diff options
Diffstat (limited to 'FSF-2020/calculus-of-several-variables')
16 files changed, 179 insertions, 7 deletions
diff --git a/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/arc-length-and-curvature/file3_curvature_interpretation.gif b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/arc-length-and-curvature/file3_curvature_interpretation.gif Binary files differnew file mode 100644 index 0000000..39489b7 --- /dev/null +++ b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/arc-length-and-curvature/file3_curvature_interpretation.gif diff --git a/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/arc-length-and-curvature/file3_curvature_interpretation.py b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/arc-length-and-curvature/file3_curvature_interpretation.py new file mode 100644 index 0000000..cf6b032 --- /dev/null +++ b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/arc-length-and-curvature/file3_curvature_interpretation.py @@ -0,0 +1,42 @@ +from manimlib.imports import * + +class interpretation(Scene): + def construct(self): + tgt = Vector((1, 2, 0), color = YELLOW) + tgtText = TextMobject(r'$r\prime (t)$').next_to(tgt, UP, buff = 0).scale(0.7) + tgt2 = DashedLine((0,0,0),(1, 2, 0), color = GRAY).shift(DOWN + 2*RIGHT) + + nm = Vector((2, -1, 0), color = BLUE) + nmText = TextMobject(r'$r\prime\prime (t)$').next_to(nm, DOWN+RIGHT, buff = 0).scale(0.7) + nm2 = DashedLine((0,0,0),(2, -1, 0), color = GRAY).shift(2*UP + RIGHT) + square = Square(fill_color = WHITE, fill_opacity = 0.2).rotate(63*DEGREES).shift(0.5*UP +1.5*RIGHT).scale(1.1) + square.set_stroke(width = 0.1) + arrow = CurvedArrow(square.get_center() + np.array([2,1,0]), square.get_center() + np.array([0.5,0,0])) + arrowText = TextMobject(r'$r\prime (t)\times r\prime\prime (t)$').next_to(arrow.get_start(), DOWN+1*RIGHT, buff = 0).scale(0.7) + + text1 = TextMobject(r'$\left|\frac{dT}{ds}\right| = \frac{\left|\frac{dT}{dt}\right|}{\left|\frac{ds}{dt}\right|}$').shift(UP+3*LEFT) + text2 = TextMobject(r'$\left|\frac{dT}{ds}\right| = \frac{\frac{r\prime\prime (t)}{\left| r\prime (t)\right|}\times\frac{r\prime (t)}{\left| r\prime (t)\right|}}{\left|r\prime (t)\right|}$').next_to(text1, DOWN, buff = 0.1) + unit = VGroup(*[tgt, tgt2, nm, nm2]) + + # self.play(FadeIn(VGroup(*[tgt, tgt2, nm, nm2, nmText, tgtText, square, arrow, arrowText]))) + tgt2text = TextMobject(r'$\frac{r\prime (t)}{\left| r\prime (t)\right|}$').shift(1.1*UP).scale(0.7).rotate(63*DEGREES ) + nm2text = TextMobject(r'$\frac{dT}{dt} = \frac{r\prime\prime (t)}{\left| r\prime (t)\right|}$').scale(0.6).shift(0.5*RIGHT+0.6*DOWN).rotate(-25*DEGREES) + unit2 = unit.copy().scale(0.5).shift(0.75*LEFT+0.25*DOWN) + + self.play(FadeIn(VGroup(*[tgt, tgtText]))) + self.wait(1) + self.play(FadeIn(VGroup(*[nm, nmText]))) + self.wait(1) + self.play(FadeIn(VGroup(*[tgt2, nm2]))) + self.wait(1) + self.play(FadeIn(VGroup(*[square, arrow, arrowText]))) + self.wait(1) + self.play(FadeIn(unit2)) + self.wait(1) + self.play(FadeIn(VGroup(*[tgt2text, nm2text]))) + self.wait(1) + self.play(FadeIn(text1)) + self.wait(1) + self.play(FadeIn(text2)) + self.wait(2) + self.play(FadeOut(VGroup(*[tgt2text, nm2text, text1, text2, tgt, tgtText,nm, nmText,tgt2, nm2,square, arrow, arrowText,unit2]))) diff --git a/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/arc-length-and-curvature/file3_curvature_intuition.gif