diff options
Diffstat (limited to 'FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file3_tnb_frame_manim.py')
| -rw-r--r-- | FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file3_tnb_frame_manim.py | 112 |
1 files changed, 102 insertions, 10 deletions
diff --git a/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file3_tnb_frame_manim.py b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file3_tnb_frame_manim.py index 176cac5..091c1e2 100644 --- a/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file3_tnb_frame_manim.py +++ b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file3_tnb_frame_manim.py @@ -11,6 +11,9 @@ class tnb(ThreeDScene): text = VGroup(*[t,n,b,frame]).move_to(ORIGIN).shift(3*UP) + c1 = TextMobject(r'$r(t) = \left\langle\cos{t}, \sin{t}, 0.4t\right\rangle\quad r\prime (t) =\left\langle -\sin{t}, \cos{t}, 0.4\right\rangle$').next_to(text, DOWN, buff = 0.1).scale(0.7) + + helix1 = ParametricFunction( lambda t: np.array([ np.cos(TAU*t), @@ -53,6 +56,95 @@ class tnb(ThreeDScene): helix_dot = Dot(radius = 0.16, color = RED) + t_tracker = ValueTracker(-2*np.pi/3) + t=t_tracker.get_value + + # t_label = TexMobject( + # "t = ",color=WHITE + # ).next_to(helix1,DOWN, buff=0.2).scale(0.6) + + cval1 = TextMobject(r'r(').next_to(c1, DOWN+16.5*LEFT, buff = 0.1).scale(0.7) + + t_text = always_redraw( + lambda: DecimalNumber( + t(), + color=WHITE, + ).next_to(cval1, RIGHT, buff=0.05).scale(0.7) + ).scale(0.6) + + + cval2 = always_redraw( + lambda: TextMobject(r') = $\left\langle$').scale(0.7).next_to(t_text, RIGHT, buff = 0.05) + ) + + cos = always_redraw( + lambda: DecimalNumber( + np.cos(t()), + color=WHITE, + ).next_to(cval2, RIGHT, buff=0.1).scale(0.7) + ).scale(0.6) + + sin = always_redraw( + lambda: DecimalNumber( + np.sin(t()), + color=WHITE, + ).next_to(cos, RIGHT, buff=0.1).scale(0.7) + ).scale(0.6) + + zpart = always_redraw( + lambda: DecimalNumber( + 0.4* t(), + color=WHITE, + ).next_to(sin, RIGHT, buff=0.1).scale(0.7) + ).scale(0.6) + + cvalend = always_redraw( + lambda: TextMobject(r' $\right\rangle$').next_to(zpart, RIGHT, buff = 0.2).scale(0.7) + ).scale(0.6) + + + valgroup = VGroup(*[cval1, cval2,cos,sin,zpart, cvalend]) + + rp1 = always_redraw( + lambda: TextMobject(r'$r\prime ($').scale(0.7).next_to(cvalend, RIGHT, buff = 0.6) + ) + + t_text2 = always_redraw( + lambda: DecimalNumber( + t(), + color=WHITE, + ).next_to(rp1, RIGHT, buff=0.05).scale(0.7) + ).scale(0.6) + + rp2 = always_redraw( + lambda: TextMobject(r') = $\left\langle$').scale(0.7).next_to(t_text2, RIGHT, buff = 0.05) + ) + + rps = always_redraw( + lambda: DecimalNumber( + -np.sin(t()), + color=WHITE, + ).next_to(rp2, RIGHT, buff=0.1).scale(0.7) + ).scale(0.6) + + + rpc = always_redraw( + lambda: DecimalNumber( + np.cos(t()), + color=WHITE, + ).next_to(rps, RIGHT, buff=0.1).scale(0.7) + ).scale(0.6) + + + const = always_redraw( + lambda: TextMobject(r'0.4 $\right\rangle$').next_to(rpc, RIGHT, buff = 0.2).scale(0.7) + ).scale(0.6).shift(0.1*DOWN) + + val2group = VGroup(*[rp1, rp2, rps, rpc, const]) + + #group = VGroup(t_text, t_text2).scale(1.5).move_to(ORIGIN).shift(3.7*DOWN) + + dot0 = Dot(np.array([np.cos(-2*np.pi/3), np.sin(-2*np.pi/3), -0.8*np.pi/3]), radius = 0.16, color=RED).shift(np.array([4.65,0,-0.8])) tgt0 = Arrow((0,0,0), (1,2,0), color = YELLOW).shift(dot0.get_center() - np.array([0.04,0.2,0])) nm0 = Arrow((0,0,0), (-2,1,0), color = BLUE).shift(dot0.get_center() + np.array([0.3,0,0])) @@ -75,20 +167,20 @@ class tnb(ThreeDScene): point2 = VGroup(*[dot2, tgt2, nm2, bnm2, plane2]) helix = VGroup(*[helix1, helix2, helix3, helix4, helix5]) - self.add_fixed_in_frame_mobjects(text) - self.play(FadeIn(helix), FadeIn(text)) + self.add_fixed_in_frame_mobjects(text, c1) + self.play(FadeIn(helix), FadeIn(text), FadeIn(c1)) self.play(ApplyMethod(helix.scale, 4)) - self.add_fixed_in_frame_mobjects(bnm0) - self.play(FadeIn(point0)) - self.play(ApplyMethod(point0.set_color, GRAY, opacity = 0.1), MoveAlongPath(helix_dot, helix1, run_time=5)) + self.add_fixed_in_frame_mobjects(bnm0, valgroup, val2group, t_text, t_text2) + self.play(FadeIn(point0), FadeIn(t_text), FadeIn(t_text2), FadeIn(valgroup), FadeIn(val2group)) + self.play(ApplyMethod(point0.set_color, GRAY, opacity = 0.1, run_time = 0.5), MoveAlongPath(helix_dot, helix1, run_time=5), t_tracker.set_value,-1.638*np.pi/3, rate_func=linear, run_time=5) self.add_fixed_in_frame_mobjects(bnm1) self.play(FadeIn(point1)) - self.play(ApplyMethod(point1.set_color, GRAY, opacity = 0.1), ApplyMethod(bnm1.set_color, GRAY, opacity = 0.1), MoveAlongPath(helix_dot, helix2, run_time = 5)) + self.play(ApplyMethod(point1.set_color, GRAY, opacity = 0.1, run_time = 0.5), ApplyMethod(bnm1.set_color, GRAY, opacity = 0.1, run_time = 0.5), MoveAlongPath(helix_dot, helix2, run_time = 5), t_tracker.set_value,-1.33*np.pi/3, rate_func=linear, run_time=5) self.add_fixed_in_frame_mobjects(bnm2) self.play(FadeIn(point2)) - self.play(ApplyMethod(point2.set_color, GRAY, opacity = 0.1), MoveAlongPath(helix_dot, helix3, run_time=5)) + self.play(ApplyMethod(point2.set_color, GRAY, opacity = 0.1, run_time = 0.5), MoveAlongPath(helix_dot, helix3, run_time=5), t_tracker.set_value,-np.pi/3, rate_func=linear, run_time=5) dot3 = Dot(np.array([np.cos(-np.pi/3), np.sin(-np.pi/3), -0.4*np.pi/3]) + np.array([3.3,-0.25,0]), radius = 0.16, color=RED) tgt3 = Arrow((0,0,0), (0,2,0), color = YELLOW).shift(helix_dot.get_center() - np.array([-0.05,0.2,0])) @@ -113,14 +205,14 @@ class tnb(ThreeDScene): self.add_fixed_in_frame_mobjects(bnm3) self.play(FadeIn(point3)) - self.play(ApplyMethod(point3.set_color, GRAY, opacity = 0.1), MoveAlongPath(helix_dot, helix4, run_time=5)) + self.play(ApplyMethod(point3.set_color, GRAY, opacity = 0.1, run_time = 0.5), MoveAlongPath(helix_dot, helix4, run_time=5), t_tracker.set_value,-1.3*np.pi/6, rate_func=linear, run_time=5) self.add_fixed_in_frame_mobjects(bnm4) self.play(FadeIn(point4)) - self.play(ApplyMethod(point4.set_color, GRAY, opacity = 0.1), MoveAlongPath(helix_dot, helix5, run_time=5)) + self.play(ApplyMethod(point4.set_color, GRAY, opacity = 0.1, run_time = 0.5), MoveAlongPath(helix_dot, helix5, run_time=5), t_tracker.set_value,0, rate_func=linear, run_time=5) self.add_fixed_in_frame_mobjects(bnm5) self.play(FadeIn(point5)) self.wait(2) - self.play(FadeOut(VGroup(*[text, helix, bnm1, point0, point1, point2, point3, point4, point5, helix_dot]))) + self.play(FadeOut(VGroup(*[valgroup, val2group, t_text, t_text2, c1, text, helix, bnm1, point0, point1, point2, point3, point4, point5, helix_dot]))) |