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Fix genus computation

This commit is contained in:
Massimiliano Corsini 2005-12-14 14:04:35 +00:00
parent 4911a7acca
commit 00d3854048
1 changed files with 38 additions and 27 deletions
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65
vcg/complex/trimesh/clean.h
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@ -24,6 +24,9 @@
History History
$Log: not supported by cvs2svn $ $Log: not supported by cvs2svn $
Revision 1.17 2005/12/12 12:11:40 cignoni
Removed unuseful detectunreferenced
Revision 1.16 2005/12/04 00:25:00 cignoni Revision 1.16 2005/12/04 00:25:00 cignoni
Changed DegeneratedFaces -> RemoveZeroAreaFaces Changed DegeneratedFaces -> RemoveZeroAreaFaces
@ -447,38 +450,46 @@ namespace vcg {
return Compindex; return Compindex;
} }
/** /**
GENUS: A topologically invariant property of a surface defined as: GENUS.
the largest number of nonintersecting simple closed curves that can be drawn on the surface without separating it.
A topologically invariant property of a surface defined as
the largest number of non-intersecting simple closed curves that can be
drawn on the surface without separating it.
Roughly speaking, it is the number of holes in a surface. Roughly speaking, it is the number of holes in a surface.
The genus g of a surface, also called the geometric genus, is related to the Euler characteristic $chi$ by $chi==2-2g$. The genus g of a closed surface, also called the geometric genus, is related to the
Euler characteristic by the relation $chi$ by $chi==2-2g$.
The genus of a connected, orientable surface is an integer representing the maximum number of cuttings along closed The genus of a connected, orientable surface is an integer representing the maximum
simple curves without rendering the resultant manifold disconnected. It is equal to the number of handles on it. number of cuttings along closed simple curves without rendering the resultant
manifold disconnected. It is equal to the number of handles on it.
*/ For general polyhedra the <em>Euler Formula</em> is:
static int MeshGenus(MeshType &m, int count_uv, int numholes, int numcomponents, int count_e)
V + F - E = 2 - 2G - B
where V is the number of vertices, F is the number of faces, E is the
number of edges, G is the genus and B is the number of <em>boundary polygons</em>.
The above formula is valid for a mesh with one single connected component.
By considering multiple connected components the formula becomes:
V + F - E = 2C - 2Gs - B
where C is the number of connected components and Gs is the sum of
the genus of all connected components.
*/
static int MeshGenus(MeshType &m, int count_uv, int numholes,
int numcomponents, int count_e)
{ {
int eulernumber = (m.vn-count_uv) + m.fn - count_e; int V = (m.vn - count_uv); // Unreferenced vertices are subtracted
return int(-( 0.5 * (eulernumber - numholes) - numcomponents )); int F = m.fn;
int E = count_e;
return -((V + F - E + numholes - 2 * numcomponents) / 2);
} }
/*
Let a closed surface have genus g. Then the polyhedral formula generalizes to the Poincaré formula
chi=V-E+F, (1)
where
chi(g)==2-2g (2)
is the Euler characteristic, sometimes also known as the Euler-Poincaré characteristic.
The polyhedral formula corresponds to the special case g==0.
*/
static int EulerCharacteristic()
{
}
static void IsRegularMesh(MeshType &m, bool Regular, bool Semiregular) static void IsRegularMesh(MeshType &m, bool Regular, bool Semiregular)
{ {