diff options
Diffstat (limited to 'FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/arc-length-and-curvature/file2_simple_visualization.py')
| -rw-r--r-- | FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/arc-length-and-curvature/file2_simple_visualization.py | 60 |
1 files changed, 41 insertions, 19 deletions
diff --git a/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/arc-length-and-curvature/file2_simple_visualization.py b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/arc-length-and-curvature/file2_simple_visualization.py index 45058d7..05cad80 100644 --- a/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/arc-length-and-curvature/file2_simple_visualization.py +++ b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/arc-length-and-curvature/file2_simple_visualization.py @@ -1,8 +1,8 @@ from manimlib.imports import * -class randomcurve(GraphScene): +class a(GraphScene): CONFIG = { - "x_min": -4, + "x_min": -3, "x_max": 6, "y_min": -6, "y_max": 10, @@ -10,12 +10,15 @@ class randomcurve(GraphScene): } def construct(self): intro = TextMobject('Consider the following curve.') - mid = TextMobject(r'Notice how the direction of the unit tangent vectors\\changes with respect to the arc length.') - outro = TextMobject(r'The rate of change of unit tangents with \\ respect to the arc length $ds$ is called curvature.\\Mathematically, curvature $ = k = \left|{\frac{dT}{ds}}\right|$') + mid = TextMobject(r'Notice how the direction of the unit tangent vector\\changes with respect to the arc length.') + outro = TextMobject(r'The rate of change of unit tangent with \\ respect to the arc length $ds$ is called curvature.\\Mathematically, curvature $ = k = \left|{\frac{dT}{ds}}\right|$') XTD = self.x_axis_width/(self.x_max- self.x_min) YTD = self.y_axis_height/(self.y_max- self.y_min) + circle = Circle(radius = 0.95, color = GRAY, fill_opacity = 0.2, fill_color = RED) + circle.set_stroke(width = 0.1) + tgt1 = Arrow((-2.2*XTD,-0.5*YTD,0),(-1*XTD,1,0)) tgt2 = Arrow((-1.2*XTD, 1.93*YTD,0),(0*XTD,1.6,0)).scale(1.2) tgt3 = Arrow((-0.3*XTD,3*YTD, 0), (1.5*XTD, 3*YTD,0)) @@ -40,30 +43,49 @@ class randomcurve(GraphScene): ds_text = TextMobject(r'$ds$').next_to(ds, UP, buff = 0.1).shift(1.3*LEFT) self.setup_axes(hideaxes=True) - graphobj = self.get_graph(self.curve) + + 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 + + # parabola_x_out = FunctionGraph(curve, x_min=-2, x_max=6, stroke_width = 2, color = BLUE) + parabola_x_out = self.get_graph(curve) + + dot_x = Dot().rotate(PI/2).set_color(YELLOW_E) + alpha_x = ValueTracker(-2) + vector_x = self.get_tangent_vector(alpha_x.get_value(),parabola_x_out,scale=1.5) + dot_x.add_updater(lambda m: m.move_to(vector_x.get_center())) + vector_x.add_updater( + lambda m: m.become( + self.get_tangent_vector(alpha_x.get_value()%1,parabola_x_out,scale=1.5) + ) + ) + self.play(FadeIn(intro)) self.wait(2) self.play(FadeOut(intro)) self.setup_axes(hideaxes=False) - self.play(ShowCreation(graphobj), FadeIn(dots), FadeIn(ds), FadeIn(ds_text), FadeIn(arc)) - self.wait(1) - self.play(FadeOut(self.axes), FadeOut(arc), FadeOut(graphobj),FadeIn(mid), FadeOut(dots), FadeOut(ds), FadeOut(ds_text)) + self.play(ShowCreation(parabola_x_out), FadeIn(dots), FadeIn(ds), FadeIn(ds_text), FadeIn(arc)) + self.wait(2) + self.play(FadeOut(self.axes), FadeOut(arc), FadeOut(parabola_x_out),FadeIn(mid), FadeOut(dots), FadeOut(ds), FadeOut(ds_text)) self.wait(3) self.play(FadeOut(mid)) - self.play(FadeIn(self.axes), FadeIn(graphobj), FadeIn(dots)) - - tangents = [tgt1, tgt2, tgt3, tgt4, tgt5, tgt6, tgt7] - for tangent in tangents: - self.play(ShowCreation(tangent), run_time = 0.2) - self.wait(1) - tangents = VGroup(*tangents) - self.play(FadeOut(self.axes), FadeOut(graphobj), FadeOut(tangents), FadeOut(dots)) - self.wait(1) + self.play(FadeIn(self.axes), FadeIn(parabola_x_out), FadeIn(dots)) + self.add(vector_x) + self.play(alpha_x.increment_value, 1, run_time=8, rate_func=linear) + self.remove(vector_x) + self.play(FadeOut(VGroup(*[self.axes, dots, parabola_x_out]))) self.play(FadeIn(outro)) self.wait(3) self.play(FadeOut(outro)) self.wait(1) - def curve(self, x): - return 3 - (3653*x**2)/5292 + (2477*x**3)/31752 + (13*x**4)/784 - (17*x**5)/5292 + (17*x**6)/63504 + + + def get_tangent_vector(self, proportion, curve, dx=0.001, scale=1): + coord_i = curve.point_from_proportion(proportion) + coord_f = curve.point_from_proportion(proportion + dx) + reference_line = Line(coord_i,coord_f) + unit_vector = reference_line.get_unit_vector() * scale + vector = Arrow(coord_i , coord_i + unit_vector, color = YELLOW, buff=0) + return vector |