diff options
Diffstat (limited to 'FSF-2020/approximations-and-optimizations')
| -rw-r--r-- | FSF-2020/approximations-and-optimizations/Critical-Points/file2_Traces_and_Tangent.py | 105 |
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) |