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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'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|$')
XTD = self.x_axis_width/(self.x_max- self.x_min)
YTD = self.y_axis_height/(self.y_max- self.y_min)
tgt1 = Arrow((-2.2*XTD,-0.5*YTD,0),(-1*XTD,1,0))
tgt2 = Arrow((-1.2*XTD, 1.93*YTD,0),(0*XTD,1.6,0)).scale(1.2)
tgt3 = Arrow((-0.3*XTD,3*YTD, 0), (1.5*XTD, 3*YTD,0))
tgt4 = Arrow((1.4*XTD, 2*YTD,0),(2.4*XTD, 1*YTD,0)).scale(2.8)
tgt5 = Arrow((2.4*XTD, 0, 0), (3.8*XTD,-2*YTD, 0)).scale(1.2).shift(0.26*RIGHT)
tgt6 = Arrow((3.8*XTD,-1*YTD, 0), (4.8*XTD, -1*YTD, 0)).scale(2.8).shift(0.26*RIGHT)
tgt7 = Arrow((5.3*XTD, 0, 0),(6.3*XTD,1,0)).shift(0.35*LEFT+0.1*DOWN).scale(1.3)
dot1 = Dot(tgt1.get_start(), color = RED)
dot2 = Dot(tgt2.get_start(), color = RED)
dot3 = Dot(tgt3.get_start(), color = RED)
dot4 = Dot(tgt4.get_start(), color = RED)
dot5 = Dot(tgt5.get_start(), color = RED)
dot6 = Dot(tgt6.get_start(), color = RED)
dot7 = Dot(tgt7.get_start(), color = RED)
dots = VGroup(*[dot1, dot2, dot3, dot4, dot5, dot6, dot7])
ds = CurvedArrow((-4, 2, 0), (tgt1.get_start() + tgt2.get_start()) / 2, color = YELLOW)
ds_text = TextMobject(r'$ds$').next_to(ds, UP, buff = 0.1).shift(1.3*LEFT)
self.setup_axes(hideaxes=True)
graphobj = self.get_graph(self.curve)
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))
self.wait(1)
self.play(FadeOut(self.axes), FadeOut(graphobj),FadeIn(mid), FadeOut(dots), FadeOut(ds), FadeOut(ds_text))
self.wait(2)
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(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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