Code for subtopic one: Gradient

1 files changed, 113 insertions, 0 deletions

diff --git a/FSF-2020/calculus-of-several-variables/div-curl-grad-and-all-that/gradient/file4-multidimensional-gradient.py b/FSF-2020/calculus-of-several-variables/div-curl-grad-and-all-that/gradient/file4-multidimensional-gradient.py
new file mode 100644
index 0000000..e9c8fd0
--- /dev/null
+++ b/FSF-2020/calculus-of-several-variables/div-curl-grad-and-all-that/gradient/file4-multidimensional-gradient.py
@@ -0,0 +1,113 @@
+from manimlib.imports import *
+import numpy as np
+
+
+class Hills(ThreeDScene):
+    def construct(self):
+        axes = ThreeDAxes(
+            number_line_config={
+                "color": GREEN,
+                "include_tip": False,
+                "exclude_zero_from_default_numbers": True,
+            }
+        )
+        self.add(axes)
+
+        self.set_camera_orientation(phi=45*DEGREES,theta=45*DEGREES,distance=40)
+        #self.begin_ambient_camera_rotation(rate=0.5)
+        self.wait()
+
+        cylinder_1 = ParametricSurface(
+            lambda u, v: np.array([
+            u,
+            v,
+            7*u*v/np.exp(u**2+v**2)
+            ]),u_min=-3,u_max=3, v_min=-1,v_max=-0.95).set_color(YELLOW_E).rotate(PI/2).shift(LEFT).fade(0.5)
+        cylinder = ParametricSurface(
+            lambda u, v: np.array([
+            u,
+            v,
+            7*u*v/np.exp(u**2+v**2)
+            ]),u_min=-3,u_max=3, v_min=-3,v_max=3).set_color(YELLOW_E).rotate(PI/2).shift(LEFT).fade(0.5)     
+        text_one = TexMobject(r"\textrm{Single variable functions slope up and down}")
+        #name = TexMobject(r"\textrm{PROBE}").next_to(text_one, DOWN, buff = SMALL_BUFF).scale(0.7)
+        text_one_a = TexMobject(r"\textrm{Position }", r" \rightarrow ").next_to(text_one, DOWN, buff = SMALL_BUFF)
+        probe = Sphere(radius = 0.2).next_to(text_one_a, RIGHT).set_color(BLUE_E)
+        text_one_b = TexMobject(r" \rightarrow ", r"\textrm{ slope }").next_to(probe, RIGHT, buff = SMALL_BUFF)
+        name = TextMobject("PROBE").next_to(probe, DOWN, buff = SMALL_BUFF).scale(0.5)
+        text = VGroup(text_one, text_one_a, probe, text_one_b, name).to_edge(UP+1.5*LEFT).scale(0.5)
+
+        text_two = TexMobject(r"\textrm{Multivariable functions slope in infinitely many directions!}")
+        #name_two = TexMobject(r"\textrm{PROBE2.0}").next_to(text_two, DOWN, buff = SMALL_BUFF).scale(0.7)
+        text_two_a = TexMobject(r"\textrm{Position, Direction }", r" \rightarrow ").next_to(text_two, DOWN, buff = SMALL_BUFF)
+        probe_two = Sphere(radius = 0.2).next_to(text_two_a, RIGHT).set_color(PURPLE_E)
+        text_two_b = TexMobject(r" \rightarrow ", r"\textrm{ slope }").next_to(probe_two, RIGHT, buff = SMALL_BUFF)
+        name_two = TextMobject("PROBE2.0").next_to(probe_two, DOWN, buff = SMALL_BUFF).scale(0.5)
+        two = VGroup(text_two, text_two_a, probe_two, text_two_b, name_two).to_edge(UP+LEFT).scale(0.5).shift(3.5*LEFT)
+
+
+
+
+
+
+        self.play(ShowCreation(cylinder_1))
+        self.wait()
+        self.add_fixed_in_frame_mobjects(text)
+        self.wait(3.5)
+        self.play(FadeOut(text))
+        self.play(ReplacementTransform(cylinder_1, cylinder))
+        self.wait()
+        self.add_fixed_in_frame_mobjects(two)
+        self.begin_ambient_camera_rotation(rate=0.5)
+        self.wait(4)
+
+class OneMore(ThreeDScene, GraphScene):
+    def setup(self):
+        GraphScene.setup(self)
+        ThreeDScene.setup(self)
+
+    def construct(self):
+        axes = ThreeDAxes(
+            number_line_config={
+                "color": GREEN,
+                "include_tip": False,
+                "exclude_zero_from_default_numbers": True,
+            }
+        )
+        self.add(axes)
+
+        self.set_camera_orientation(phi=90*DEGREES,theta=90*DEGREES,distance=40)
+        #self.begin_ambient_camera_rotation(rate=0.5)
+        self.wait()
+
+        shape = ParametricSurface(
+            lambda u, v: np.array([
+            u,
+            v,
+            2 - u**2 - v**2,
+            ]),u_min=0,u_max =0.01, v_min=-2,v_max=2).set_color(GREEN_C)
+
+        shape_A = ParametricSurface(
+            lambda u, v: np.array([
+            0*u,
+            0,
+            v,
+            ]),u_min=-2,u_max = 2, v_min=-2,v_max=2).set_color(GREEN_C)
+
+
+        '''
+        path = self.get_graph(lambda u,v: np.array([
+            u,
+            2 - u**2 - v**2]), u_min=-2,u_max=2, v_min=-2,v_max=2)
+        location = np.array([-2,-2, -2]) #location: Point
+        dot = Dot(location)
+        '''
+
+        self.play(ShowCreation(shape))
+        self.add(shape_A)
+        #self.play(ShowCreation(path), ShowCreation(dot))
+        #self.play(MoveAlongPath(dot, path))
+        #self.wait(3)
+        self.play(ApplyMethod(shape.fade, 0.5))
+        self.begin_ambient_camera_rotation(rate = 0.5)
+        self.wait(3)