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from manimlib.imports import *
class randomcurve(GraphScene):
CONFIG = {
"x_min": -4,
"x_max": 6,
"y_min": -6,
"y_max": 10,
"graph_origin": ORIGIN
}
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'This 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)
self.setup_axes(hideaxes=True)
graphobj = self.get_graph(self.curve)
self.play(FadeIn(intro))
self.wait(2)
self.play(FadeOut(intro))
self.setup_axes(hideaxes=False)
self.play(ShowCreation(graphobj))
self.wait(1)
self.play(FadeOut(self.axes), FadeOut(graphobj),FadeIn(mid))
self.wait(2)
self.play(FadeOut(mid))
self.play(FadeIn(self.axes), FadeIn(graphobj))
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))
tgt4 = Arrow((1.4*XTD, 2*YTD,0),(2.4*XTD, 1*YTD,0)).scale(2.8)
tangents = [tgt1, tgt2, tgt3, tgt4]
for tangent in tangents:
self.play(ShowCreation(tangent))
self.wait(1)
tangents = VGroup(*tangents)
self.play(FadeOut(self.axes), FadeOut(graphobj), FadeOut(tangents))
self.wait(1)
self.play(FadeIn(outro))
self.wait(2)
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
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