b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/arc-length-and-curvature/file3_curvature_intuition.gif Binary files differdeleted file mode 100644 index 0d6fdcf..0000000 --- a/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/arc-length-and-curvature/file3_curvature_intuition.gif +++ /dev/null diff --git a/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/arc-length-and-curvature/file4_different_curvature_single_curve.py b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/arc-length-and-curvature/file4_different_curvature_single_curve.py index 3ecd57c..56b7fbb 100644 --- a/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/arc-length-and-curvature/file4_different_curvature_single_curve.py +++ b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/arc-length-and-curvature/file4_different_curvature_single_curve.py @@ -8,7 +8,9 @@ class GR(GraphScene): "x_max": 6, "y_min": -6, "y_max": 10, - "graph_origin": ORIGIN + "graph_origin": ORIGIN, + 'x_tick_frequency': 20, + 'y_tick_frequency': 20 } def construct(self): @@ -21,7 +23,7 @@ class GR(GraphScene): tracker = ValueTracker(-3) - text = TextMobject(r'The curvature at point $P_{1}$ is \\ lesser than that at point $P_{2}$: \\ as $\kappa = \frac{1}{R}$').shift(3.2*RIGHT+3*UP).scale(0.6) + text = TextMobject(r'$\because R_{1} > R_{2}$, the curvature at \\ point $P_{1}$ is less than that \\ at point $P_{2}$ as $\kappa = \frac{1}{R}$').shift(3.2*RIGHT+3*UP).scale(0.6) dot1 = Dot((0,3,0), color = YELLOW) dot1label = TextMobject(r'$P_{1}$').next_to(dot1, UP+RIGHT, buff = 0.1) @@ -50,12 +52,18 @@ class GR(GraphScene): circle1 = Circle(radius = 0.8, color = GREY, opacity = 0.2).shift(2.2*UP) tgt1 = Line((-2,3,0), (2,3,0), color = GREY, opacity = 0.2).scale(0.4) - curvature1 = VGroup(*[circle1, tgt1]) + r1 = Line(circle1.get_center(), circle1.get_center() + np.array([0,0.8,0]), color=GREEN_SCREEN) + r1label = TextMobject(r'$R_{1}$',color=WHITE).next_to(r1, RIGHT, buff = 0.1).scale(0.6) + + curvature1 = VGroup(*[circle1, tgt1, r1, r1label]) circle2 = Circle(radius = 0.6, color = GREY, opacity = 0.2).shift(0.4*DOWN + 4*RIGHT) tgt2 = Line((4,-2,0), (6, -2, 0), color = GREY, opacity = 0.2).scale(0.5).shift(LEFT + UP) - curvature2 = VGroup(*[circle2, tgt2]) + r2 = Line(circle2.get_center(), circle2.get_center() + np.array([0,-0.6,0]), color=GREEN_SCREEN) + r2label = TextMobject(r'$R_{2}$', color=WHITE).next_to(r2, 0.9*RIGHT, buff = 0).scale(0.6) + + curvature2 = VGroup(*[circle2, tgt2, r2, r2label]) line = always_redraw(get_tangent_line) diff --git a/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/general-parametric-curves/file2_cycloid.gif b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/general-parametric-curves/file2_cycloid.gif Binary files differdeleted file mode 100644 index 39656de..0000000 --- a/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/general-parametric-curves/file2_cycloid.gif +++ /dev/null diff --git a/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file1_tnb_basic.gif b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file1_tnb_basic.gif Binary files differdeleted file mode 100644 index c028db4..0000000 --- a/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file1_tnb_basic.gif +++ /dev/null diff --git a/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file1_tnb_creation.gif b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file1_tnb_creation.gif Binary files