# envelopeArea_and_Perimeter: Calculate the area and perimeter of the envelope In PlotRegionHighlighter: Creates an envelope that surrounds a set of points plotted in a two dimensional space.

## Description

Calculate the area and perimeter of the envelope

## Usage

 `1` ```envelopeArea_and_Perimeter(segments, centers, r) ```

## Arguments

 `segments` The tangent points output by the generateEnvelope function `centers` a numeric matrix with each row containing the coordinates for a point with the x and y coordinates as the two columns. `r` a numeric vector containing the radii for each point

## Details

Calculations are done in the units of the graph

## Value

a numeric vector. The area is the first value and the perimeter is the second value

Elliot Noma

## References

http://en.wikipedia.org/wiki/Belt_problem

## 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 28 29 30 31 32 33 34 35 36 37 38 39``` ```############################################################ # plot plotCircles <- function(center, r, color="red", ...) { a <- createCircle(center, r, ...) grid.polygon(x = a[,1], y = a[,2], gp=gpar(col=color, lwd=2)) a } ncircles <- sample(3:7,1) centers <- matrix(runif(2*ncircles, min=.2, max=.8), byrow=TRUE, ncol=2) r <- runif(ncircles,min=.10, max=.20) envelope <- generateEnvelope(centers, r) print(envelope\$tangent_Points) require(grid) grid.newpage() colors <- rainbow(ncircles * 3 + 3) for (i in 1:ncircles) circles<- plotCircles(centers[i,], r[i], color=colors[i]) grid.text(1:ncircles, centers[,1], centers[,2]) # plot the envelope containing the circles envelopeXY <- envelope\$envelopeXY segments <- envelope\$tangent_Points grid.lines(envelopeXY[,1], envelopeXY[,2], gp=gpar(col="orange", lwd=5), default.units="npc") grid.points(segments[,"x"], segments[,"y"], pch=16, gp=gpar(col="red"), default.units="npc") # calculate the area and perimeter of the envelope envelopeStats <- envelopeArea_and_Perimeter(segments, centers, r) cat("envelope area = ", envelopeStats["area"], " perimeter = ", envelopeStats["perimeter"],"\n") cat("circle radii = ", r, "\n") cat("circle area = ", pi * r^2, " = ", sum(pi * r^2), "\ncircle perimenter = ", 2 * pi * r, " = ", 2 * pi * sum(r), "\n") ```

PlotRegionHighlighter documentation built on May 30, 2017, 12:38 a.m.