mvmesh (version 1.6)

HollowTube: Define tubes in n-dimensions

Description

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

Value

an object of class "mvmesh" as described in mvmesh.

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.

Examples

# NOT RUN {
HollowTube( n=3 )
SolidTube( n=3 )

# }
# NOT RUN {
plot( HollowTube(  n=3, k.x=3, k.circumference=2 ), show.faces=TRUE, col='red', alpha=0.5 )
plot( SolidTube( n=3, k.x=5, k.circumference=2 ), col='blue' )

# use non-Euclidean sphere to define wall of tube 
plot( HollowTube(  n=3, k.x=10, k.circumference=2, p=0.6 ), col='green')
# }