pol2car {frechet}

Transform polar to Cartesian coordinates

Description

Transform polar to Cartesian coordinates

Usage

pol2car(p)

Arguments

p

A vector of length d (d\ge 2) with the first element being the radius and the others being the angles, where p[2] takes values in [0,2\pi] and p[i] takes values in [-\pi/2,\pi/2], for all i>2 if any.

Value

A vector of length d holding the corresponding Cartesian coordinates

\left(r\prod_{i=1}^{d-1}\cos\theta_i, r\sin\theta_1\prod_{i=2}^{d-1}\cos\theta_i, r\sin\theta_2\prod_{i=3}^{d-1}\cos\theta_i,\dots, r\sin\theta_{d-2}\cos\theta_{d-1}, r\sin\theta_{d-1}\right),

where r is given by p[1] and \theta_i is given by p[i+1] for i=1,\dots,d-1.

Examples

pol2car(c(1, 0, pi/4)) # should equal c(1,0,1)/sqrt(2)
pol2car(c(1, pi, 0)) # should equal c(-1,0,0)