differnew file mode 100644 index 0000000..eae8686 --- /dev/null +++ b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file1_tnb_creation.gif diff --git a/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file1_tnb_creation.py b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file1_tnb_creation.py new file mode 100644 index 0000000..80372ee --- /dev/null +++ b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file1_tnb_creation.py @@ -0,0 +1,66 @@ +from manimlib.imports import * + +class tnb(ThreeDScene): + def construct(self): + self.set_camera_orientation(phi = 75*DEGREES, theta=45*DEGREES) + + helix1 = ParametricFunction( + lambda t: np.array([ + np.cos(TAU*t), + np.sin(TAU*t), + 0.4*t + ]), t_min = -2*np.pi/3, t_max = -1.638*np.pi/3, color = WHITE + ) + + helix2 = ParametricFunction( + lambda t: np.array([ + np.cos(TAU*t), + np.sin(TAU*t), + 0.4*t + ]), t_min = -1.638*np.pi/3, t_max = -1.33*np.pi/3, color = WHITE + ) + + pointText = TextMobject(r'Consider an arbitrary point \\ on the given curve.').scale(0.8).shift(1.5*UP) + tgtText = TextMobject(r'Unit', ' tangent ', r'vector at \\ this point is given as:').scale(0.8).shift(1.5*UP) + tgtText.set_color_by_tex_to_color_map({ + "tangent": YELLOW + }) + normalText = TextMobject(r'Unit', ' normal ', r'vector at \\ this point is given as:').scale(0.8).shift(1.5*UP) + normalText.set_color_by_tex_to_color_map({ + "normal": BLUE + }) + planeText = TextMobject(r'$\overrightarrow{T}$ and $\overrightarrow{N}$ \\ prescribe a plane.').scale(0.8).shift(1.5*UP) + bnmText = TextMobject(r'The vector normal to this plane \\ is called the', ' binormal ', 'vector.').scale(0.8).shift(1.5*UP) + bnmText.set_color_by_tex_to_color_map({ + "binormal": GREEN_E + }) + + dot1 = Dot(np.array([np.cos(-np.pi/3), np.sin(-np.pi/3), -0.4*np.pi/3]) + np.array([0,0.2,0]), radius = 0.16, color=RED) + tgt1 = Arrow((0,0,0), (-2,-0.55,0), color = YELLOW).shift(dot1.get_center() + np.array([0.18,0.04,0])) + nm1 = Arrow((0,0,0), (0.4,-2,0), color = BLUE).shift(dot1.get_center() + np.array([0,0.26,0])) + bnm1 = Arrow((0,0,0), (0,2,0), color=GREEN_E).shift(2.1*RIGHT+2*DOWN) + plane1 = Square(color = DARK_BROWN, fill_color = WHITE, fill_opacity=0.3).shift(dot1.get_center() + np.array([-0.4, -0.6, 0])).rotate(13*DEGREES).scale(1.2) + point1 = VGroup(*[dot1, tgt1, nm1, plane1]).scale(0.8).shift(np.array([1,4.86,0])).rotate(-15*DEGREES) + + + + helix = VGroup(*[helix1, helix2]) + self.play(FadeIn(helix)) + self.play(ApplyMethod(helix.scale, 4)) + self.add_fixed_in_frame_mobjects(pointText) + self.play(FadeIn(dot1), FadeIn(pointText)) + self.wait(2) + self.add_fixed_in_frame_mobjects(tgtText) + self.play(Write(tgt1), ReplacementTransform(pointText, tgtText)) + self.wait(2) + self.add_fixed_in_frame_mobjects(normalText) + self.play(Write(nm1), ReplacementTransform(tgtText, normalText)) + self.wait(2) + self.add_fixed_in_frame_mobjects(planeText) + self.play(FadeIn(plane1), ReplacementTransform(normalText, planeText)) + self.wait(2) + self.add_fixed_in_frame_mobjects(bnmText) + self.add_fixed_in_frame_mobjects(bnm1) + self.play(ReplacementTransform(planeText, bnmText), Write(bnm1)) + self.wait(2) + self.play(FadeOut(VGroup(*[helix, bnm1, bnmText, dot1, tgt1, nm1, plane1]))) diff --git a/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file2_tnb_basic.gif b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file2_tnb_basic.gif Binary