rmvmesh: Simulate from a mesh
In mvmesh: Multivariate Meshes and Histograms in Arbitrary Dimensions

Description Usage Arguments Details Value Examples

Simulate from a mvmesh object

1	rmvmesh( n, mesh, weights=rep(1,ncol(mesh$SVI) ) )

`mesh`	object of class "mvmesh"
`n`	number of vectors to simulate
`weights`	weights used for simulation

rmvmesh allows you to sample from an mvmesh object, simplex j is sampled with probability weights[j]. Note that if the simplices are of different sizes, and the weights are uniform, this will result in uniform sampling among the simplices, but different densities on different faces. See the example below with alternating weights. If you want to get a uniform density, set the weights equal to the m dimensional volume of the simplices that make up the meshes.

rmvmesh works for any mesh where the m dimensional simplices are convex combinations of (m+1) vertices i.e. vps=m+1. This works whatever the dimension of the embedding space is, and whether or not things have been rotated, scaled or shifted by AffineTransform. It also works with an unaltered SolidRectangle or HollowRectangle. mvmesh does not currently work with mvmesh objects of type PolarSphere, PolarBall, HollowTube, or SolidTube; nor does it work with rectangles that have been altered by AffineTransform.

Note that rmvmesh samples from the mesh, not from the idealized object. In particular, in the example below with a unit sphere, the sampled points are from the tessellation approximation to the sphere, not from the unit sphere itself. So (with probability one), all points will have length less than 1.

A matrix of values x: x[1, ],x[2, ],...,x[n, ] are vectors sampled from the mesh.

## Not run: 
sphere <- UnitSphere( n=3, k=2 )
plot(sphere)
x <- rmvmesh( 1000, sphere )
points3d( x, col='red' )

box <- HollowRectangle( a=c(0,2,-1), b=c(1,5,3), breaks=3 )
plot(box)
x <- rmvmesh( 500, box )
points3d( x, col='blue', size=5 )


plot(box)
nS <- ncol(box$SVI) # number of simplices in box
weights <- rep( c(0,1), nS/2 )  # alternating 0,1 weights
x <- rmvmesh( 10000, box, weights )
points3d( x, col='green', size=5 )


## End(Not run)