Plot 68

##############################################################

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

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

##############################################################

### 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/Plot68/"

savePngVerbose( paste(path, "Plot68.png", sep=""), plotInvParabolaWithTangents, w=dh, h=dh, un="px" )

}

### Draw inverted parabola with tangent lines

plotInvParabolaWithTangents = function( lineLength=1 ) {

coeff = c( 3, 0, -1 )

x = c( -2, 0, 2 )

y = evalPoly( x, coeff )

xLimits = axisLimits( x, xMargin )

yLimits = axisLimits( y, yMargin )

polyDerivCoeff = getPolyDerivCoeff( coeff )

plotTitle = expression( paste( "y = ", -x^2 + 3, ",  y' = -2x" ) )

plot( x, y, main=plotTitle, axes=FALSE, xlim = xLimits, ylim = yLimits, asp=1, cex.lab=lf,

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

addAxisLabels()

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

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

box()

grid()

xc = ( xLimits[1] + xLimits[2] )/2

text( -3.2, 4, "Tangent Slopes: 4, 0, -4", cex=1.4*fontScale, adj=0 )

xPred = seq( x[1] - 1, x[length(x)] + 1, length.out=200 )

yPred = evalPoly( xPred, coeff )

lines( xPred, yPred, col="blue", lwd=lw )

plotTangents( x, coeff, lineLength=lineLength, tanOffset=0.2 )

text( -2.5, -1, "m = 4", cex=1.4*fontScale, adj=1 )

text( -0.4, 3.4, "m = 0", cex=1.4*fontScale, adj=0 )

text( 2.5, -1, "m = -4", cex=1.4*fontScale,adj=0 )

}

### Compute f(x) for a polynomial and a vector of x-coordinates

evalPoly = function( x, coeff ) {

if ( length( coeff ) < 1 ) return( c(0) ) 

termSum = 0

for ( i in 1:length(coeff) ) {

termSum = termSum + coeff[i] * x^(i-1)

}

return( termSum )

}

### Compute polynomial coefficients for derivative of argument polynomial

getPolyDerivCoeff = function( coeff ) {

if ( length(coeff) < 2 ) return( c(0) )

derivCoeff = c()

for ( i in 2:length( coeff ) ) {

termPower = i - 1

derivCoeff[ length( derivCoeff ) + 1 ] = termPower * coeff[i]

}

return( derivCoeff )

}

### Plot tangent(s) to polynomial at x[i], y[i]

### Will not look correct unless both x and y axes are same scale (1:1 aspect ratio)

plotTangents = function( x, coeff, lineLength=1, tanOffset=0.2, col="red", lwd=2 ) {

if ( length(coeff) < 2 ) return() 

y = evalPoly( x, coeff )

polyDerivCoeff = getPolyDerivCoeff( coeff )

tanLineSlopes = evalPoly( x, polyDerivCoeff )

tanLineYInts = y - tanLineSlopes * x

for ( i in 1:length(x) ) {

lineCoeff = c( tanLineYInts[i], tanLineSlopes[i] )

plotTangentLine( x[i], y[i], lineCoeff, lineLength=lineLength, tanOffset=tanOffset, col=col, lwd=lwd )

}

}

### Get tangentl line ends point about center point (x,y)

getTanLineEndPts = function( x, y, lineCoeff, lineLength=1.0, tanOffset=0.2 ) {

x1 = x - 1

x2 = x + 1

y1 = evalPoly( x1, lineCoeff )

y2 = evalPoly( x2, lineCoeff )

xComp = x2 - x1

yComp = y2 - y1

vMag = sqrt( xComp^2 + yComp^2 )

vUnit = c( xComp/vMag, yComp/vMag )

vOffset = rotVecCcw( vUnit[1], vUnit[2], 90 )

ox = vOffset[1] * tanOffset

oy = vOffset[2] * tanOffset

xComp = xComp/vMag * lineLength

yComp = yComp/vMag * lineLength

fromX = x - xComp/2 - ox

fromY = y - yComp/2 - oy

toX = x + xComp/2 - ox

toY = y + yComp/2 - oy

return( list(fromX=fromX, fromY=fromY, toX=toX, toY=toY) )

}

### Plot one tangent line segment

plotTangentLine = function( x, y, lineCoeff, lineLength=1, tanOffset=0.2, col="red", lwd=1 ) {

endPts = getTanLineEndPts( x, y, lineCoeff, lineLength=lineLength, tanOffset=tanOffset )

lines( c(endPts$fromX, endPts$toX), c(endPts$fromY, endPts$toY), col=col, lwd=lwd )

}

### Rotate vector CCW

rotVecCcw = function( xComp, yComp, deg ) {

theta = deg/180 * pi

rotXComp = cos(theta) * xComp + sin(theta) * yComp;

rotYComp = -sin(theta) * xComp + cos(theta) * yComp;

return( c(rotXComp, rotYComp) )

}

### Compute plot axis limits to fit range of data

axisLimits = function( v, margin=0 ) {

lowerLimit = floor( min(v) ) - margin

upperLimit = ceiling( max(v) ) + margin

c( lowerLimit, upperLimit )

}

### 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()