swissRoll {intrinsicDimension}

Swiss roll with or without 3-sphere inside

Description

Generates a sample from a uniform distribution on a Swiss roll-surface, possibly together with a sample from a uniform distribution on a 3-sphere inside the Swiss roll.

Usage

swissRoll(Ns, a = 1, b = 2, nturn = 1.5, h = 4)
swissRoll3Sph(Ns, Nsph, a = 1, b = 2, nturn = 1.5, h = 4)

Arguments

Ns

number of data points on the Swiss roll.

Nsph

number of data points on the 3-sphere.

a

minimal radius of Swiss roll and radius of 3-sphere.

b

maximal radius of Swiss roll.

nturn

number of turns of the surface.

h

height of Swiss roll.

Value

swissRoll returns three-dimensional data points. swissRoll3Sph returns four-dimensional data points with the Swiss roll in the three first dimensions (columns). The Ns first data points lie on the Swiss roll and the Nsph last data points lie on the 3-sphere.

Author(s)

Kerstin Johnsson, Lund University.

Examples

datap <- swissRoll3Sph(300, 100)
par(mfrow = c(1, 3))
plot(datap[,1], datap[,2])
plot(datap[,1], datap[,3])
plot(datap[,1], datap[,4])