files differnew file mode 100644 index 0000000..67aaea2 --- /dev/null +++ b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file2_tnb_basic.gif diff --git a/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file1_tnb_basic.py b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file2_tnb_basic.py index 5c68f69..c870210 100644 --- a/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file1_tnb_basic.py +++ b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file2_tnb_basic.py @@ -6,8 +6,12 @@ class tnb(ThreeDScene): n = TextMobject(r'N', color = BLUE).next_to(t, RIGHT, buff=0) b = TextMobject(r'B', color = GREEN_E).next_to(n, RIGHT, buff=0) frame = TextMobject(r'Frame').next_to(b, RIGHT, buff=0.2) + f1 = TextMobject(r'$\overrightarrow{B}$ ', color = GREEN_E) + f2 = TextMobject(r' = $\overrightarrow{T}$', color = YELLOW).next_to(f1, RIGHT, buff=0.2) + f3 = TextMobject(r'$\times\overrightarrow{N}$', color = BLUE).next_to(f2, RIGHT, buff=0.1) + formula = VGroup(*[f1, f2, f3]).move_to(ORIGIN).shift(3*UP) - text = VGroup(*[t,n,b,frame]).move_to(ORIGIN).shift(3*UP) + # text = VGroup(*[t,n,b,frame]).move_to(ORIGIN).shift(3*UP) curve = ParametricFunction( lambda t: np.array([ np.sin(TAU*t), @@ -22,10 +26,11 @@ class tnb(ThreeDScene): square = Square(color = DARK_BROWN, fill_color = WHITE, fill_opacity=0.3).move_to(tgt.get_start()).rotate(27*DEGREES).shift(UP+0.4*RIGHT).scale(1.2) group = VGroup(*[dot, tgt, normal, square, binormal]).shift(np.array([-1.24,-1,0])) - self.add_fixed_in_frame_mobjects(text) + self.add_fixed_in_frame_mobjects(formula) self.add(curve, group) self.wait(1) self.move_camera(phi = 75*DEGREES, theta=45*DEGREES, run_time = 2) + self.add_fixed_in_frame_mobjects(formula) self.begin_ambient_camera_rotation(rate = 0.5) self.wait(5) - self.play(FadeOut(VGroup(*[text, curve, dot, tgt, normal, square, binormal]))) + self.play(FadeOut(VGroup(*[formula, curve, dot, tgt, normal, square, binormal]))) diff --git a/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file2_tnb_frame_manim.gif b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file3_tnb_frame_manim.gif Binary files differindex 78e3aa3..78e3aa3 100644 --- a/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file2_tnb_frame_manim.gif +++ b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file3_tnb_frame_manim.gif diff --git a/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file2_tnb_frame_manim.py b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file3_tnb_frame_manim.py index 176cac5..176cac5 100644 --- a/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file2_tnb_frame_manim.py +++ b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file3_tnb_frame_manim.py diff --git a/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file4_fs1.gif b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file4_fs1.gif Binary files differnew file mode 100644 index 0000000..6b4b438 --- /dev/null +++ b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file4_fs1.gif diff --git a/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file4_fs1.py b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file4_fs1.py new file mode 100644 index 0000000..c719a1d --- /dev/null +++ b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file4_fs1.py @@ -0,0 +1,23 @@ +from manimlib.imports import * + +class fs1(ThreeDScene): + def construct(self): + + + self.set_camera_orientation(phi = 