Plot 69

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### Copyright (c) Richard Creamer 2019 - All Rights Reserved

### Inquiries: email 2to32minus1@gmail.com

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### Globals

fontScale = 1.2    # Global font size variable

lf        = 1.2    # Enlarge font of plot labels

verbose   = FALSE  # Verbose printing

lw        = 2      # Line width

xMargin   = 1      # X-axis margin for plots

yMargin   = 1      # Y-axis margin for plots

de        = 0.01   # Small constant for estimating derivatives numerically

smlPts    = 1      # Small  data point/circle

medPts    = 1.5    # Medium data point/circle

lrgPts    = 2.0    # Large  data point/circle

### Run this function to generate this plot

runFunc = function() {

dw = 1000

dh = 750

path = "D:/Code/R/LeastSquaresPlay/PlotsAndAssocCode/Plot69/"

savePngVerbose( paste(path, "Plot69.png", sep=""), plotInvParabolaWithVertexTangent, w=dw, h=dw, un="px" )

}

### Plot inverted parabola with a tangent line at vertex

plotInvParabolaWithVertexTangent = function() {

f = function( x ) { return( -(x-3)*(x-3) + 5 ) }

x = -1:7

y = f(x)

xLimits = c( min(x), max(x) )

yLimits = c( min(y), max(y) + 6 )

plot( x, y, axes=FALSE, ylim=yLimits, xlim=xLimits, main="Parabola + Tangent at Vertex", cex.lab=lf,

  xlab="", ylab="", cex=lrgPts, lwd=lw+1, cex.main=1.4*fontScale, cex.axis=1.3 )

addAxisLabels()

axis( side=1, at=xLimits[1]:xLimits[2], cex.axis=1.3 )

axis( side=2, at=yLimits[1]:yLimits[2], las=2, cex.axis=1.3 )

box()

xVertex = 3

yVertex = f( xVertex )

xs = seq( x[1], x[length(x)], length.out=500 )

ys = f(xs)

lines( xs, ys, col=4, lwd=lw )

lines( c( xVertex - 3, xVertex + 3), c( yVertex, yVertex ), col="red", lwd=lw+1 )

lines( c(3,3), c(gpl()$yLim[1],f(3)), col="chartreuse4", lwd=lw+1, lty=2 )

eqText = expression( paste( "y = ", -x^2 + 6*x - 4, ",  y' = -2x + 6,  y'(3) = 0" ) )

text( 3, 11, eqText, cex=1.4*fontScale )

text( 3, 9, "x-coord of maxima is where deriv and tangent slope = 0", cex=1.4*fontScale )

}

### Get Plot Limits : gpl()$xLim[1] --> left x-coord

gpl = function() {

u = par( "usr" )

return( list( xLim=u[1:2], yLim=u[3:4] ) )

}

### Convience method to add x/y axis labels

addAxisLabels = function( xLabel="x", yLabel="y", cexVal=1.3 ) {

mtext( text=xLabel, side=1, line=2.5, cex=cexVal )

mtext( text=yLabel, side=2, line=2.5, cex=cexVal )

}

### Save to PNG file, specify width and height

savePngVerbose = function( path, plotFunc, w=512, h=512, un="px", doCopyright=TRUE, ... ) {

png( filename = path, type="cairo", units=un, width=w, height=h, pointsize=12, res=96 )

plotFunc( ... )

if ( doCopyright )

addCopyright()

dev.off()

}

### Add copyright notice to plot via text()

addCopyright = function() {

mtext( "Copyright \uA9 2019 Richard Creamer - All Rights Reserved", side=4, line=0, adj=0, cex=1.1 )

mtext( "Email: 2to32minus1@gmail.com", side=4, line=1, adj=0, cex=1.1 )

}

runFunc()