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Michael Migliore
VTK
Commits
2e3e1758
Commit
2e3e1758
authored
Jan 09, 2018
by
Guillaume Jacquenot
Committed by
Guillaume Jacquenot
Jan 09, 2018
Browse files
Update vtkCurvatures.h doc that poorly render with Doxygen
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82b68fc0
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Filters/General/vtkCurvatures.h
Filters/General/vtkCurvatures.h
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Filters/General/vtkCurvatures.h
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2e3e1758
...
...
@@ 21,31 +21,32 @@
*
* Gauss Curvature
* discrete Gauss curvature (K) computation,
* \f$K(vertex v) = 2*
PI\sum_
{facet neighbs f of v} (angle_f at v)\f$
* The contribution of every facet is for the moment weighted by \f$Area(facet)/3\f$
* The units of Gaussian Curvature are \f$[1/m^2]\f$
* \f$K(
\text{
vertex v
}
) = 2*
\pi  \sum_{\text
{facet neighbs f of v}
}
(
\text{
angle_f at v
}
)\f$
.
* The contribution of every facet is for the moment weighted by \f$Area(facet)/3\f$
.
* The units of Gaussian Curvature are \f$[1/m^2]\f$
.
*
* Mean Curvature
* \f$H(vertex v) = average over edges neighbs e of H(e)\f$
* \f$H(edge e) = length(e)*dihedral_angle(e)\f$
* \f$H(vertex v) = \text{average over edges neighbs e of H(e)}\f$,
* \f$H(edge e) = length(e) * dihedral\_angle(e)\f$.
*
* NB: dihedral_angle is the ORIENTED angle between PI and PI,
* this means that the surface is assumed to be orientable
* the computation creates the orientation
* The units of Mean Curvature are [1/m]
* the computation creates the orientation
.
* The units of Mean Curvature are [1/m]
.
*
* Maximum (\f$k_max\f$) and Minimum (\f$k_min\f$) Principal Curvatures
* \f$k_max = H + sqrt
(
H^2  K
)
\f$
* \f$k_min = H  sqrt
(
H^2  K
)
\f$
* Excepting spherical and planar surfaces which have equal principal
curvatures,
* the curvature at a point on a surface varies with the direction
one "sets off"
* from the point. For all directions, the curvature will pass
through two extrema:
* a minimum (\f$k_min\f$) and a maximum (\f$k_max\f$)
which occur at mutually orthogonal
* directions to each other.
* Maximum (\f$k_
\
max\f$) and Minimum (\f$k_
\
min\f$) Principal Curvatures
* \f$k_
\
max = H +
\
sqrt
{
H^2  K
}
\f$
,
* \f$k_
\
min = H 
\
sqrt
{
H^2  K
}
\f$
* Excepting spherical and planar surfaces which have equal principal
*
curvatures,
the curvature at a point on a surface varies with the direction
*
one "sets off"
from the point. For all directions, the curvature will pass
*
through two extrema:
a minimum (\f$k_
\
min\f$) and a maximum (\f$k_
\
max\f$)
*
which occur at mutually orthogonal
directions to each other.
*
* NB. The sign of the Gauss curvature is a geometric ivariant, it should be
+ve
* when the surface looks like a sphere,

ve when it looks like a
saddle,
* however
,
the sign of the Mean curvature is not, it depends on the
* convention for normals

This code assumes that normals point outwards (i
e
* NB. The sign of the Gauss curvature is a geometric i
n
variant, it should be
*
positive
when the surface looks like a sphere,
negati
ve when it looks like a
*
saddle,
however the sign of the Mean curvature is not, it depends on the
* convention for normals
.
This code assumes that normals point outwards (i
.e.
* from the surface of a sphere outwards). If a given mesh produces curvatures
* of opposite senses then the flag InvertMeanCurvature can be set and the
* Curvature reported by the Mean calculation will be inverted.
...
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