Plot 31

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### 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/Plot31/"

savePngVerbose( paste(path, "Plot31.png", sep=""), gradDemo, w=dw, h=dw, un="px" )

}

### Draw inverted gaussian surface with a few gradient vectors with proportional magnitudes

gradDemo = function( zFunc=elevFunc, xyAngle=30, vertAngle=45, sigma=3, peakHt=10, col="white", lwd=lw, expand=0.2 ) {

peakHt = 0.5

x = seq( -10, 10, length=21 )

y = x

z = outer( x, y, elevFunc, sigma, peakHt )

xform = persp( x, y, t(z), xlim=c(-10,10), ylim=c(-10,10), cex.lab=1.3, zlab="Elevation",

main="Gaussian Gradients - Direction + Magnitude",

theta = xyAngle, phi = vertAngle, expand = 0.3, shade=0.4,

col = "lightblue", ticktype="detailed", cex.main=1.3*fontScale, cex.axis=1.3 )

arrowLen = 80

x1 = c( -4, 0, 4, -4, 0, 4, 7, -7, -5.8, 5.8, -5.8, 5.8 )

y1 = c( 4, 7, 4, -4, -7, -4, 0, 0, 5.8, 5.8, -5.8, -5.8 )

z1 = elevFunc( x1, y1, sigma, peakHt )

gradX = -gaussDzDx( x1, y1, sigma, peakHt )

gradY = -gaussDzDy( x1, y1, sigma, peakHt )

mags = sqrt( gradX^2 + gradY^2 )

gradX = arrowLen * gradX

gradY = arrowLen * gradY

x2 = x1 + gradX

y2 = y1 + gradY

z2 = z1

pt1 = trans3d( x1, y1, z1, xform )

pt2 = trans3d( x2, y2, z2, xform )

arrows( pt1$x, pt1$y, pt2$x, pt2$y, col=col, lwd=lwd, angle=15, length = 0.125 )

}

### Returns an elevation value as f(x,y) for down-oriented gaussian w/base at z=bias

elevFunc = function( x, y, sigma=3, peakHt=0.5, bias=1 ) {

r = sqrt( x^2 + y^2 )

elev = bias - peakHt * exp( -0.5 * (r/sigma)^2 )

return( elev )

}

### Exact analytical value for dz/dx for inverted gaussian

gaussDzDx = function( x, y, sigma, peakHt ) {

return( ( (peakHt*x)/sigma^2 ) * exp( -(x^2 + y^2)/(2*sigma^2) ) )

}

### Exact analytical value for dz/dy for inverted gaussian

gaussDzDy = function( x, y, sigma, peakHt ) {

return( ( (peakHt*y)/sigma^2 ) * exp( -(x^2 + y^2)/(2*sigma^2) ) )

}

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

}

runFunc()

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