mfGeomPlanarSizeShape: Planar Size and Shape Space Geometry
In Almond-S/manifoldboost: Boosting Regression Models for Manifold Valued Data
mfGeomPlanarSizeShape R Documentation
Planar Size and Shape Space Geometry
Description
Geometry of the 'classic' size-and-shape space identifying planar
configurations with a centered and complex vector and treating them as rotation
invariant.
Super classes
manifoldboost::mfGeometry -> manifoldboost::mfGeomEuclidean -> manifoldboost::mfGeomUnitSphere -> manifoldboost::mfGeomPlanarShape -> mfGeomPlanarSizeShape
Methods
Public methods
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Inherited methods
manifoldboost::mfGeometry$distance()manifoldboost::mfGeomEuclidean$align()manifoldboost::mfGeomEuclidean$innerprod()manifoldboost::mfGeomPlanarShape$initialize()manifoldboost::mfGeomPlanarShape$structure()manifoldboost::mfGeomPlanarShape$structure_weights()manifoldboost::mfGeomPlanarShape$unstructure()manifoldboost::mfGeomPlanarShape$unstructure_weights()manifoldboost::mfGeomPlanarShape$validate()
Method register()
center y_.
Usage
mfGeomPlanarSizeShape$register(y_)
Arguments
y_a complex vector on the sphere, orthogonal to the constant.
Method register_v()
orthogonally project v_ into the tangent space of y0_.
Usage
mfGeomPlanarSizeShape$register_v(v_, y0_ = self$pole_)
Arguments
v_a complex tangent vector.
y0_a complex vector on the sphere, orthogonal to the constant.
Method log()
y_-y0_ after aligning y_ to y0_.
Usage
mfGeomPlanarSizeShape$log(y_, y0_ = self$pole_)
Arguments
y_a complex vector on the sphere, orthogonal to the constant.
y0_a complex vector on the sphere, orthogonal to the constant.
Method exp()
y0_+v_ assuming v_ in the tangent space of y0_.
Usage
mfGeomPlanarSizeShape$exp(v_, y0_ = private$.pole_)
Arguments
v_a complex tangent vector.
y0_a complex vector on the sphere, orthogonal to the constant.
Method transport()
size-and-shape parallel transport
Usage
mfGeomPlanarSizeShape$transport(v0_, y0_, y1_, method = c("horizontal"))
Arguments
v0_a complex tangent vector.
y0_a complex vector on the sphere, orthogonal to the constant.
y1_a complex vector on the sphere, orthogonal to the constant.
methodcurrently, only "horizontal" assuming y0_, y1_ aligned
and v0_ a proper horizontal tangent vector at y0_.
Method plot()
default plotting function for planar shapes, plotting y_
in front of y0_ (after alignment).
Usage
mfGeomPlanarSizeShape$plot(
y_ = self$y_,
y0_ = self$pole_,
yaxt = "s",
bty = "n",
...
)
Arguments
y_a complex vector on the sphere, orthogonal to the constant.
y0_a complex vector on the sphere, orthogonal to the constant.
...other arguments passed to base::plot.
col, pch, typegraphical parameters passed to base::plot referring to y_.
ylab, xlab, xlim, ylim, xaxt, yaxt, asp, btygraphical parameters passed to base::plot
with modified defaults.
y0_pargraphical parameters for y0_.
seg_pargraphical parameters for line segments connecting y_
and y0_.
Method get_normal()
Obtain "design matrix" of tangent space normal vectors in
unstructured long format.
Usage
mfGeomPlanarSizeShape$get_normal(y0_ = self$pole_, weighted = FALSE)
Arguments
y0_a complex vector on the sphere, orthogonal to the constant.
weightedlogical, should inner product weights be pre-multiplied to
normal vectors?
Method clone()
The objects of this class are cloneable with this method.
Usage
mfGeomPlanarSizeShape$clone(deep = FALSE)
Arguments
deepWhether to make a deep clone.
