1 files changed, 30 insertions, 14 deletions
diff --git a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/partial-derivatives/file7_partial_deriv_clariant_rule.py b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/partial-derivatives/file7_partial_deriv_clariant_rule.py
index 313c6cd..b48f172 100644
--- a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/partial-derivatives/file7_partial_deriv_clariant_rule.py
+++ b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/partial-derivatives/file7_partial_deriv_clariant_rule.py
@@ -12,9 +12,13 @@ class ClariantRule(ThreeDScene):
             ]),u_min=0,u_max=PI,v_min=0,v_max=2*PI, color = BLUE_C, fill_color = BLUE_C, fill_opacity = 0.1,
             resolution=(15, 32)).scale(1)
 
-        
-        function_copy1 = function.copy()
-        function_copy2 = function.copy()
+        function_x = ParametricSurface(
+            lambda u, v: np.array([
+                3.5*np.sin(u)*np.cos(v),
+                3.5*np.sin(u)*np.sin(v),
+                -4*3.5*3.5*3.5*np.sin(u)*np.sin(u)*np.sin(u)*(2*np.sin(v)*np.sin(v))*np.exp(1 - 3.5*3.5*np.sin(u)*np.sin(u)) 
+            ]),u_min=0,u_max=PI,v_min=0,v_max=2*PI, color = BLUE_C, fill_color = BLUE_C, fill_opacity = 0.1,
+            resolution=(15, 32)).scale(1)
         
         func_x =ParametricFunction(
                 lambda u : np.array([
@@ -38,8 +42,11 @@ class ClariantRule(ThreeDScene):
         plane_y = Polygon(np.array([0,-3.5,-3]),np.array([0,3.5,-3]),np.array([0,3.5,3]),np.array([0,-3.5,3]),np.array([0,-3.5,-3]), color = GREEN_E, fill_color = GREEN_B, fill_opacity = 0.1)
         plane_text_y = TextMobject(r"$x = 0$", color = GREEN_C).move_to(np.array([0,4,2.7])).scale(0.7)
         
-        surface_eqn = TextMobject("Surface", r"$z = (x^2 + 3y^2)e^{(1 - x^2 - y^2)}$", color = YELLOW_C).scale(0.6).move_to(np.array([4.6*LEFT+3.5*UP]))
+        surface_eqn = TextMobject("Surface", r"$z = f(x,y) = (x^2 + 3y^2)e^{(1 - x^2 - y^2)}$", color = YELLOW_C).scale(0.6).move_to(np.array([4.1*LEFT+3.8*UP]))
         surface_eqn[0].set_color(BLUE_C)
+        number_plane = NumberPlane()
+
+        line = Line(np.array([0,-1,3]), np.array([0,-1,-3]), color = PURPLE)
 
         self.set_camera_orientation(phi=60 * DEGREES, theta = 45*DEGREES)
 
@@ -54,15 +61,20 @@ class ClariantRule(ThreeDScene):
         self.add_fixed_orientation_mobjects(axis[1])
 
         self.play(ShowCreation(function))
+        self.wait()
+        self.play(ShowCreation(number_plane))
 
         self.add_fixed_in_frame_mobjects(surface_eqn)
 
-        self.play(ShowCreation(plane_x), ShowCreation(plane_y))
+        self.play(ShowCreation(plane_x), ShowCreation(plane_y), ShowCreation(line))
         self.add_fixed_orientation_mobjects(plane_text_x, plane_text_y)
 
-        self.play(ShowCreation(func_x), ShowCreation(func_y))
+        self.move_camera(phi=0* DEGREES,theta=45*DEGREES)
+        self.wait(3)
+        self.move_camera(phi=60* DEGREES,theta=45*DEGREES)
+        #self.play(ShowCreation(func_x), ShowCreation(func_y))
         
-        dot_x = Dot().rotate(PI/2).set_color(YELLOW_E)
+        dot_x = Dot().rotate(PI/2).set_color(YELLOW_C)
         alpha_x = ValueTracker(0)
         vector_x = self.get_tangent_vector(alpha_x.get_value(),func_x,scale=1.5)
         dot_x.add_updater(lambda m: m.move_to(vector_x.get_center()))
@@ -92,17 +104,21 @@ class ClariantRule(ThreeDScene):
             )
         self.add(vector_x,dot_x)
         
-        self.play(alpha_x.increment_value, 1, run_time=10, rate_func=linear)
+        self.play(alpha_x.increment_value, 1, run_time=5, rate_func=linear)
 
         self.add(vector_y,dot_y)
-        self.play(alpha_y.increment_value, 1, run_time=10, rate_func=linear)
+        self.play(alpha_y.increment_value, 1, run_time=5, rate_func=linear)
 
         self.wait(2)
-       
-
-       
-
+        
 
-            
+    def get_tangent_vector(self, proportion, curve, dx=0.001, scale=1):
+        coord_i = curve.point_from_proportion(proportion)
+        coord_f = curve.point_from_proportion(proportion + dx)
+        reference_line = Line(coord_i,coord_f)
+        unit_vector = reference_line.get_unit_vector() * scale
+        vector = Line(coord_i - unit_vector, coord_i + unit_vector, color = ORANGE, buff=0)
+        return vector
+