post-review updates

9 files changed, 168 insertions, 0 deletions

diff --git a/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/general-parametric-curves/__pycache__/file1_parametric_circle.cpython-38.pyc b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/general-parametric-curves/__pycache__/file1_parametric_circle.cpython-38.pyc
new file mode 100644
index 0000000..ad30b2a
--- /dev/null
+++ b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/general-parametric-curves/__pycache__/file1_parametric_circle.cpython-38.pyc
diff --git a/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/general-parametric-curves/__pycache__/file4_helix_visualization.cpython-38.pyc b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/general-parametric-curves/__pycache__/file4_helix_visualization.cpython-38.pyc
new file mode 100644
index 0000000..144d78d
--- /dev/null
+++ b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/general-parametric-curves/__pycache__/file4_helix_visualization.cpython-38.pyc
diff --git a/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/general-parametric-curves/file1_parametric_circle.py b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/general-parametric-curves/file1_parametric_circle.py
new file mode 100644
index 0000000..40b5150
--- /dev/null
+++ b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/general-parametric-curves/file1_parametric_circle.py
@@ -0,0 +1,78 @@
+from manimlib.imports import *
+
+class parametricCircle(ThreeDScene, GraphScene):
+    def construct(self):
+        self.x_min = -5
+        self.y_min = -5
+        self.graph_origin = ORIGIN
+        self.x_max = 5
+        self.y_max = 5
+        self.x_axis_label =  ""
+        self.y_axis_label =  ""
+        self.x_axis_width = 10
+        self.y_axis_height = 10
+
+        axes = []
+
+        self.setup_axes()
+        self.axes.scale(0.5).shift(3*LEFT)
+        axes.append(self.axes)
+        self.setup_axes()
+        self.axes.scale(0.3).shift(3*RIGHT + 2*UP)
+        axes.append(self.axes)
+        self.setup_axes()
+        self.axes.scale(0.3).shift(3*RIGHT + 2*DOWN)
+        axes.append(self.axes)
+
+        axes = VGroup(*axes)
+        t_value = ValueTracker(-3.14)
+        t_tex = DecimalNumber(t_value.get_value()).add_updater(lambda v: v.set_value(t_value.get_value()))
+        t_label = TexMobject("t = ")
+        group = VGroup(t_tex,t_label).shift(3*DOWN)
+        t_label.next_to(t_tex,LEFT, buff=0.2,aligned_edge=t_label.get_bottom())
+
+        asint_text = TextMobject(r'$x = a\sin{t}$').scale(0.7).shift(4*RIGHT + 3*UP)
+        xlabel1 = TextMobject(r'$x$').shift(3.3*RIGHT + 3.7*UP).scale(0.7)
+        tlabel1 = TextMobject(r'$t$').shift(4.8*RIGHT + 2*UP).scale(0.7)
+        up_text = VGroup(*[asint_text, xlabel1, tlabel1])
+        asint = ParametricFunction(
+        lambda t: np.array([
+        t,
+        np.sin(t),
+        0
+        ]), t_min = -np.pi, t_max = np.pi, color = GREEN_E
+        ).shift(3*RIGHT + 2*UP).scale(0.4)
+
+        acost_text = TextMobject(r'$y = a\cos{t}$').scale(0.7).shift(4*RIGHT + DOWN)
+        ylabel1 = TextMobject(r'$y$').shift(3.3*RIGHT+0.3*DOWN).scale(0.7)
+        tlabel2 = TextMobject(r'$t$').shift(4.8*RIGHT + 2*DOWN).scale(0.7)
+        down_text = VGroup(*[acost_text, ylabel1, tlabel2])
+        acost = ParametricFunction(
+        lambda t: np.array([
+        t,
+        np.cos(t),
+        0
+        ]), t_min = -np.pi, t_max = np.pi, color = BLUE
+        ).shift(3*RIGHT + 2*DOWN).scale(0.4)
+
+        up_dot = Dot(color = RED)
+        down_dot = Dot(color = RED)
+        circle_dot = Dot(color = RED)
+
+        ylabel2 = TextMobject(r'$y$').scale(0.7).shift(3*UP + 3*LEFT)
+        xlabel2 = TextMobject(r'$x$').scale(0.7)
+        ellipse_text = TextMobject(r'$x = a\sin{t}$ \\ $y = a\cos{t}$').scale(0.7).shift(2*UP + 1.3*LEFT)
+        main_text = VGroup(*[xlabel2, ylabel2, ellipse_text])
+        circle = ParametricFunction(
+                lambda t: np.array([
+                np.cos(t),
+                np.sin(t),
+                0
