spatstat.utils (version 1.17-0)

taperoff: Taper Functions

Description

Computes a function that tapers smoothly from 0 to 1.

Usage

taperoff(x, zeropoint = 0, onepoint = 1,
         type = c("smooth", "cosine", "Gaussian"))

Arguments

x

Function argument. A number or a numeric vector.

zeropoint

Value of x that should return a function value of 0.

onepoint

Value of x that should return a function value of 1.

type

Character string (partially matched) specifying which taper function to use.

Value

A numeric vector of the same length as x.

Details

A taper is a mathematical function that exhibits a gradual transition between the values 0 and 1.

By default, the function value \(f(x)\) is equal to 0 if \(x \le 0\), is equal to 1 if \(x \ge 1\), and lies between 0 and 1 when \(0 < x < 1\).

If type="cosine", the function is the cosine taper \(f(x) = (1 - \cos(\pi x))/2\).

If type="smooth" the function is the smooth partition of unity \(f(x) = \theta(x)/(\theta(x) + \theta(1-x))\) where \(\theta(x) = \exp(-1/x)\).

If type="Gaussian" the function is the cumulative distribution function of the Gaussian (normal) distribution with mean \(1/2\) and standard deviation \(1/6\).

If zeropoint and onepoint are specified, then the function value is equal to 0 when x=zeropoint, equal to 1 when x=onepoint, and lies between 0 and 1 when x lies between zeropoint and onepoint.

Examples

# NOT RUN {
  curve(taperoff(x, type="smooth"))
  curve(taperoff(x, type="cosine"), add=TRUE, col="green")
  curve(taperoff(x, type="Gaussian"), add=TRUE, col="blue")
# }