good filters for downsampling. The question for you should be: what do I want to have as the final result (quality of the mesh) and for which tasks do I need them for setting up a maximum limit for the size of the data. If you want to reprocess your data f.e. with 3dsMax be patient of Max's maximum handable number of Polygons! I usually recalculate meshes down to max. 4MB/each single object with the "QuadricEdgeCollapseDecimation"-filter in Meshlab.
Rhino will do and trial version is free with full features - no time limit but gives you only 25 saves.
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