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2e3e1758
Commit
2e3e1758
authored
Jan 09, 2018
by
Guillaume Jacquenot
Committed by
Guillaume Jacquenot
Jan 09, 2018
1
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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 i
variant, it should be +v
e
*
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 (ie
* NB. The sign of the Gauss curvature is a geometric i
nvariant, it should b
e
*
positive when the surface looks like a sphere, negative 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.
...
...
Robert Maynard
@robertmaynard
mentioned in commit
527f4885
·
Oct 23, 2018
mentioned in commit
527f4885
mentioned in commit 527f4885810c178134af25372a2c306f9257045c
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