Define a 'horizontal' tube, either hollow or solid, in n dimensions
Usage
HollowTube( n, k.x=1, k.circumference=2, method="dyadic", p=2 )
SolidTube( n, k.x=1, k.circumference=2, method="dyadic", p=2 )
Arguments
n
Dimension of the space
k.x
Number of subdivisions along the x[1] direction (first component)
k.circumference
Number of subdivisions around the circumference; note the meaning of
this depends on the value of method.
method
"dyadic" or "edgewise": the former recursively subdivides the sphere to get
a more uniform grid; the latter uses a faster method using one edgewise subdivision.
p
Power used in the l^p norm; p=2 is the Euclidean norm
Details
HollowTube computes an approximation to a tube, an (n-1) dimensional
surface in n space. The tube is 'horizontal', e.g. the center line of the tube is the x-axis with
0 <= x[1] <= 1 and radius 1;
use AffineTransform to rotate, stretch or translate.
The mesh is basically constructed by taking the cross product of an x[1] subdivision
with an (n-1) dimensional sphere; the optional arguments k.circumference, method, p are used in
a call to UnitSphere to specify the sphere. The default value of p=2 gives a tube
with round/Euclidean cross section; using a different p will make the cross sections of the tube
a ball in the Lp norm.
SolidTube computes an approximation to a solid tube, an n dimensional solid in
n space.
Value
an object of class "mvmesh" as described in mvmesh.