# shape2d: Returns a 2D volume function or 2D probability content... In denpro: Visualization of Multivariate Functions, Sets, and Data

## Description

Calculates a 2D volume function or 2D probability content function from a sequence of shape trees, corresponding to a sequence of level sets of a multivariate function to be visualized. A 2D volume function and 2D probability content function are visualizations of a multivariate density with a 2D function. One joins a series of radius functions or tail probability functions to get a 2D visualization. Radius functions and tail probability functions are 1D functions which visualize the shape of level sets of a multivariate density.

## Usage

 ```1 2 3``` ```shape2d(shtseq, gnum = 500, type = "radius", type2 = "slice", gnum2 = 1000, ngrid = 30, norma = FALSE, xmax = 10, modelim = 2, exmalim = NULL, maxnum = NULL) ```

## Arguments

 `shtseq` A list of shape trees, made by function "stseq"; the shape trees in the list correspond to a grid of level sets of the function to be visualized `gnum` Number of grid points in the radius function or in the tail probability function (used when one transforms a shape tree to a 1D function) `type` "radius" or "proba"; whether a 2D volume function or 2D probability content function will be calculated `type2` "slice" or "boundary"; whether the 1D functions are slices or level sets of the 2D function. The option "boundary" is not recommended at the moment `gnum2` when type2="boundary", then gnum*gnum is the size of the grid of the 2D function, and "gnum2" is the grid used for transforming shape trees to 1D functions `ngrid` positive integer; one prunes the 1D functions to have "ngrid" level sets `norma` TRUE if one uses dimension normalization for the volumes; then volumes are tranformed to (volume/V)pow(1/d), where V is the volume of the d-dimensional unit ball `xmax` internal `modelim` internal `exmalim` internal `maxnum` internal

## Value

A list containing elements x, y, z, whose meaning is the same as in function "persp".

Jussi Klemela

## References

Jussi Klemela (2005). Visualization of the spread of multivariate distributions.

`stseq`, `plotvolu2d`
 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19``` ```N<-c(30,30) lnum<-20 func<-"gumbel" marginal<-"normal" g<-2 ver<-3 support<-c(-ver,ver,-ver,ver) st<-stseq(N,lnum,func=func,marginal=marginal,g=g,support=support) gnum<-50 ngrid=50 vd<-shape2d(st,gnum=gnum,ngrid=ngrid) plotvolu2d(vd) type<-"proba" vd3<-shape2d(st,gnum=gnum,type=type,ngrid=ngrid,norma=TRUE) plotvolu2d(vd3) ```