diff options
2 files changed, 52 insertions, 39 deletions
diff --git a/FSF-2020/approximations-and-optimizations/Tangent-Plane-Approximations/file1_TangentPlanes.py b/FSF-2020/approximations-and-optimizations/Tangent-Plane-Approximations/file1_TangentPlanes.py deleted file mode 100644 index 8e3a19e..0000000 --- a/FSF-2020/approximations-and-optimizations/Tangent-Plane-Approximations/file1_TangentPlanes.py +++ /dev/null @@ -1,39 +0,0 @@ -from manimlib.imports import* - -class TangenttoSurface(ThreeDScene): - def construct(self): - axes = ThreeDAxes() - - #parabola: -x**2-y**2 - p = 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=[BLUE_C,TEAL_D], - resolution=(20, 20)).scale(1).shift(1*RIGHT+2*UP) - self.set_camera_orientation(phi = 35 * DEGREES,theta = -40 * DEGREES ) - - r = Rectangle(side_length=2,side_breadth= 1, fill_color=PURPLE, fill_opacity=0.2).shift(ORIGIN-1+3*UP+2*RIGHT).scale(0.7) #---tangent plane along x axis - - r_text = TextMobject("Tangent Plane along $x$ axis",color = '#FFE4E1').scale(0.6).to_corner(UL) - r2_text = TextMobject("Tangent Plane along $y$ axis",color = '#FFE4E1').scale(0.6).to_corner(UL) - - a = Arrow(color = '#FFFFF0').shift(ORIGIN-1+3*UP+4*RIGHT).scale(0.5) - a2 = Arrow(color = '#FFFFF0').shift(ORIGIN+0.5+3*UP+RIGHT).scale(0.5) - a2.rotate(1.571) #----1.571 radian = 90 degrees - - self.add(axes) - self.play(Write(p)) - self.begin_ambient_camera_rotation(rate = 0.1) - self.add_fixed_in_frame_mobjects(r_text) - self.play(ShowCreation(r)) - self.play(ShowCreation(a)) - self.wait(1) - self.play(FadeOut(r),FadeOut(a),FadeOut(r_text)) - - r.rotate(1.571) #---tangent plane along y axis - self.play(ShowCreation(r)) - self.play(ShowCreation(a2)) - self.add_fixed_in_frame_mobjects(r2_text) - self.wait(2) diff --git a/FSF-2020/approximations-and-optimizations/Tangent-Plane-Approximations/file1_Tangent_Plane.py b/FSF-2020/approximations-and-optimizations/Tangent-Plane-Approximations/file1_Tangent_Plane.py new file mode 100644 index 0000000..3632d7e --- /dev/null +++ b/FSF-2020/approximations-and-optimizations/Tangent-Plane-Approximations/file1_Tangent_Plane.py @@ -0,0 +1,52 @@ +from manimlib.imports import* + +#---- tangent plane is parallel to the surface of the funtion at a point +class firstScene(ThreeDScene): + def construct(self): + + s1_text=TextMobject("Suppose, the point $(x,y)$ lies on the surface of the function.").scale(0.5).shift(2*UP) + s2_text=TextMobject("When zooming on that point, the surface would appear more and more like a plane.").scale(0.5).shift(1*UP) + s3_text=TextMobject("This plane is called the tangent plane.").scale(0.5) + + #---- graph of 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_B,YELLOW_C,YELLOW_D, YELLOW_E]).shift([0,0,0]).scale(1) + + + d = Dot([0,0,0],color = '#800000') #---- critical point + + r = Rectangle(color = PURPLE,fill_opacity=0.2).shift([0.1,0,0]).scale(0.3) #---- tangent plane + + s = 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_B,YELLOW_C,YELLOW_D, YELLOW_E]).shift([0,0,0]).scale(3.5) + + d2 = Dot([0,0,2.5],color = '#800000') #---- changing position of critical point + + r2 = Rectangle(color = PURPLE,fill_opacity=0.5).shift([0.1,0,2.5]).scale(0.3) #---- changing position of tangent plane + + self.set_camera_orientation(phi = 50 * DEGREES, theta = 45 * DEGREES) + self.add_fixed_in_frame_mobjects(s1_text) + self.add_fixed_in_frame_mobjects(s2_text) + self.add_fixed_in_frame_mobjects(s3_text) + self.wait(2) + self.play(FadeOut(s1_text)) + self.play(FadeOut(s2_text)) + self.play(FadeOut(s3_text)) + self.wait(1) + self.play(Write(f)) + self.play(Write(d)) + self.play(Write(r)) + self.wait(2) + self.play(ReplacementTransform(f,s),ReplacementTransform(d,d2),ReplacementTransform(r,r2)) + self.wait(2) + + |