diff options
Diffstat (limited to 'FSF-2020/approximations-and-optimizations')
| -rw-r--r-- | FSF-2020/approximations-and-optimizations/Critical-Points/file4_Types_of_critical_points.py | 88 |
1 files changed, 63 insertions, 25 deletions
diff --git a/FSF-2020/approximations-and-optimizations/Critical-Points/file4_Types_of_critical_points.py b/FSF-2020/approximations-and-optimizations/Critical-Points/file4_Types_of_critical_points.py index f9c1ef0..42703ba 100644 --- a/FSF-2020/approximations-and-optimizations/Critical-Points/file4_Types_of_critical_points.py +++ b/FSF-2020/approximations-and-optimizations/Critical-Points/file4_Types_of_critical_points.py @@ -1,6 +1,7 @@ from manimlib.imports import * -class TypescpAnimation(ThreeDScene): + +class MaximaScene(ThreeDScene): def construct(self): axes = ThreeDAxes() @@ -16,19 +17,74 @@ class TypescpAnimation(ThreeDScene): ]),v_min = -1, v_max = 1, u_min = -1, u_max = 1, checkerboard_colors = [YELLOW_B,YELLOW_C,YELLOW_D, YELLOW_E], resolution = (20, 20)).scale(1.5).shift([0,0,-0.51]).fade(0.3) - r2_text = TextMobject("Saddle Point at ORIGIN",color ='#87CEFA') - f2_text = TextMobject("$f(x,y) = -x^2+y^2$").to_corner(UL) + d = Dot(np.array([0,0,0]), color = '#800000') #---- critical point + + self.set_camera_orientation(phi = 75 * DEGREES, theta = -45 * DEGREES ) + self.add_fixed_in_frame_mobjects(r_text) + self.wait(1) + self.play(FadeOut(r_text)) + self.add(axes) + self.play(Write(f),Write(d)) + self.add_fixed_in_frame_mobjects(f_text) + self.wait(2) + self.play(FadeOut(axes),FadeOut(f),FadeOut(f_text),FadeOut(d)) + +class SaddlePoint(ThreeDScene): + def construct(self): - #----graph of second function f(x,y) = -x**2+y**2 + r2_text = TextMobject("Saddle Point",color ='#87CEFA') + axes = ThreeDAxes() + + #----graph of third function f(x,y) = -x**2+y**2 f2 = ParametricSurface( lambda u, v: np.array([ u, v, -u**2+v**2 - ]),v_min = -1, v_max = 1, u_min = -1, u_max = 1, checkerboard_colors = [RED_B,RED_C,RED_D, RED_E], - resolution = (20, 20)).scale(1.5).shift([0,0.2,0]).fade(0.3) + ]),v_min = -1, v_max = 1, u_min = -1, u_max = 1,checkerboard_colors = [PURPLE_B,PURPLE_C,PURPLE_D,PURPLE_E]).scale(1.5).shift([0,0,0]) + + #---- trace along y axis + a = ParametricSurface( + lambda u, v: np.array([ + u, + v, + v**2 + ]),v_min = -1, v_max = 1, u_min = -0.2, u_max = 0.2).shift([0,0,0.36]).scale(1.5).set_color(GREEN) + + #---- trace along x axis + b = ParametricSurface( + lambda u, v: np.array([ + u, + v, + -u**2 + ]),v_min = -0.2, v_max = 0.2, u_min = -1, u_max = 1).scale(1.6).shift([0,0,-0.1]).set_color(GREEN) + + d = Dot(color = '#800000').shift([0,0,0.1]) #---- critical point + + f2_text = TextMobject("$f(x,y) = -x^2+y^2$").to_corner(UL) + + self.add_fixed_in_frame_mobjects(r2_text) + self.wait(1) + self.set_camera_orientation(phi=75*DEGREES,theta=10*DEGREES) + self.play(FadeOut(r2_text)) + self.add(axes) + self.begin_ambient_camera_rotation(rate=0.4) + self.add_fixed_in_frame_mobjects(f2_text) + self.play(Write(f2)) + self.add(b) + self.wait(1) + self.add(a) + self.wait(3) + self.add(d) + self.wait(2) + + +class MinimaScene(ThreeDScene): + def construct(self): r3_text = TextMobject("Relative Minimum at ORIGIN",color ='#87CEFA') + axes = ThreeDAxes() + f3_text = TextMobject("$f(x,y) = x^2+y^2$").to_corner(UL) #----graph of third function f(x,y) = x**2+y**2 @@ -42,25 +98,7 @@ class TypescpAnimation(ThreeDScene): self.set_camera_orientation(phi = 75 * DEGREES, theta = -45 * DEGREES ) d = Dot(np.array([0,0,0]), color = '#800000') #---- critical point - - self.add_fixed_in_frame_mobjects(r_text) - self.wait(1) - self.play(FadeOut(r_text)) - self.add(axes) - self.play(Write(f),Write(d)) - self.add_fixed_in_frame_mobjects(f_text) - self.wait(2) - self.play(FadeOut(axes),FadeOut(f),FadeOut(f_text),FadeOut(d)) - - self.add_fixed_in_frame_mobjects(r2_text) - self.wait(1) - self.play(FadeOut(r2_text)) - self.add(axes) - self.play(Write(f2),Write(d)) - self.add_fixed_in_frame_mobjects(f2_text) - self.wait(2) - self.play(FadeOut(axes),FadeOut(f2),FadeOut(f2_text),FadeOut(d)) - + self.add_fixed_in_frame_mobjects(r3_text) self.wait(1) self.play(FadeOut(r3_text)) |