from manim import *
import math
import numpy as np


class Ex_5_7_14(Scene):
	def construct(self):
		numberplane = NumberPlane()
		self.add(numberplane)

		c1 = 1
		c2 = 0

		dot = Dot([c1-c2,3*c1,0])

		self.t_offset = 0
		rate = 0.5

		def move_on_path(mob, dt):
			self.t_offset += (dt * rate)
			mob.move_to([(c1-c2)*np.cos(3*self.t_offset)+(c1+c2)*np.sin(3*self.t_offset),3*c1*np.cos(3*self.t_offset)+3*c2*np.sin(3*self.t_offset),0])

		dot.add_updater(move_on_path)
		trace = TracedPath(dot.get_center, stroke_color=WHITE)
		self.add(dot, trace)

		self.wait(8)

		self.remove_updater(move_on_path)