PlotRegionHighlighter (version 1.0)

generateEnvelope: Generate an minimum-perimeter envelope that surrounds a set of points in a graph

Description

The generateEnvelope function is called with the coordinates for points in the envelope along with a vector of radii for the circles surrounding each point. The function generates a list of points defining the envelope surrounding the entire set of points. These coordinates may be displayed using either the line or polygon graphics commands

Usage

generateEnvelope(centers, r, ...)

Arguments

centers

a numeric matrix with each row containing the xy coordinates for each point.

r

a numeric vector containing the radius of each point

...

additional parameters such as the number of points to return when defining the arcs in the envelope

Value

envelopeXY

The x and y coordinates for the points defining the envelope

tangent_Points

The tangent points defining the transition between arcs and lines along with the angle relative to the centorid of the input points

References

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

Examples

############################################################
# 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")

#################################################
# plot envelopes around two randomly generated set of points
require(grid)
grid.newpage()
ncircles <- sample(10:25,1)
centers <- matrix(runif(2*ncircles, min=.2, max=.5), byrow=TRUE, ncol=2)
r <- rep(0.1, ncircles)

envelopeXY <- generateEnvelope(centers, r)$envelopeXY
grid.polygon(envelopeXY[,1], envelopeXY[,2], gp=gpar(fill="pink", col="transparent", lwd=5), default.units="npc")
grid.points(centers[,1], centers[,2], pch=16, gp=gpar(col="black", cex=1.5), default.units="npc")

ncircles <- sample(10:20,1)
centers <- matrix(runif(2*ncircles, min=.6, max=.8), byrow=TRUE, ncol=2)
r <- rep(0.025, ncircles)

grid.points(centers[,1], centers[,2], pch=16, gp=gpar(col="blue", cex=1.5), default.units="npc")

envelopeXY <- generateEnvelope(centers, r)$envelopeXY
grid.lines(envelopeXY[,1], envelopeXY[,2], gp=gpar(col="blue", lwd=5), default.units="npc")