# HollowRectangle: Subdivide a hyperrectangle with a standard grid In mvmesh: Multivariate Meshes and Histograms in Arbitrary Dimensions

## Description

`EdgeSubdivision` implements the

## Usage

 ```1 2 3 4``` ```HollowRectangle( a, b, breaks=5, silent=FALSE ) SolidRectangle( a, b, breaks=5, silent=FALSE ) mvmeshRectBreaks( a, b, breaks, silent ) NextMultiIndex( i, n ) ```

## Arguments

 `a` vector specifying the "lower left" vertex of the rectangle `b` vector specifying the "upper right" vertex of the rectangle `breaks` a specification of the subdivision scheme. See details below. `silent` indicates whether or not to warn the caller if the subdivision determined by 'breaks' covers the whole hyperrectangle [a,b]. `i` integer vector `n` integer vector

## Details

`RectangularMesh` computes an rectangular mesh on the hyperrectangle [a,b] = [a[1],b[1]] x [a[2],b[2]] x ... x [a[n],b[n]]. It is similar to the function `mesh` in CRAN package plot3D, but works for dimension d=2,3,4,...

'breaks' determines how each component is divided, it is motivated by the argument breaks in `hist`. If 'breaks' is a vector of length n, then breaks[i] gives the number of evenly sized bins in coordinate i, spread out over the range [a[i],b[i]]. If 'breaks' is a single number m, then each component is subdivided into that many bins, i.e. this is equivalent to breaks=rep(m,n). Thus the default breaks=6 subdivides each coordinate into 6 bins. Finally, if a more complicated subdivision is desired, 'breaks' can a list with n fields. breaks[[i]] should be a vector of dividing points for coordinate i. See the example below. In this last case, where the bin boundaries are explictly defined, 'a' and 'b' are not used (other than a possible warning if the specified bins do not cover the rectangle given by 'a' and 'b').

## Value

An object of class "mvmesh" as described in `mvmesh`.

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27``` ```SolidRectangle( a=c(1,3), b=c(2,7), breaks=2 ) SolidRectangle( a=c(1,3), b=c(2,7), breaks=c(4,10) ) SolidRectangle( a=c(1,3), b=c(2,7), breaks=list( seq(1,3,by=0.25), seq(2,7,by=1) ) ) HollowRectangle( a=c(1,3), b=c(2,7), breaks=2 ) HollowRectangle( a=c(1,3), b=c(2,7), breaks=c(4,10) ) HollowRectangle( a=c(1,3), b=c(2,7), breaks=list( seq(1,3,by=0.25), seq(2,7,by=1) ) ) ## Not run: plot( SolidRectangle( a=c(1,3), b=c(2,7), breaks=3 ), show.labels=TRUE ) plot( SolidRectangle( a=c(1,3), b=c(2,7), breaks=c(4,10) ), show.labels=TRUE ) plot( SolidRectangle( a=c(1,3), b=c(2,7), breaks=list( seq(1,3,by=0.25), seq(2,7,by=1) ) ), show.labels=TRUE ) plot( SolidRectangle( a=c(1,3), b=c(2,7), breaks=3 ), show.labels=TRUE, label.values=letters[1:9], col='green' ) plot( HollowRectangle( a=c(1,3,0), b=c(6,7,6), breaks=3 ), show.labels=TRUE, col='blue') plot( HollowRectangle( a=c(1,3), b=c(2,7), breaks=3 ), show.labels=TRUE ) plot( HollowRectangle( a=c(1,3), b=c(2,7), breaks=c(4,10) ), show.labels=TRUE ) plot( HollowRectangle( a=c(1,3), b=c(2,7), breaks=list( seq(1,3,by=0.25), seq(2,7,by=1) ) ), show.labels=TRUE ) plot( HollowRectangle( a=c(1,3), b=c(2,7), breaks=3 ), show.labels=TRUE, label.values=letters[1:9], col='green' ) ## End(Not run) ```

mvmesh documentation built on Feb. 12, 2020, 1:09 a.m.