diff options
Diffstat (limited to 'FSF-2020/approximations-and-optimizations')
4 files changed, 187 insertions, 0 deletions
diff --git a/FSF-2020/approximations-and-optimizations/Critical Points/example.py b/FSF-2020/approximations-and-optimizations/Critical Points/example.py new file mode 100644 index 0000000..3a41be7 --- /dev/null +++ b/FSF-2020/approximations-and-optimizations/Critical Points/example.py @@ -0,0 +1,32 @@ +from manimlib.imports import* + +class ExampleAnimation(ThreeDScene): + def construct(self): + axes = ThreeDAxes() + + f_text = TextMobject("$f(x,y) = (y-x)(1-2x-3y)$").to_corner(UL) + d = Dot(np.array([0,0,0]), color = '#800000') #---- Critical Point + d_text = TextMobject("$(0.2,0.2)$",color = '#DC143C').scale(0.5).shift(0.2*UP) #----x = 0.2, y = 0.2 + r_text=TextMobject("Critical Point",color = '#00FFFF').shift(0.3*DOWN).scale(0.6) + + #----f(x,y) = (y-x)(1-2x-3y) + f = ParametricSurface( + lambda u, v: np.array([ + u, + v, + (v-u)*(1-2*u-3*v) + ]),v_min = -1, v_max = 1, u_min = -1, u_max = 1, checkerboard_colors = [PURPLE_D, PURPLE_E], + resolution=(20, 20)).scale(1) + + self.set_camera_orientation(phi = 75 * DEGREES) + self.begin_ambient_camera_rotation(rate=0.5) + + self.add_fixed_in_frame_mobjects(f_text) + self.wait(1) + self.add(axes) + self.play(Write(f),Write(d)) + self.wait(1) + self.add_fixed_in_frame_mobjects(d_text) + self.wait(1) + self.add_fixed_in_frame_mobjects(r_text) + self.wait(3) diff --git a/FSF-2020/approximations-and-optimizations/Critical Points/motivation.py b/FSF-2020/approximations-and-optimizations/Critical Points/motivation.py new file mode 100644 index 0000000..27354ef --- /dev/null +++ b/FSF-2020/approximations-and-optimizations/Critical Points/motivation.py @@ -0,0 +1,30 @@ +from manimlib.imports import* + +class MotivationAnimation(Scene): + def construct(self): + + r = Rectangle(height = 7,breadth = 2,color = BLUE, fill_opacity = 0.3).scale(0.6) #----metal strip + b = Brace(r,UP) + r_text = TextMobject("$x$ metres",color = YELLOW).shift(3*UP) + m_text = TextMobject("Metal Strip").shift(3*DOWN) + a = Arc(radius=2).rotate(1).shift(LEFT+0.5*UP) + a2 = Arc(radius=2).rotate(5).shift(0.7*LEFT+0.9*UP).scale(0.2) + START = [1,0,0] + END = [0,3,0] + l = Line(START,END,color = RED).shift(0.9*DOWN) + a2_text = TextMobject("$\\theta$",color = PINK).shift(1.6*UP+0.4*RIGHT) + + group1 = VGroup(r_text,b,a,l,a2,a2_text) + f_text = TextMobject("$A = f(x,\\theta)$").shift(2*DOWN) + + ring = Annulus(inner_radius = 0.7, outer_radius = 1, color = BLUE) #--bent metal strip + + self.play(Write(r)) + self.wait(1) + self.play(ShowCreation(m_text)) + self.wait(1) + self.play(Write(group1)) + self.wait(2) + self.play(FadeOut(group1)) + self.wait(1) + self.play(ReplacementTransform(r,ring),ShowCreation(f_text)) diff --git a/FSF-2020/approximations-and-optimizations/Critical Points/theorem.py b/FSF-2020/approximations-and-optimizations/Critical Points/theorem.py new file mode 100644 index 0000000..7c82aa9 --- /dev/null +++ b/FSF-2020/approximations-and-optimizations/Critical Points/theorem.py @@ -0,0 +1,55 @@ +from manimlib.imports import* + +class TheoremAnimation(ThreeDScene): + def construct(self): + + axes = ThreeDAxes() + + #----parabola: x**2+y**2 + parabola1 = 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 = [TEAL_E], + resolution = (20, 20)).scale(1) + + #----parabola: -x**2-y**2 + parabola2 = 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 = [PURPLE_E,PURPLE_E], + resolution = (20, 20)).scale(1) + + self.set_camera_orientation(phi = 75 * DEGREES) + self.begin_ambient_camera_rotation(rate = 0.4) + + d = Dot(np.array([0,0,0]), color = '#800000') #---- critical point + r = Rectangle(fill_color = '#C0C0C0',fill_opacity = 0.3).move_to(ORIGIN) #----tangent plane + + parabola1_text = TextMobject("Maximum with horizontal tangent plane").scale(0.7).to_corner(UL) + + parabola2_text = TextMobject("Minimum with horizontal tangent plane").scale(0.7).to_corner(UL) + + self.add(axes) + self.add_fixed_in_frame_mobjects(parabola2_text) + self.wait(1) + self.play(Write(parabola1)) + self.wait(1) + self.play(ShowCreation(d)) + self.wait(1) + self.play(ShowCreation(r)) + self.wait(2) + self.play(FadeOut(parabola2_text),FadeOut(parabola1),FadeOut(r),FadeOut(d)) + + self.wait(1) + self.add_fixed_in_frame_mobjects(parabola1_text) + self.wait(1) + self.play(Write(parabola2)) + self.wait(1) + self.play(ShowCreation(d)) + self.wait(1) + self.play(ShowCreation(r)) + self.wait(2) diff --git a/FSF-2020/approximations-and-optimizations/Critical Points/types_of_cp.py b/FSF-2020/approximations-and-optimizations/Critical Points/types_of_cp.py new file mode 100644 index 0000000..f9055e6 --- /dev/null +++ b/FSF-2020/approximations-and-optimizations/Critical Points/types_of_cp.py @@ -0,0 +1,70 @@ +from manimlib.imports import * + +class TypescpAnimation(ThreeDScene): + def construct(self): + axes = ThreeDAxes() + + r_text = TextMobject("Relative Maximum at ORIGIN",color ='#87CEFA') + f_text = TextMobject("$f(x,y) = -x^2-y^2$").to_corner(UL) + + #----graph of first function f(x,y) = -x**2-y**2 + f = 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 = [YELLOW_D, YELLOW_E], + resolution = (20, 20)).scale(1) + + r2_text = TextMobject("Saddle Point at ORIGIN",color ='#87CEFA') + f2_text = TextMobject("$f(x,y) = -x^2+y^2$").to_corner(UL) + + #----graph of second 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_D, RED_E], + resolution = (20, 20)).scale(1) + + r3_text = TextMobject("Relative Minimum at ORIGIN",color ='#87CEFA') + f3_text = TextMobject("$f(x,y) = x^2+y^2$").to_corner(UL) + + #----graph of third function f(x,y) = x**2+y**2 + f3 = 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 = [GREEN_D, GREEN_E], + resolution = (20, 20)).scale(1) + + 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)) + self.add(axes) + self.play(Write(f3),Write(d)) + self.add_fixed_in_frame_mobjects(f3_text) + self.wait(2) |