export const cart2polar = ({x, y}) => {
  const r = Math.sqrt(x*x + y*y);
  const θ = Math.atan(y/x);
  return {r, θ};
};

export const polar2cart = ({r, θ}) => {
  const x = r * Math.cos(θ);
  const y = r * Math.sin(θ);
  return {x, y};
}

export const translate = dx => dy => ({x, y}) => {
  return {left: x+dx, right: y+dy};
}

export const rotate = dθ => ({r, θ}) => {
  return {r, θ: θ+dθ};
}

export const scale = dr => ({r, θ}) => {
  return {r: r+dr, θ};
}