random_point_in_triangle {tigers}

Random Points in Triangle

Description

Generates random points inside a triangle using Osada et al.'s (2002, Sect. 4.2) method.

Usage

  random_point_in_triangle(n, X, rfun1 = runif, rfun2 = runif)
  rpit(n, X, rfun1 = runif, rfun2 = runif)

Arguments

n

an integer giving the number of points to generate.

X

a numeric matrix with 3 rows and 2 columns giving the coordinates of the triangle.

rfun1

a function generating random values in [0,1]. By default, the values are generated under a uniform distribution.

rfun2

same as the previous argument (see details).

Details

By default, the points are uniformly distributed in the triangle. The Beta function offers an interesting alternative to generate points concentrated in a specific part of the triangle (see examples).

Value

A numeric matrix with n rows and two columns giving the coordinates of the points.

Author(s)

Emmanuel Paradis

References

Osada, R., Funkhouser, T., Chazelle, B., and Dobkin, D. (2002) Shape distributions. ACM Transactions on Graphics, 21, 807–832. <doi:10.1145/571647.571648>

Examples

## a random triangle in [0,1]^2:
P <- matrix(runif(6), 3, 2)

## n points uniformly distributed in the triangle P:
n <- 10000
x <- rpit(n, P)

layout(matrix(1:2, 1))

plot(P, type = "n", asp = 1)
polygon(P, col = "yellow", border = NA)
points(x, pch = ".", col = "blue")

## using Beta distributions:
foo <- function(n) rbeta(n, 1, 10)
bar <- function(n) rbeta(n, 1, 1)
y <- rpit(n, P, foo, bar)

plot(P, type = "n", asp = 1)
polygon(P, col = "yellow", border = NA)
points(y, pch = ".", col = "blue")

layout(1)