+                ]), t_min = -np.pi, t_max = np.pi, color = WHITE
+                ).shift(3*LEFT)
+        self.play(FadeIn(axes), FadeIn(asint), FadeIn(acost), FadeIn(circle), FadeIn(up_text), FadeIn(down_text), FadeIn(main_text), FadeIn(group))
+        self.wait(1)
+        self.play(MoveAlongPath(up_dot, asint, run_time = 7), MoveAlongPath(down_dot, acost, run_time = 7), MoveAlongPath(circle_dot, circle, run_time = 7), t_value.set_value,3.14, rate_func=linear, run_time=7)
+        self.wait(1)
+        self.play(FadeOut(VGroup(*[axes, asint, acost, circle, up_text, down_text, main_text, up_dot, down_dot, circle_dot, group])))
+        self.wait(1)
diff --git a/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/general-parametric-curves/file2_cycloid.gif b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/general-parametric-curves/file2_cycloid.gif
new file mode 100644
index 0000000..39656de
--- /dev/null
+++ b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/general-parametric-curves/file2_cycloid.gif
diff --git a/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/general-parametric-curves/file2_cycloid_manim.gif b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/general-parametric-curves/file2_cycloid_manim.gif
new file mode 100644
index 0000000..e68b841
--- /dev/null
+++ b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/general-parametric-curves/file2_cycloid_manim.gif
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))
diff --git a/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/general-parametric-curves/file3_brachistochrone.gif b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/general-parametric-curves/file3_brachistochrone.gif
new file mode 100644
index 0000000..8daf4c0
--- /dev/null
+++ b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/general-parametric-curves/file3_brachistochrone.gif
diff --git a/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/general-parametric-curves/file3_brachistochrone.py b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/general-parametric-curves/file3_brachistochrone.py
new file mode 100644
index 0000000..633e500
--- /dev/null
+++ b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/general-parametric-curves/file3_brachistochrone.py
@@ -0,0 +1,13 @@
+from manimlib.imports import *
+
+class brachistochrone(Scene):
+    def construct(self):
+        curve = ParametricFunction(
+        lambda t: np.array([
+        0.5*(t - np.sin(t)),
+        0.5*(1 - np.cos(t)),
+        0
+        ]), t_max = np.pi
+        ).scale(5).rotate(540*DEGREES)
+        dot = Dot(color = RED, radius = 0.2)
+        self.play(FadeIn(curve), MoveAlongPath(dot, curve, run_time = 2))
diff --git a/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/general-parametric-curves/file4_helix_visualization.py b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/general-parametric-curves/file4_helix_visualization.py
new file mode 100644
index 0000000..eddd3fe
--- /dev/null
+++ b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/general-parametric-curves/file4_helix_visualization.py
@@ -0,0 +1,31 @@
+from manimlib.imports import *
+
+class helix_(ThreeDScene):
+    CONFIG = {
+    "x_min": -6,
+    "x_max": 6,
+    "y_min": -6,
+    "y_max": 6,
+    "graph_origin": ORIGIN
+    }
+    def construct(self):
+        axes = ThreeDAxes()
+        helix = ParametricFunction(
+            lambda t: np.array([
+                1.5*np.cos(TAU*t),
+                1.5*np.sin(TAU*t),
+                2*t
+            ]), t_min = -1, t_max = 2, color = RED
+        )
+        cylinder = ParametricSurface(
+        lambda u, v: np.array([
+        1.5*np.cos(TAU*v),
+        1.5*np.sin(TAU*v),
+        2*u
+        ]), u_min = -1, u_max = 2, fill_opacity = -.4, fill_color = WHITE, color = WHITE
+        )
+        self.set_camera_orientation(phi=60* DEGREES,theta=45*DEGREES)
+        self.play(FadeIn(axes), FadeIn(cylinder), ShowCreation(helix, run_time = 4))
+        self.begin_ambient_camera_rotation(rate=0.5)
+        self.wait(5)
+        self.play(FadeOut(axes),FadeOut(helix), FadeOut(cylinder))