Merge branch 'master' into master

1 files changed, 46 insertions, 0 deletions

diff --git a/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/general-parametric-curves/file2_cycloid_manim.py b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/general-parametric-curves/file2_cycloid_manim.py
new file mode 100644
index 0000000..7b6c0d1
--- /dev/null
+++ b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/general-parametric-curves/file2_cycloid_manim.py
@@ -0,0 +1,46 @@
+from manimlib.imports import *
+
+t_offset = 0
+c_t = 0
+
+class cycloid(Scene):
+    def construct(self):
+
+        cycl = ParametricFunction(
+        lambda t: np.array([
+        t - np.sin(t),
+        1 - np.cos(t),
+        0
+        ]), t_min = -2.75*np.pi, t_max = 3*np.pi, color = BLUE
+        ).shift(0.73*RIGHT)
+        wheel_radius = 1
+        wheel_function_path = lambda x : 0 + wheel_radius
+
+        line = FunctionGraph(lambda x : 0, color = BLACK)
+        wheel_path = FunctionGraph(wheel_function_path)
+
+        velocity_factor = 0.25
+        frame_rate = self.camera.frame_rate
+        self.dt = 1 / frame_rate
+
+        wheel = Circle(color = BLACK, radius = 1)
+        dot = Dot(radius = 0.16, color = RED)
+        #dot.move_to(wheel.get_arc_center() + np.array([0,2,0]))
+
+        def update_dot(mob,dt):
+            global t_offset,c_t
+            if dt == 0 and c_t == 0:
+                rate= - velocity_factor * self.dt
+                c_t += 1
+            else:
+                rate = - dt*velocity_factor
+            if dt > 0:
+                c_t = 0
+            mob.move_to(wheel.point_from_proportion(((t_offset + rate))%1))
+            t_offset += rate
+            #self.add(mob.copy())
+
+        #dot.move_to(wheel.get_arc_center() + np.array([0,2,0]))
+        dot.add_updater(update_dot)
+        self.add(wheel,dot, line, cycl)
+        self.play(MoveAlongPath(wheel, wheel_path, run_time = 9, rate_func = linear))