1 files changed, 103 insertions, 0 deletions
diff --git a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/directional-derivatives/file2_gradient.py b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/directional-derivatives/file2_gradient.py
new file mode 100644
index 0000000..e9fef50
--- /dev/null
+++ b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/directional-derivatives/file2_gradient.py
@@ -0,0 +1,103 @@
+from manimlib.imports import *
+
+class Gradient(ThreeDScene):
+    def construct(self):
+        axes = ThreeDAxes() # creates a 3D Axis
+        
+
+        quadrant = ParametricSurface(
+            lambda u, v: np.array([
+                2*np.sin(u)*np.cos(v),
+                2*np.sin(u)*np.sin(v),
+                2*np.cos(u)
+            ]),u_min=0,u_max=PI/3,v_min=0,v_max=PI/2,checkerboard_colors=[GREEN_C, GREEN_E],
+            resolution=(15, 32)).scale(1)
+
+        quadrant_curve = ParametricSurface(
+            lambda u, v: np.array([
+                2*np.sin(u)*np.cos(v),
+                2*np.sin(u)*np.sin(v),
+                2*np.cos(u)
+            ]),u_min=34*DEGREES,u_max=38*DEGREES,v_min=0,v_max=PI/2,checkerboard_colors=[YELLOW_C, YELLOW_E],
+            resolution=(15, 32)).scale(1)
+
+
+
+        dot1 =Sphere(radius=0.05).move_to(np.array([1,1,0])).set_fill(YELLOW_C)
+        dot2 =Sphere(radius=0.05).move_to(np.array([1,1,1.732])).set_fill(YELLOW_C)
+
+        dot1_line = DashedLine(np.array([1,1,1.732]), np.array([0,2,2]), color = WHITE)
+        dot1_lab = TextMobject(r"$P_0(x_0,y_0,z_0)$").move_to(np.array([0,2.1,2.2])).set_color(YELLOW_C).scale(0.6)
+        #dot2_line = Line(np.array([0.8,0.8,0]), np.array([1,0.6,0]), color = PINK)
+
+        positive_vector = Arrow(np.array([1,1,0]), np.array([0.5,0.5,0]), buff=0.001, color = BLUE_C)
+        positive_gradient = Arrow(np.array([1,1,1.732]), np.array([0.5,0.5,1.9362]), buff=0.001, color = BLUE_C)
+        positive_gradient_lab = TextMobject(r"$\nabla f$").move_to(np.array([0.5,0.3,0])).set_color(BLUE_C).scale(0.5)
+
+        negative_vector = Arrow(np.array([1,1,0]), np.array([1.5,1.5,0]), buff=0.001, color = RED_C)
+        negative_gradient = Arrow(np.array([1,1,1.732]), np.array([1.5,1.5,1.322]), buff=0.001, color = RED_C)
+        negative_gradient_lab = TextMobject(r"$-\nabla f$").move_to(np.array([1.6,1.6,0])).set_color(RED_C).scale(0.5)
+
+        positive_vector_line = DashedLine(np.array([0.8,0.8,0]), np.array([1,-2,0]), color = WHITE)
+        positive_vector_lab = TextMobject(r"Most Rapid increase in $f$").move_to(np.array([1.6,-3.6,0])).set_color(BLUE_C).scale(0.6)
+        negative_vector_line = DashedLine(np.array([1.2,1.2,0]), np.array([3,-1.5,0]), color = WHITE)
+        negative_vector_lab = TextMobject(r"Most Rapid decrease in $f$").move_to(np.array([3.6,-3,0])).set_color(RED_C).scale(0.6)
+
+
+
+        line1 = DashedLine(np.array([0.5,0.5,0]), np.array([0.5,0.5,1.9362]), color = BLUE_C)
+        line2 = DashedLine(np.array([1,1,0]), np.array([1,1,1.732]), color = YELLOW_C)
+        line3 = DashedLine(np.array([1.5,1.5,0]), np.array([1.5,1.5,1.322]), color = RED_C)
+
+        curve_vector1 = Arrow(np.array([1,1,0]), np.array([1.5,0.5,0]), buff=0.001, color = YELLOW_C)
+        curve_vector2 = Arrow(np.array([1,1,0]), np.array([0.5,1.5,0]), buff=0.001, color = YELLOW_C)
+
+        curve_vector1_line = DashedLine(np.array([1.2,0.8,0]), np.array([1,2.5,0]), color = WHITE)
+        curve_vector2_line = DashedLine(np.array([0.8,1.2,0]), np.array([1,2.5,0]), color = WHITE)
+        curve_vector_lab = TextMobject(r"Zero Change in $f$").move_to(np.array([0.7,3.6,0])).set_color(PINK).scale(0.6)
+
+        #square = Square(side_length = 0.5).rotate(45*DEGREES).move_to(np.array([1.025,0.975,0]))
+        line_x = Line(np.array([0.8,0.8,0]), np.array([1,0.6,0]), color = PINK)
+        line_y = Line(np.array([1.2,0.8,0]), np.array([1,0.6,0]), color = PINK)
+
+        ninety_degree = VGroup(line_x, line_y)
+        
+        self.set_camera_orientation(phi=60* DEGREES, theta = 20*DEGREES)
+
+        self.add(axes)
+
+        axis = TextMobject(r"X",r"Y",r"Z")
+        axis[0].move_to(6*RIGHT)
+        axis[1].move_to(6*UP)
+        axis[2].move_to(np.array([0,0,3.7]))
+
+        self.add_fixed_orientation_mobjects(axis[2])
+        self.add_fixed_orientation_mobjects(axis[0])
+        self.add_fixed_orientation_mobjects(axis[1]) 
+
+        self.play(ShowCreation(quadrant))
+        self.wait()
+        self.play(ShowCreation(dot1),  ShowCreation(dot2))
+        self.wait()
+        self.play(GrowArrow(positive_vector), GrowArrow(positive_gradient))
+        self.wait()
+        self.play(GrowArrow(negative_vector), GrowArrow(negative_gradient))
+        self.wait()
+        self.play(GrowArrow(line1), GrowArrow(line2), GrowArrow(line3))
+        self.wait()
+        self.play(ShowCreation(quadrant_curve))
+        self.wait()
+        self.play(GrowArrow(curve_vector1), GrowArrow(curve_vector2), ShowCreation(ninety_degree))
+        self.wait()
+        self.play(GrowArrow(dot1_line))
+        self.add_fixed_orientation_mobjects(dot1_lab)
+        self.wait()
+        self.play(GrowArrow(curve_vector1_line), GrowArrow(curve_vector2_line))
+        self.add_fixed_orientation_mobjects(curve_vector_lab)
+        self.wait()
+        self.add_fixed_orientation_mobjects(positive_gradient_lab, negative_gradient_lab)
+        self.wait()
+        self.play(GrowArrow(positive_vector_line), GrowArrow(negative_vector_line))
+        self.add_fixed_orientation_mobjects(positive_vector_lab, negative_vector_lab)
+        self.begin_ambient_camera_rotation(rate=0.1)
+        self.wait(3)
+\ No newline at end of file