conformalPredict: Conformal mapping

In conformal: Conformal mapping from a polygon to a disk

Description

Apply the solutions of the Schwartz-Christoffel equations to a new complex vector.

Usage

conformalPredict(fit, x, polygon2disk = TRUE)

Arguments

fit	an object returned by conformalFit
x	a complex vector or a real vector representing a complex vector (see C2R).
polygon2disk	if TRUE then apply the transformation in the direction that maps the polygon to the unit circle. Otherwise apply in the direction from unit circle to polygon.

Value

a real vector representing a complex vector that is the result of transforming x.

Author(s)

Nick Ellis, [e-mail]

References

Trefethen, LN (1980) Numerical computation of the Schwarz-Christoffel transformation, Siam J. Sci. Stat. Comp. 1, 82-102.

See Also

conformalFit

Examples

CircleGrid <- function(nradial) { # create a random pattern to fill a disk
  r <- seq(0,1,len=nradial)
  nth <- pmax(1,ceiling(2*pi*r*(nradial-1)))
  th0 <- runif(nth,-pi/nth,pi/nth)
  list(
    x=unlist(lapply(1:nradial, function(i,r,nth,th0)
      r[i]*cos(th0[i]+seq(0,2*pi,len=nth[i]+1)[-nth[i]-1]),r=r,nth=nth,th0=th0)),
    y=unlist(lapply(1:nradial, function(i,r,nth,th0)
      r[i]*sin(th0[i]+seq(0,2*pi,len=nth[i]+1)[-nth[i]-1]),r=r,nth=nth,th0=th0))
  )
}
disk <- listxy2R(CircleGrid(30))
poly <- list(
  x=c(0.81,0.00,-0.73,-0.72,0.07,0.59,0.90),
  y=c(0.26,0.52,0.18,-0.44,-0.75,-0.39,0.01)
)
#poly <- locator(type='l')
fit <- conformalFit(poly)
pred <- conformalPredict(fit, disk, polygon2disk=FALSE)
cDisk <- R2C(disk)
cPred <- R2C(pred)
cols <- hsv(h=Arg(cDisk)/2/pi+0.5,s=pmin(1,Mod(cDisk)))
par(mfrow=c(1,2))
plot(cDisk, col=cols, asp=1, pch=16, main="Colour wheel")
lines(poly)
plot(cDisk, type='n', asp=1, main="Colour wheel\nmapped to polygon")
points(cPred, col=cols,pch=16)
circ <- abs(Mod(cDisk)-1) < 1e-6
segments(Re(cDisk[circ]),Im(cDisk[circ]),Re(cPred[circ]),Im(cPred[circ]), col=cols[circ])
lines(poly)

conformal documentation built on May 2, 2019, 5:47 p.m.