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-rw-r--r--FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/space-curves/README.md11
-rw-r--r--FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/space-curves/file1_parametric_ellipse.gifbin0 -> 340180 bytes
-rw-r--r--FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/space-curves/file1_parametric_ellipse.py78
-rw-r--r--FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/space-curves/file2_parametric_helix.gifbin0 -> 389637 bytes
-rw-r--r--FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/space-curves/file2_parametric_helix.py91
-rw-r--r--FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/space-curves/file3_circletosphere.gifbin0 -> 1811911 bytes
-rw-r--r--FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/space-curves/file3_circletosphere.py45
-rw-r--r--FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/space-curves/file4_cone.gifbin0 -> 987693 bytes
-rw-r--r--FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/space-curves/file4_cone.py33
9 files changed, 258 insertions, 0 deletions
diff --git a/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/space-curves/README.md b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/space-curves/README.md
new file mode 100644
index 0000000..42f5df1
--- /dev/null
+++ b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/space-curves/README.md
@@ -0,0 +1,11 @@
+**file1_parametric_ellipse.py** <br>
+![file1_parametric_ellipse.py](https://raw.githubusercontent.com/saarthdeshpande/FSF-mathematics-python-code-archive/master/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/space-curves/file1_parametric_ellipse.gif)
+
+**file2_parametric_helix.py** <br>
+![file2_parametric_helix.py](https://raw.githubusercontent.com/saarthdeshpande/FSF-mathematics-python-code-archive/master/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/space-curves/file2_parametric_helix.gif)
+
+**file3_circletosphere.py** <br>
+![file3_circletosphere.py](https://raw.githubusercontent.com/saarthdeshpande/FSF-mathematics-python-code-archive/master/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/space-curves/file3_circletosphere.gif)
+
+**file4_cone.py** <br>
+![file4_cone.py](https://raw.githubusercontent.com/saarthdeshpande/FSF-mathematics-python-code-archive/master/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/space-curves/file4_cone.gif)
diff --git a/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/space-curves/file1_parametric_ellipse.gif b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/space-curves/file1_parametric_ellipse.gif
new file mode 100644
index 0000000..90c0349
--- /dev/null
+++ b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/space-curves/file1_parametric_ellipse.gif
Binary files differ
diff --git a/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/space-curves/file1_parametric_ellipse.py b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/space-curves/file1_parametric_ellipse.py
new file mode 100644
index 0000000..1ce29d7
--- /dev/null
+++ b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/space-curves/file1_parametric_ellipse.py
@@ -0,0 +1,78 @@
+from manimlib.imports import *
+
+class parametricEllipse(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)
+
+ bcost_text = TextMobject(r'$y = b\cos{t}$').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(*[bcost_text, ylabel1, tlabel2])
+ bcost = ParametricFunction(
+ lambda t: np.array([
+ t,
+ 1.5*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)
+ ellipse_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'$x = a\sin{t}$ \\ $y = b\cos{t}$').scale(0.7).shift(2*UP + 1.3*LEFT)
+ main_text = VGroup(*[xlabel2, ylabel2, ellipse_text])
+ ellipse = ParametricFunction(
+ lambda t: np.array([
