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-rw-r--r--FSF-2020/approximations-and-optimizations/Critical-Points/file2_Traces_and_Tangent.py105
1 files changed, 50 insertions, 55 deletions
diff --git a/FSF-2020/approximations-and-optimizations/Critical-Points/file2_Traces_and_Tangent.py b/FSF-2020/approximations-and-optimizations/Critical-Points/file2_Traces_and_Tangent.py
index 6be4c6a..95c3af9 100644
--- a/FSF-2020/approximations-and-optimizations/Critical-Points/file2_Traces_and_Tangent.py
+++ b/FSF-2020/approximations-and-optimizations/Critical-Points/file2_Traces_and_Tangent.py
@@ -1,93 +1,88 @@
from manimlib.imports import*
import math as m
-
+#---- tangent to the trace with x constant
class firstScene(ThreeDScene):
def construct(self):
- axes = ThreeDAxes().scale(1.15)
+ axes = ThreeDAxes().scale(1)
+ label_x= TextMobject("$x$").shift([5.8,-0.5,0])
+ label_y= TextMobject("$y$").shift([-0.5,-5.6,0]).rotate(-4.5)
+
+ #---- graph of f(x,y) = -x^2-y^2
surface = ParametricSurface(
lambda u, v: np.array([
u,
v,
- m.exp(-10*u**2-10*v**2) #---- f(x,y)
- ]),u_min=-2,u_max=1, v_min=-1,v_max=1,checkerboard_colors=[PURPLE_C,PURPLE_D,PURPLE_E,PURPLE_B]).scale(3).shift([1.1,0.48,1.731])
-
- trace = ParametricSurface(
+ -u**2-v**2
+ ]),u_min=-1,u_max=1, v_min=-1,v_max=1,checkerboard_colors=[PURPLE_C,PURPLE_D,PURPLE_E,PURPLE_B]).scale(1.5).shift([0,0,2]).rotate(0.2)
+
+ #---- curve(trace) along y axis
+ curve = ParametricSurface(
lambda u, v: np.array([
- m.exp(np.cos(v)+np.sin(v)),
- v,
- u/4
- ]), v_min = -1, v_max= 2).rotate(1.571,DOWN).shift(2.15*LEFT+[0.6,-0.4,1.54]).scale(1).set_color('#800000')
+ u*0.4,
+ v,
+ -v**2
+ ]),v_min =-1 , v_max =1 , u_min = -0.1, u_max = 0.1).scale(1.6).shift([0.02,0.1,2.3]).set_color("#800000").rotate(0.1)
-
-
- d = Dot(color =YELLOW).shift([1.9,0.7,4.1]) #---- critical point
- tangent_line = Line(color = '#228B22').scale(1).shift([1.9,0.7,4.1]).rotate(4.5) #---- tangent along y axis
+ d = Dot(color =YELLOW).shift([-0.05,-0.2,2.3]) #---- critical point
- label_x = TextMobject("$x$").shift([5.8,-0.5,0])
- label_y = TextMobject("$y$").shift([-0.5,5.6,0]).rotate(-4.5)
+ x_text = TextMobject("Tangent to the trace with $x$ constant at critical point").shift(3*RIGHT+2*UP).scale(0.5).to_corner(UL)
+ tangent_line = Line([-0.05,-1.5,2.3],[-0.05,1.5,2.3],color = '#228B22')
- f_text = TextMobject("Tangent to the trace with $y$ constant at critical point").shift(3*RIGHT+2*UP).scale(0.5).to_corner(UL)
-
self.add(axes)
- self.set_camera_orientation(phi=60*DEGREES,theta=15*DEGREES)
+ self.set_camera_orientation(phi = 40 * DEGREES, theta = 55 * DEGREES)
+ self.begin_ambient_camera_rotation(rate = 0.1)
