July 2004
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Surface mesh reconstruction
from unorganized point clouds
Spatial subdivision methods using or referring to the Medial Axis
The Medial Scaffold of unorganized point sets
Reference: Frederic F. Leymarie Ph.D.
thesis and recent papers.
NB: The shock curve and its associated A_1^3-2 source (and associated
interpolating triangle) correspond to the notion of Gabriel complex
introduced by Petijean and Boyer.
NB: Cases (b) and (c) are denoted as non-regular by Petijean and Boyer.
NB: Cases (b) and (c) give bad "poles" in the nomenclature of
Amenta et al.
Segregation of the Medial scaffold (2002)
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3200 generators; uniform sampling.
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Medial scaffold
(without shock curves off to infinity).
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Idea of segregation of shock curves:
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Partition in two classes the shock curves based on geometric properties
of their associated interpolants (triangles).
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Build from the "lower" class a surface interpolant by front
propagation from "seeds."
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Lower class of shock curves after segregation.
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Higher class of shock curves.
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NB: Shock curves correspond to edges of Voronoi cells. Hence, according
to Amenta et al., as sampling density augments, they tend to align
themselves along the normal field to the (unknown) surface M.
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Recovered surface mesh (triangulation).
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Recovered medial scaffold for a the surface mesh.
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Feature of the method:
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No particular assumptions made on regularity.
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No assumptions on the absence of holes.
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The medial axis is explicitly represented and constructed at each step,
via the scaffolds.
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The various geometric ingredients involved in previous methods are part
of the scaffold representation.
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Petitjean and Boyer: Shock curve sources and Gabriel complices
(triangles)
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Amenta et al.: Shock vertices (Voronoi diagram) and
shock curves (Voronoi cell edges).
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The method combines aspects of the three classes of surface meshing
methods:
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It computes explicitly a distance field, and is implicitly related to
the level-set schemes (shocks are critical values of the distance flow
from generators).
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Propagation along a probable surface (tangent space) is used.
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A partition of space is explicitly computed by the medial scaffold
(which includes the Boundary of the Voronoi diagram, and add to it a
flow field and special nodes, i.e., at shock points).
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From Cyberware, Inc. 30500 points.
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21500 points. NB: holes and
negative curvature areas.
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Difficulties:
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Regions of negative curvature where sampling is often poor.
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Regions where multiple distinct surface patches are in the same
vicinity.
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Last Updated: July 8, 2004