+ 1.5*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(bcost), FadeIn(ellipse), 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, bcost, run_time = 7), MoveAlongPath(ellipse_dot, ellipse, run_time = 7), t_value.set_value,3.14, rate_func=linear, run_time=7)
+ self.wait(1)
+ self.play(FadeOut(VGroup(*[axes, asint, bcost, ellipse, up_text, down_text, main_text, up_dot, down_dot, ellipse_dot, group])))
+ self.wait(1)
diff --git a/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/space-curves/file2_parametric_helix.gif b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/space-curves/file2_parametric_helix.gif
new file mode 100644
index 0000000..4f349b1
--- /dev/null
+++ b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/space-curves/file2_parametric_helix.gif
Binary files differ
diff --git a/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/space-curves/file2_parametric_helix.py b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/space-curves/file2_parametric_helix.py
new file mode 100644
index 0000000..3791752
--- /dev/null
+++ b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/space-curves/file2_parametric_helix.py
@@ -0,0 +1,91 @@
+from manimlib.imports import *
+
+class parametricHelix(ThreeDScene, GraphScene):
+ def construct(self):
+ self.x_min = -5
+ self.y_min = -4
+ self.graph_origin = ORIGIN
+ self.x_max = 5
+ self.y_max = 4
+ self.x_axis_label = ""
+ self.y_axis_label = ""
+ self.x_axis_width = 10
+ self.y_axis_height = 7.5
+ ax1 = ThreeDAxes().scale(0.65).shift(2.6*RIGHT+DOWN+np.array([0,0,0.5]))
+ axes_group = []
+
+ self.setup_axes()
+ self.axes.shift(3*RIGHT + 2*UP).scale(0.3)
+ axes_group.append(self.axes)
+
+ self.setup_axes()
+ self.axes.shift(3*RIGHT + 2*DOWN).scale(0.3)
+ axes_group.append(self.axes)
+
+ axes_group = VGroup(*axes_group)
+
+ 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(5*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 = -4*np.pi, t_max = 4*np.pi, color = GREEN_E
+ ).shift(3*RIGHT + 2*UP).scale(0.12)
+
+ 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(5*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 = -4*np.pi, t_max = 4*np.pi, color = BLUE
+ ).shift(3*RIGHT + 2*DOWN).scale(0.12)
+
+ up_dot = Dot(color = RED).scale(0.6)
+ down_dot = Dot(color = RED).scale(0.6)
+ helix_dot = Dot(radius = 0.16, color = RED)
+
+ zlabel = TextMobject(r'$z$').scale(0.7).shift(3*UP + 2.8*LEFT)
+ ylabel2 = TextMobject(r'$y$').scale(0.7).shift(0.3*DOWN+0.15*RIGHT)
+ xlabel2 = TextMobject(r'$x$').scale(0.7).shift(0.5*DOWN + 6.4*LEFT)
+ helix_text = TextMobject(r'$x = a\sin{t}$ \\ $y = a\cos{t}$ \\ $z = ct$').scale(0.7).shift(2.3*UP + 1.3*LEFT)
+ main_text = VGroup(*[xlabel2, ylabel2, zlabel, helix_text])
+ helix = ParametricFunction(
+ lambda t: np.array([
+ np.cos(TAU*t),
+ np.sin(TAU*t),
+ 0.4*t
+ ]), t_min = -2*np.pi/3, t_max = 1.8*np.pi/3, color = WHITE
+ ).shift(ax1.get_center())
+
+ self.set_camera_orientation(phi = 75*DEGREES, theta=45*DEGREES)
+
+ t_tracker = ValueTracker(-12.56)
+ t=t_tracker.get_value
+
+ t_label = TexMobject(
+ "t = ",color=WHITE
+ ).next_to(helix_text,DOWN, buff=0.2).scale(0.6)
+
+ t_text = always_redraw(
+ lambda: DecimalNumber(
+ t(),
+ color=WHITE,
+ ).next_to(t_label, RIGHT, buff=0.2)
+ ).scale(0.6)
+
+ group = VGroup(t_text,t_label).scale(1.5).move_to(ORIGIN).shift(2*DOWN)
+ self.add_fixed_in_frame_mobjects(axes_group, main_text, up_text, down_text, acost, asint)
+ self.play(FadeIn(ax1), FadeIn(axes_group), FadeIn(asint), FadeIn(acost), FadeIn(helix), FadeIn(up_text), FadeIn(down_text), FadeIn(main_text))
+ #self.begin_ambient_camera_rotation(rate = 0.06)
+ self.add_fixed_in_frame_mobjects(up_dot, down_dot, group)
+ self.play(MoveAlongPath(up_dot, asint, run_time = 8), MoveAlongPath(down_dot, acost, run_time = 8), MoveAlongPath(helix_dot, helix, run_time = 8), t_tracker.set_value,12.56, rate_func=linear, run_time=8)
