diff options
Diffstat (limited to 'FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/arc-length-and-curvature/file1_arc_length.py')
| -rw-r--r-- | FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/arc-length-and-curvature/file1_arc_length.py | 89 |
1 files changed, 68 insertions, 21 deletions
diff --git a/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/arc-length-and-curvature/file1_arc_length.py b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/arc-length-and-curvature/file1_arc_length.py index e295c7a..361e2be 100644 --- a/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/arc-length-and-curvature/file1_arc_length.py +++ b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/arc-length-and-curvature/file1_arc_length.py @@ -1,32 +1,79 @@ from manimlib.imports import * -class arcl(GraphScene): - CONFIG = { - "x_min" : 0, - "x_max" : 10, - "y_min" : 0, - "y_max" : 6, - "graph_origin": ORIGIN, - "x_axis_width": 10, - "y_axis_height": 6 , - "x_tick_frequency": 2, - "y_tick_frequency": 2, - "Func":lambda x : 1+x**1.3*np.exp(-.12*(x-2)**2)*np.sin(x/4), - } +class arcl(MovingCameraScene): def construct(self): - self.setup_axes(hideaxes = True) + # self.setup() def curve_(x): return 3 - (3653*x**2)/5292 + (2477*x**3)/31752 + (13*x**4)/784 - (17*x**5)/5292 + (17*x**6)/63504 curve = FunctionGraph(curve_, x_min=-2, x_max=6, stroke_width = 2, color = BLUE).scale(0.1).move_to(ORIGIN) - lines = [Line(length = 0.05, color = RED) for i in range(10)] - lines[0].move_to(np.array([curve_(-2),-2, 0])) + lines = [Line(length = 0.05, color = RED).scale(0.2).move_to(ORIGIN).shift(np.array([-4 + 0.1*i, curve_(-2.5 + 0.1*i), 0])).rotate(-25*DEGREES) for i in range(4)] + lines2 = [Line(length = 0.05, color = RED).scale(0.2).move_to(ORIGIN).shift(np.array([-4 + 0.125*i, curve_(-2.5 + 0.1*i), 0])).rotate(-25*DEGREES) for i in range(4, 9)] + # lines[0].rotate(-25*DEGREES).shift(np.array([-4,curve_(-2.5), 0])) + # lines[1].rotate(-25*DEGREES).shift(np.array([-3.78,curve_(-2.3), 0])) + # lines3 = [Line(length = 0.05, color = RED).scale(0.2).move_to(ORIGIN + 1.5*UP + 0.6*RIGHT).shift(np.array([-1 + 0.2*i, -1.5 - 0.2*i, 0])).rotate(30*DEGREES) for i in range(4)] + # lines2b = VGroup(*lines3).rotate(-8*DEGREES) + # lines4 = [Line(length = 0.05, color = RED).scale(0.2).move_to(ORIGIN + 1.6*UP + 0.5*RIGHT).shift(np.array([-1 + 0.18*i, -1.65 - 0.2*i, 0])).rotate(22*DEGREES) for i in range(4, 9)] + # lines5 = [Line(length = 0.05, color = RED).scale(0.2).move_to(ORIGIN + 7*RIGHT).shift(np.array([-4 + 0.1*i, curve_(-2.5 + 0.1*i), 0])).rotate(-25*DEGREES) for i in range(4)] + # lines6 = [Line(length = 0.05, color = RED).scale(0.2).move_to(ORIGIN +7.25*RIGHT).shift(np.array([-4 + 0.053*i, curve_(-2.5 + 0.1*i), 0])).rotate(-26*DEGREES) for i in range(4, 9)] + # lc1 = [Line(length = 0.05, color = RED).scale(0.2).rotate((-25 + i*2) * DEGREES).shift(np.array([-1 + 0.125*i, curve_(-1.5 + 0.1*i), 0])) for i in range(2)] + # lc1b = VGroup(*lc1).shift(1.7*LEFT + 0.2*DOWN) + text = TextMobject(r'$r(t) = \left\langle t, t^{3} - 2t, 0\right\rangle$ \\ $r\prime (t) = \left\langle 1, 3t^{2} - 2, 0\right\rangle$').scale(0.7).shift(3*UP + 3*LEFT) - # self.play(FadeIn(curve)) - # self.wait(2) - self.play(ApplyMethod(curve.scale, 10)) - self.play(FadeIn(VGroup(*lines))) - self.wait(5) + # l = VGroup(*lines, *lines2, lines2b, *lines4, *lines5, *lines6, lc1b).shift(curve.get_center()) + l = VGroup(*lines, *lines2) + arc = Line(lines[3].get_center(), lines2[0].get_center() + np.array([0.005, 0 ,0]), color = GREEN_SCREEN).rotate(12*DEGREES) + arctext = TextMobject(r'$ds$', color = GREEN_SCREEN).scale(0.15).next_to(arc.get_center(), 0.001*DOWN + 0.01*RIGHT,buff = 0.01) + dy = Arrow(arc.get_start(), np.array([arc.get_start()[0], lines2[0].get_center()[1] + 0.01, 0]), color = YELLOW) + dx = Arrow(arc.get_start(), np.array([lines2[0].get_center()[0] - 0.01, arc.get_start()[1], 0]), color = BLUE) + dxt = DashedLine(dy.get_end(), dy.get_end() + np.array([0.13, 0 ,0])) + dyt = DashedLine(dx.get_end(), dx.get_end() + np.array([0, 0.3 ,0])) + dxtext = TextMobject(r'$dx$').scale(0.2).next_to(dx, RIGHT, buff = 0.01) + dytext = TextMobject(r'$dy$').scale(0.2).next_to(dy, LEFT, buff = 0.01) + formula = TextMobject(r"Using Pythagoras' theorem, \\ $ds = \sqrt{(dx)^{2} + (dy)^{2}}$").scale(0.35).shift(5*LEFT + 0.2*UP) + + compute = TextMobject(r'To compute the arc length from \\ $t = -1.4$ to $t = -1.1$, \\ summation of all small arcs $ds$ \\ is given by $L = \int_{-1.4}^{-1.1} ds$ \\').scale(0.7).shift(6.8*LEFT + 1.5*UP) + compute_ = TextMobject(r'L = $ \int_{-1.4}^{-1.1} \sqrt{(\frac{dx}{dt})^{2} + (\frac{dy}{dt})^{2}}\quad dt$ \\ = $\int_{-1.4}^{-1.1} \sqrt{1^{2} + (3t^{2} - 2)^{2}}\quad dt$').scale(0.7).shift(6.8*LEFT + 0.6*DOWN) + compute = VGroup(*[compute, compute_]) + compute2 = TextMobject(r'$ = \int_{-1.4}^{-1.1} \sqrt{9t^{4} - 12t^{2} + 5}\quad dt$').scale(0.7).shift(6.8*LEFT + 1.7*DOWN) + compute3 = TextMobject(r'$L = 0.8693$').scale(0.7).shift(6.8*LEFT + 2.2*DOWN) + + dsd = TextMobject(r'We can divide the curve \\ into multiple small arcs $ds$').scale(0.35).shift(5.2*LEFT + 0.2*UP) + + self.play(FadeIn(curve)) + self.play(ApplyMethod(curve.scale, 10), FadeIn(text)) + # self.play(FadeIn(l)) + self.wait(2) + self.play(self.camera_frame.set_width, 5, + self.camera_frame.move_to, 3.8*LEFT+0.4*DOWN, + text.shift, 2.3*LEFT + 2.25*DOWN, + text.scale, 0.5, run_time = 4) + long = ArcBetweenPoints(lines[1].get_center() + 0.01, lines2[3].get_center(), color = YELLOW, angle = 10*DEGREES).rotate(180*DEGREES) + # self.play(ApplyMethod(VGroup(*[curve, l]).scale,0.1, run_time = 4)) + # self.play(ApplyMethod(VGroup(*[curve, l]).scale,10, run_time = 4)) + # self.activate_zooming(animate = True) + + self.play(Write(dsd), Write(l)) + self.wait(2) + self.play(FadeOut(dsd), Transform(l, VGroup(*[lines[3], lines2[0]])), FadeIn(VGroup(*[arc, arctext, dy, dx, dxt, dyt, dxtext, dytext]))) + self.wait(1) + self.play(FadeIn(formula)) + # self.play(FadeIn(VGroup(*[arc, dy, dx, dxt, dyt, dxtext, dytext]))) + self.wait(2) + self.play(FadeOut(VGroup(*[arc, arctext, dy, l, dx, dxt, dyt, dxtext, dytext, formula]))) + self.play(self.camera_frame.set_width, 15, + self.camera_frame.move_to, 3*LEFT, + text.shift, 2.5*LEFT + 2.25*UP, + text.scale, 2, run_time = 4) + self.play(FadeIn(long), FadeIn(compute)) + self.wait(4) + self.play(FadeIn(compute2)) + self.wait(1) + self.play(FadeIn(compute3)) + # self.play(FadeOut(VGroup(*[curve, arc, dy, dx, dxt, dyt, dxtext, dytext, l]))) + # self.play(FadeOut(self.zoomed_camera.frame), FadeOut(self.zoomed_display)) + self.wait(1) + self.play(FadeOut(VGroup(*[curve, text, compute, compute2, compute3, long]))) |