taperoff {spatstat.utils}

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.

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.

Value

A numeric vector of the same length as x.

Author(s)

Adrian Baddeley

Examples

  curve(taperoff(x, type="smooth"))
  curve(taperoff(x, type="cosine"), add=TRUE, col="green")
  curve(taperoff(x, type="Gaussian"), add=TRUE, col="blue")