Eigen C++: Best Way To Convert 2D Polar To Cartesian

Question

I am currently doing:

Eigen::Vector2d polar(2.5, 3 * M_PI / 4);
Eigen::Vector2d cartesian = polar.x() * Vector2d(cos(polar.y()), sin(polar.y()));

but I'm not sure if this is the correct way to use Eigen or if there is some better built in way.

Thanks!

Answer 1

That looks right to me if you're wanting to stick with using Eigen.

Generally though since the polar representation has angles, it might be good to avoid using the Eigen::Vector2d just for the sake of reducing mistakes that may be made in the future (like adding multiple angles together and not dealing with the fact that 0 == 2*PI). Maybe you could do it with structs instead:

struct Polar { double range; double angle; };
struct Cartesian { double x; double y; };

Cartesian to_cartesian(const Polar& p) {
    double c = cos(p.angle);
    double s = sin(p.angle);
    return {p.range * c, p.range * s};
}

Polar to_polar(const Cartesian& c) {
    return {std::sqrt(c.x * c.x + c.y * c.y), std::atan2(c.y, c.x)};
}