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from manimlib.imports import *
class tangent(ThreeDScene):
def construct(self):
axes = ThreeDAxes()
text = TextMobject(r'Tangent', r' to the ', 'space curve', r' \\ at point ', r'$P_{1}$', ' is given by:').scale(0.7).shift(3*UP + 3.5*LEFT)
text.set_color_by_tex_to_color_map({
"Tangent": YELLOW,
'$P_{1}$': RED,
'space curve': BLUE
})
text.bg=BackgroundRectangle(text,fill_opacity=1, color = BLACK)
text_gr =VGroup(text.bg,text)
self.set_camera_orientation(phi = 125*DEGREES, theta = 135*DEGREES)
h = ParametricFunction(
lambda t: np.array([
4*(t**3) + 5,
t**2 + 2*(t**4),
-2*np.log(2*t)
]), t_min = -3, t_max = 1.18, color = BLUE
).shift(5*LEFT)
tgtR = Line((4,3,-2*np.log(2)), (19.5, 16, -4.772588), color=YELLOW)
tgtL =Line((4,3,-2*np.log(2)), (-11.5, -10, 2), color=YELLOW)
dot = Dot((4,3,-2*np.log(2)), color=RED, radius=0.08)
dotl = TextMobject(r'$P_{1}$', color = RED).scale(0.7).shift(2*DOWN + 5*LEFT)
self.add_fixed_in_frame_mobjects(text_gr, dotl)
self.play(FadeIn(axes),FadeIn(h), FadeIn(dot), FadeIn(dotl))
self.wait(2)
self.play(FadeIn(tgtL), FadeIn(tgtR))
self.begin_ambient_camera_rotation(rate=0.2)
self.play(FadeOut(dotl))
self.wait(5)
self.play(FadeOut(axes), FadeOut(h), FadeOut(text_gr), FadeOut(dot), FadeOut(tgtL), FadeOut(tgtR))
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