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frechet (version 0.3.0)

pol2car: Transform polar to Cartesian coordinates

Description

Transform polar to Cartesian coordinates

Usage

pol2car(p)

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 \(i=1,\dots,d-1\).

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.

Examples

Run this code
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)

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