Almond-S/manifoldboost documentation built on June 23, 2022, 11:06 a.m.
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| mfGeomPlanarSizeShape | R Documentation |
Planar Size and Shape Space Geometry
Description
Geometry of the 'classic' size-and-shape space identifying planar configurations with a centered and complex vector and treating them as rotation invariant.
Super classes
manifoldboost::mfGeometry -> manifoldboost::mfGeomEuclidean -> manifoldboost::mfGeomUnitSphere -> manifoldboost::mfGeomPlanarShape -> mfGeomPlanarSizeShape
Methods
Public methods
Inherited methods
manifoldboost::mfGeometry$distance()manifoldboost::mfGeomEuclidean$align()manifoldboost::mfGeomEuclidean$innerprod()manifoldboost::mfGeomPlanarShape$initialize()manifoldboost::mfGeomPlanarShape$structure()manifoldboost::mfGeomPlanarShape$structure_weights()manifoldboost::mfGeomPlanarShape$unstructure()manifoldboost::mfGeomPlanarShape$unstructure_weights()manifoldboost::mfGeomPlanarShape$validate()
Method register()
center y_.
Usage
mfGeomPlanarSizeShape$register(y_)
Arguments
y_a complex vector on the sphere, orthogonal to the constant.
Method register_v()
orthogonally project v_ into the tangent space of y0_.
Usage
mfGeomPlanarSizeShape$register_v(v_, y0_ = self$pole_)
Arguments
v_a complex tangent vector.
y0_a complex vector on the sphere, orthogonal to the constant.
Method log()
y_-y0_ after aligning y_ to y0_.
Usage
mfGeomPlanarSizeShape$log(y_, y0_ = self$pole_)
Arguments
y_a complex vector on the sphere, orthogonal to the constant.
y0_a complex vector on the sphere, orthogonal to the constant.
Method exp()
y0_+v_ assuming v_ in the tangent space of y0_.
Usage
mfGeomPlanarSizeShape$exp(v_, y0_ = private$.pole_)
Arguments
v_a complex tangent vector.
y0_a complex vector on the sphere, orthogonal to the constant.
Method transport()
size-and-shape parallel transport
Usage
mfGeomPlanarSizeShape$transport(v0_, y0_, y1_, method = c("horizontal"))Arguments
v0_a complex tangent vector.
y0_a complex vector on the sphere, orthogonal to the constant.
y1_a complex vector on the sphere, orthogonal to the constant.
methodcurrently, only "horizontal" assuming
y0_, y1_aligned andv0_a proper horizontal tangent vector aty0_.
Method plot()
default plotting function for planar shapes, plotting y_
in front of y0_ (after alignment).
Usage
mfGeomPlanarSizeShape$plot( y_ = self$y_, y0_ = self$pole_, yaxt = "s", bty = "n", ... )
Arguments
y_a complex vector on the sphere, orthogonal to the constant.
y0_a complex vector on the sphere, orthogonal to the constant.
...other arguments passed to
base::plot.col, pch, typegraphical parameters passed to
base::plotreferring toy_.ylab, xlab, xlim, ylim, xaxt, yaxt, asp, btygraphical parameters passed to
base::plotwith modified defaults.y0_pargraphical parameters for
y0_.seg_pargraphical parameters for line segments connecting
y_andy0_.
Method get_normal()
Obtain "design matrix" of tangent space normal vectors in unstructured long format.
Usage
mfGeomPlanarSizeShape$get_normal(y0_ = self$pole_, weighted = FALSE)
Arguments
y0_a complex vector on the sphere, orthogonal to the constant.
weightedlogical, should inner product weights be pre-multiplied to normal vectors?
Method clone()
The objects of this class are cloneable with this method.
Usage
mfGeomPlanarSizeShape$clone(deep = FALSE)
Arguments
deepWhether to make a deep clone.
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