# tpsgrid: Thin-plate spline transformation grids In shapes: Statistical Shape Analysis

## Description

Thin-plate spline transformation grids from one set of landmarks to another.

## Usage

 ```1 2``` ```tpsgrid(TT, YY, xbegin=-999, ybegin=-999, xwidth=-999, opt=1, ext=0.1, ngrid=22, cex=1, pch=20, col=2,zslice=0, mag=1, axes3=FALSE) ```

## Arguments

 `TT` First object (source): (k x m matrix) `YY` Second object (target): (k x m matrix) `xbegin` lowest x value for plot: if -999 then a value is determined `ybegin` lowest y value for plot: if -999 then a value is determined `xwidth` width of plot: if -999 then a value is determined `opt` Option 1: (just deformed grid on YY is displayed), option 2: both grids are displayed `ext` Amount of border on plot in 2D case. `ngrid` Number of grid points: size is ngrid * (ngrid -1) `cex` Point size `pch` Point symbol `col` Point colour `zslice` For 3D case the scaled z co-ordinate(s) for the grid slice(s). The values are on a standardized scale as a proportion of height from the middle of the z-axis to the top and bottom. Values in the range -1 to 1 would be sensible. `mag` Exaggerate effect (mag > 1). Standard effect has mag=1. `axes3` Logical. If TRUE then the axes are plotted in a 3D plot.

## Details

A square grid on the first configuration is deformed smoothly using a pair of thin-plate splines in 2D, or a triple of splines in 3D, to a curved grid on the second object. For 3D data the grid is placed at a constant z-value on the first figuure, indicated by the value of zslice.

For 2D data the covariance function in the thin-plate spline is \$sigma(h) = |h|^2 log |h|^2\$ and in 3D it is given by \$sigma(h) = -| h |\$.

## Value

No returned value

Ian Dryden

## References

Bookstein, F.L. (1989). Principal warps: thin-plate splines and the decomposition of deformations, IEEE Transactions on Pattern Analysis and Machine Intelligence, 11, 567–585.

Dryden, I.L. and Mardia, K.V. (2016). Statistical Shape Analysis, with Applications in R (Second Edition). Wiley, Chichester. Chapter 12.

 ``` 1 2 3 4 5 6 7 8 9 10``` ```data(gorf.dat) data(gorm.dat) #TPS grid with shape change exaggerated (2x) gorf<-procGPA(gorf.dat) gorm<-procGPA(gorm.dat) TT<-gorf\$mshape YY<-gorm\$mshape tpsgrid(TT,YY,mag=2) title("TPS grid: Female mean (left) to Male mean (right)") ```