self.add(label_x)
self.add(label_y)
self.play(Write(surface))
- self.wait(1)
- self.add_fixed_in_frame_mobjects(s_text)
- self.add(trace)
+ self.add_fixed_in_frame_mobjects(x_text)
+ self.add(curve)
self.wait(1)
self.play(Write(tangent_line),Write(d))
- self.wait(2)
-
-
+ self.wait(1)
+
+
+
+#---- tangent to the trace with y constant
class secondScene(ThreeDScene):
def construct(self):
- axes = ThreeDAxes().scale(1.15)
+ axes = ThreeDAxes().scale(1)
+ label_x= TextMobject("$x$").shift([5.8,-0.5,0])
+ label_y= TextMobject("$y$").shift([-0.5,-5.6,0]).rotate(-4.5)
+
+ #---- graph of f(x,y) = -x^2-y^2
surface = ParametricSurface(
lambda u, v: np.array([
u,
v,
- m.exp(-10*u**2-10*v**2) #---- f(x,y)
- ]),u_min=-1,u_max=1, v_min=-1,v_max=1,checkerboard_colors=[PURPLE_C,PURPLE_D,PURPLE_E,PURPLE_B]).scale(3).shift([1.1,0.48,1.731])
+ -u**2-v**2
+ ]),u_min = -1, u_max = 1, v_min = -1, v_max = 1, checkerboard_colors = [PURPLE_B,PURPLE_C,PURPLE_D,PURPLE_E]).scale(1.5).shift([0,0,2]).rotate(0.2)
- trace = ParametricSurface(
+ #---- curve(trace) along x axis
+ curve = ParametricSurface(
lambda u, v: np.array([
- m.exp(np.cos(v)+np.sin(v)),
- v,
- u/4
- ]), v_min = -1, v_max= 2).rotate(1.571,DOWN).shift(2.15*LEFT+[0.6,-0.4,1.54]).scale(1).set_color('#800000')
-
-
+ u,
+ v*0.4,
+ -u**2
+ ]),v_min = -0.1, v_max = 0.1, u_min = -1, u_max = 1).scale(1.6).shift([0.07,0.1,2.3]).set_color("#800000")
- d = Dot(color =YELLOW).shift([1.9,0.7,4.1]) #---- critical point
-
- label_x = TextMobject("$x$").shift([5.8,-0.5,0])
- label_y = TextMobject("$y$").shift([-0.5,5.6,0]).rotate(-4.5)
-
- f_text = TextMobject("Tangent to the trace with $y$ constant at critical point").shift(3*RIGHT+2*UP).scale(0.5).to_corner(UL)
+ d = Dot(color = YELLOW).shift([0,-0.2,2.3]) #---- critical point
- tangent_line = Line(color = '#228B22').scale(1).shift([1.9,0.7,4.1]) #---- tangent along x axis
-
+ tangent_line = Line(color = '#228B22').scale(1).shift([0,-0.2,2.3]).rotate(m.radians(190),LEFT)
+
+ y_text = TextMobject("Tangent to the trace with $y$ constant at critical point").shift(3*RIGHT+2*UP).scale(0.5).to_corner(UL)
self.add(axes)
- self.set_camera_orientation(phi=60*DEGREES,theta=15*DEGREES)
+ self.set_camera_orientation(phi = 40 * DEGREES, theta = 55 * DEGREES)
self.add(label_x)
self.add(label_y)
+ self.begin_ambient_camera_rotation(rate = 0.1)
self.play(Write(surface))
- self.wait(1)
- self.add_fixed_in_frame_mobjects(f_text)
- trace.rotate(-5).shift(0.2*RIGHT+0.8*UP+[0.6,-0.4,0.6])
- self.add(trace)
+ self.add_fixed_in_frame_mobjects(y_text)
+ self.add(curve)
+ self.wait(1.5)
self.play(Write(tangent_line),Write(d))
- self.wait(1)
-
-
-
-
-
-
+ self.wait(0.5)