75*DEGREES, theta=45*DEGREES) + dot1 = Dot(np.array([np.cos(-np.pi/3), np.sin(-np.pi/3), -0.4*np.pi/3]) + np.array([0,0.2,0]), radius = 0.16, color=RED) + tgt1 = Arrow((0,0,0), (-2,-0.55,0), color = YELLOW).shift(dot1.get_center() + np.array([0.18,0.04,0])) + nm1 = Arrow((0,0,0), (0.4,-2,0), color = BLUE).shift(dot1.get_center() + np.array([0,0.26,0])).shift(np.array([0.8,4.76,0])).rotate(-15*DEGREES).scale(0.8) + bnm1 = Arrow((0,0,0), (0,2,0), color=GREEN_E).shift(2.1*RIGHT+2*DOWN) + plane1 = Square(color = DARK_BROWN, fill_color = WHITE, fill_opacity=0.3).shift(dot1.get_center() + np.array([-0.4, -0.6, 0])).rotate(13*DEGREES).scale(1.2) + point1 = VGroup(*[dot1, tgt1, plane1]).scale(0.8).shift(np.array([1,4.86,0])).rotate(-15*DEGREES) + t = TextMobject(r'$T$', color = YELLOW).move_to(ORIGIN).shift(3.2*RIGHT + DOWN) + n = TextMobject(r'$N$', color = BLUE).shift(DOWN + RIGHT) + b = TextMobject(r'$B$', color = GREEN_E).next_to(bnm1, UP, buff = 0.1) + text = VGroup(*[t, n, b]) + self.add_fixed_in_frame_mobjects(bnm1, text) + self.play(FadeIn(point1), FadeIn(bnm1), FadeIn(text)) + self.wait() + self.play(TransformFromCopy(tgt1, nm1, run_time = 2)) + self.wait(2) + self.play(FadeOut(VGroup(*[bnm1, text, point1, nm1]))) diff --git a/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file5_fs2.gif b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file5_fs2.gif Binary files differnew file mode 100644 index 0000000..ce367b6 --- /dev/null +++ b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file5_fs2.gif diff --git a/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file5_fs2.py b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file5_fs2.py new file mode 100644 index 0000000..0261fed --- /dev/null +++ b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file5_fs2.py @@ -0,0 +1,28 @@ +from manimlib.imports import * + +class fs1(ThreeDScene): + def construct(self): + + + self.set_camera_orientation(phi = 75*DEGREES, theta=45*DEGREES) + dot1 = Dot(np.array([np.cos(-np.pi/3), np.sin(-np.pi/3), -0.4*np.pi/3]) + np.array([0,0.2,0]), radius = 0.16, color=RED) + tgt1 = Arrow((0,0,0), (-2,-0.55,0), color = YELLOW).shift(dot1.get_center() + np.array([0.18,0.04,0])) + nm1 = Arrow((0,0,0), (0.4,-2,0), color = BLUE).shift(dot1.get_center() + np.array([0,0.26,0])).shift(np.array([0.8,4.76,0])).rotate(-15*DEGREES).scale(0.8) + bnm1 = Arrow((0,0,0), (0,2,0), color=GREEN_E).shift(2.1*RIGHT+2*DOWN) + + bnms = Line((0,0,0), (0,0,1.6), color = GREEN_E).shift(np.array([3.1,5.2,0])).scale(0.6) + bnmsa = ArrowTip(color = GREEN_E).next_to(bnms, np.array([0,0,1]), buff = 0).rotate(45*DEGREES) + bns = VGroup(*[bnms, bnmsa]) + + plane1 = Square(color = DARK_BROWN, fill_color = WHITE, fill_opacity=0.3).shift(dot1.get_center() + np.array([-0.4, -0.6, 0])).rotate(13*DEGREES).scale(1.2) + point1 = VGroup(*[dot1, tgt1, plane1]).scale(0.8).shift(np.array([1,4.86,0])).rotate(-15*DEGREES) + t = TextMobject(r'$T$', color = YELLOW).move_to(ORIGIN).shift(3.2*RIGHT + DOWN) + n = TextMobject(r'$N$', color = BLUE).shift(DOWN + RIGHT) + b = TextMobject(r'$B$', color = GREEN_E).next_to(bnm1, UP, buff = 0.1) + text = VGroup(*[t, n, b]) + self.add_fixed_in_frame_mobjects(bnm1, text) + self.play(FadeIn(point1), FadeIn(text), FadeIn(bnm1)) + self.wait() + self.play(TransformFromCopy(bnms, nm1, run_time = 3)) + self.wait(2) + self.play(FadeOut(VGroup(*[bnms, text, point1, nm1, bnm1]))) |
