# cart2pol: Transformation from Cartesian to polar coordinates In beadarrayMSV: Analysis of Illumina BeadArray SNP data including MSV markers

## Description

Cartesian coordiantes are transformed to polar coordinates using a specified distance measure

## Usage

 `1` ```cart2pol(x, y, dist = "euclidean", pNorm = NULL) ```

## Arguments

 `x` Cartesian abscissa value `y` Cartesian ordinate value `dist` One of “manhattan”, “euclidean” (default), or “minkowski”, defining which distance measure to use `pNorm` The exponent “p” in the p-norm (Minkowski) distance

## Details

The Manhattan distance is the special case of the Minkowski distance of norm 1, the Euclidean distance equals the Minkowski distance of norm 2. The unit circle of the Minkowski distance changes from a diamond shape (1-norm), through an Euclidean circle (2-norm), to a square (infinity-norm) as `pNorm` increases from 1 to infinity. Any norm between 2 and infinity results in a unit circle resembling a square with more or less rounded corners.

For non-transformed signal, the 1-norm is the most accurate representation, however a higher norm is called for after root- or log-transformations.

## Value

A list holding the polar coordinates

 `r ` Signal intensity `th ` Polar angle

## Author(s)

Lars Gidskehaug

`preprocessBeadSet`, `setNormOptions`

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19``` ```## Points defining a 4-norm unit-circle in the first quadrant x <- seq(0,1,.01)^(1/4) y <- (1-x^4)^(1/4) ## Polar coordinates using different distance-measures eucl <- cart2pol(x,y) mink <- cart2pol(x,y,'minkowski',4) ## Not run: ## Plot in cartesian coordinates dev.new() plot(x,y,type='b',main='4-norm unit circle') ## Plot polar coordinates on cartesian axes dev.new() plot(eucl\$th,eucl\$r,type='b',col='red',xlab='theta',ylab='r') points(mink\$th,mink\$r,type='b',col='blue') title(main='Euclidean (red) and 4-norm (blue) distance') ## End(Not run) ```

### Example output

```Loading required package: Biobase

Attaching package: 'BiocGenerics'

The following objects are masked from 'package:parallel':

clusterApply, clusterApplyLB, clusterCall, clusterEvalQ,
clusterExport, clusterMap, parApply, parCapply, parLapply,
parLapplyLB, parRapply, parSapply, parSapplyLB

The following objects are masked from 'package:stats':

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Filter, Find, Map, Position, Reduce, anyDuplicated, append,
as.data.frame, cbind, colMeans, colSums, colnames, do.call,
duplicated, eval, evalq, get, grep, grepl, intersect, is.unsorted,
lapply, lengths, mapply, match, mget, order, paste, pmax, pmax.int,
pmin, pmin.int, rank, rbind, rowMeans, rowSums, rownames, sapply,
setdiff, sort, table, tapply, union, unique, unsplit, which,
which.max, which.min

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