+ self.play(FadeOut(VGroup(*[ax1, axes_group, asint, acost, helix, up_text, down_text, main_text, up_dot, down_dot, helix_dot, group])))
+ self.wait(1)
diff --git a/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/space-curves/file3_circletosphere.gif b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/space-curves/file3_circletosphere.gif
new file mode 100644
index 0000000..d6a8afc
--- /dev/null
+++ b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/space-curves/file3_circletosphere.gif
Binary files differ
diff --git a/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/space-curves/file3_circletosphere.py b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/space-curves/file3_circletosphere.py
new file mode 100644
index 0000000..6c0e810
--- /dev/null
+++ b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/space-curves/file3_circletosphere.py
@@ -0,0 +1,45 @@
+from manimlib.imports import *
+
+class sphere(GraphScene, ThreeDScene):
+ CONFIG = {
+ 'x_min': -10,
+ 'x_max': 10,
+ 'y_min': -10,
+ 'y_max': 10,
+ 'graph_origin': ORIGIN,
+ "x_axis_width": 10,
+ "y_axis_height": 10,
+ }
+ def construct(self):
+ XTD = self.x_axis_width/(self.x_max- self.x_min)
+ YTD = self.y_axis_height/(self.y_max- self.y_min)
+ circleeqn = TextMobject(r'Hence, $x^{2} + y^{2} = 2(r^{2} - u^{2})$')
+ plottext = TextMobject(r'$x = \sqrt{r^{2} - u^{2}}cos\theta$ \\ $y = \sqrt{r^{2} - u^{2}}sin\theta$').shift(2*UP + 3*RIGHT)
+
+
+ self.setup_axes()
+ self.play(FadeIn(self.axes), FadeIn(plottext))
+
+ dots = []
+ for t in range(19):
+ dot = Dot().shift((3*XTD*np.cos(t), 3*YTD*np.sin(t),0))
+ dots.append(dot)
+ self.play(FadeIn(dot), run_time = 0.2)
+ dots = VGroup(*dots)
+ circle = Circle(radius = 3*XTD).set_color(WHITE).set_stroke(width = 10)
+ self.play(FadeIn(circle), FadeOut(dots), FadeOut(plottext))
+ self.wait(2)
+
+
+ axes = ThreeDAxes(**self.CONFIG)
+ sph = Sphere(radius = 3).scale(0.5)
+ text2 = TextMobject(r'Setting $u = 3$,\\$z = u$').shift(4*YTD*UP + 5*XTD*RIGHT)
+
+ self.play(Transform(self.axes,axes), ReplacementTransform(circle, sph))
+ self.add(text2)
+ self.wait(2)
+ self.remove(text2)
+ self.move_camera(phi = 60*DEGREES, theta=45*DEGREES,run_time=5)
+ self.begin_ambient_camera_rotation(rate=0.03)
+ self.play(FadeOut(axes), FadeOut(sph), FadeOut(self.axes))
+ self.wait(1)
diff --git a/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/space-curves/file4_cone.gif b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/space-curves/file4_cone.gif
new file mode 100644
index 0000000..b126d20
--- /dev/null
+++ b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/space-curves/file4_cone.gif
Binary files differ
diff --git a/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/space-curves/file4_cone.py b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/space-curves/file4_cone.py
new file mode 100644
index 0000000..e6ae1c6
--- /dev/null
+++ b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/space-curves/file4_cone.py
@@ -0,0 +1,33 @@
+from manimlib.imports import *
+
+class cone(ThreeDScene):
+ def construct(self):
+ axes = ThreeDAxes()
+ eqn = TextMobject(r'$z^{2} = x^{2} + y^{2}$')
+
+ conecurve = ParametricFunction(
+ lambda t: np.array([
+ t*np.cos(TAU*t),
+ t*np.sin(TAU*t),
+ t
+ ]), t_min = -2.6, t_max = 2.6
+ ).scale(0.85)
+
+ conesurface = ParametricSurface(
+ lambda u,v: np.array([
+ 3*np.sin(u)*np.cos(TAU*v),
+ 3*np.sin(u)*np.sin(TAU*v),
+ 2.7*u
+ ]), u_min = -1
+ ).scale(0.85)
+
+ self.play(FadeIn(eqn))
+ self.wait(2)
+ self.play(FadeOut(eqn))
+ self.set_camera_orientation(phi = 75*DEGREES, theta=50*DEGREES)
+ self.play(FadeIn(axes), ShowCreation(conecurve, run_time = 3))
+ self.play(FadeOut(conecurve), FadeIn(conesurface))
+ self.begin_ambient_camera_rotation(rate=0.03)
+ self.wait(2)
+ self.play(FadeOut(axes), FadeOut(conesurface))
+ self.wait(2)