[radians] Radians on a unit circle. #manim #geometry #math #radian #animation #arc

20230910_radian.py

from manim import *

class radClone(Scene):
    def construct(self):
        npl = NumberPlane(
            y_range=[-1.5,1.5,0.5],
            y_length=8,
            x_range=[-16/9*1.5,+16/9*1.5,0.5],
            x_length=16/9*8
        )
        self.add(npl)
        centerDot = Dot(color=WHITE).move_to(npl.c2p(0,0))
        movingDot1 = centerDot.copy().set_color(RED)
        movingDot2 = centerDot.copy().set_color(RED)
        self.play(Create(centerDot))
        self.play(Create(movingDot1),Create(movingDot2))
        radiusLine = Line(npl.c2p(0,0),npl.c2p(1,0), color=RED)
        self.play(
            Create(radiusLine),
            movingDot2.animate.move_to(npl.c2p(1,0)),
            rate_func = rate_functions.linear
        )
        circle = Circle(
            radius = np.linalg.norm(npl.c2p(1,0)-npl.c2p(0,0)),
            color = BLUE,
            stroke_width=2,
        )
        self.play(
            Create(circle),
            Rotate(movingDot2, 2*PI, about_point=npl.c2p(0,0)),
            Rotate(radiusLine, 2*PI, about_point=npl.c2p(0,0)),
            rate_func = rate_functions.linear,
            run_time = 2
        )
        self.play(
            Rotate(movingDot1, -PI/2, about_point=npl.c2p(1,0)),
            Rotate(radiusLine, -PI/2, about_point=npl.c2p(1,0)),
            rate_func = rate_functions.linear,
            run_time = 1
        )
        radiusLine.reverse_direction()
        arc = Arc(
            arc_center=circle.get_center(),
            radius=circle.radius, 
            start_angle=0, angle=1, 
            stroke_width=5,
            color=RED
        )
        self.play(
            ReplacementTransform(radiusLine, arc),
            movingDot1.animate.move_to(circle.point_at_angle(1)),
            rate_func = rate_functions.linear,
            run_time = 1
        )
        radiusLine1 = Line(circle.point_at_angle(0),circle.get_center(), color=TEAL)
        radiusLine2 = Line(circle.get_center(),circle.point_at_angle(1), color=TEAL)
        angle = always_redraw(lambda:
            Sector(
                start_angle=0,
                angle=radiusLine2.get_angle() % (2*PI),
                outer_radius=0.2*circle.radius, 
                stroke_width=3, 
                color=TEAL, 
                fill_opacity=0.6
            )
        )
        self.play(Create(radiusLine1))
        self.play(Create(radiusLine2))
        self.play(Create(angle))
        for i in range(5):
            self.add(radiusLine2.copy())
            self.play(
                Rotate(
                    VGroup(
                        radiusLine2,
                        movingDot1,
                        movingDot2,
                        arc,
                    ),
                    angle=1,
                    about_point=circle.get_center()
                )
            )
            self.wait()
        self.wait()