笛卡尔到极坐标的转换

Question

How can I write a code that would show me this transformation, in the same format as the equation not like carrying it to the complex plain etc. because I want to play with it for other functions as well.

I tried myself a little bit and came up with this code that might be useful howeever I couldn't work it out to give me polar coordinates.

class Transformation(LinearTransformationScene):
    def construct(self):
        
        line = Line(start=np.array([0,0,0]),
    end=np.array([2,1,0]))
        
        function = lambda pos: np.dot(np.array(pos[0]*np.cos(pos[1]), pos[0]*np.sin(pos[1])), pos)

        self.add_transformable_mobject(line)

        self.apply_nonlinear_transformation(function, run_time=5)

        self.wait(3)

Answer 1

To transform cartesian coordinates to polar ones, you need this formula:

fi = numpy.arctan2(y, x)
r = numpy.hypot(y, x)