spatstat.geom (version 3.7-2)

SupportFun: Support Function

Description

Create the support function of a two-dimensional domain.

Usage

SupportFun(W, origin = c(0, 0))

Value

A function in the R language with one argument theta.

Details

The support function \(h_W(\theta)\) of a set \(W\) is defined by $$ h_W(\theta) = \sup\{ x \cos\theta + y\sin\theta : (x,y) \in W \} $$ defined for all angles \(theta\) in \((0, 2\pi)\).

For any direction theta (in radians), \(h_W(\theta)\) is the signed distance from the origin to a line which is tangent to W and perpendicular to theta.

The result of SupportFun(W) is a function in the R language with one argument theta. This function can be applied to any vector of values of \(\theta\) to compute the values of the support function.

See Also

FeretDiamFun, polarbody

Examples

  W <- letterR
  Frame(W) <- grow.rectangle(Frame(W), 0.2)
  plot(W, main="")

  f <- SupportFun(W)
  p <- f(pi/6)
  plot(infline(p=p, theta=pi/6), col="red", lwd=2)

  ## as a function
  curve(f, to=2*pi)