tnb

3 files changed, 125 insertions, 0 deletions

diff --git a/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file2_TNB_frame.gif b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file2_tnb_frame.gif
index 097652f..097652f 100644
--- a/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file2_TNB_frame.gif
+++ b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file2_tnb_frame.gif
diff --git a/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file2_tnb_frame_manim.gif b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file2_tnb_frame_manim.gif
new file mode 100644
index 0000000..784b6a6
--- /dev/null
+++ b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file2_tnb_frame_manim.gif
diff --git a/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file2_tnb_frame_manim.py b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file2_tnb_frame_manim.py
new file mode 100644
index 0000000..ee5e717
--- /dev/null
+++ b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file2_tnb_frame_manim.py
@@ -0,0 +1,125 @@
+from manimlib.imports import *
+
+class tnb(ThreeDScene):
+    def construct(self):
+        self.set_camera_orientation(phi = 75*DEGREES, theta=45*DEGREES)
+
+        t = TextMobject(r'T', color = YELLOW)
+        n = TextMobject(r'N', color = BLUE).next_to(t, RIGHT, buff=0)
+        b = TextMobject(r'B', color = GREEN_E).next_to(n, RIGHT, buff=0)
+        frame = TextMobject(r'Frame').next_to(b, RIGHT, buff=0.2)
+
+        text = VGroup(*[t,n,b,frame]).move_to(ORIGIN).shift(3*UP)
+
+        helix1 = ParametricFunction(
+                lambda t: np.array([
+                np.cos(TAU*t),
+                np.sin(TAU*t),
+                0.4*t
+                ]), t_min = -2*np.pi/3, t_max = -1.638*np.pi/3, color = WHITE
+                )
+
+        helix2 = ParametricFunction(
+                lambda t: np.array([
+                np.cos(TAU*t),
+                np.sin(TAU*t),
+                0.4*t
+                ]), t_min = -1.638*np.pi/3, t_max = -1.33*np.pi/3, color = WHITE
+                )
+
+        helix3 = ParametricFunction(
+                lambda t: np.array([
+                np.cos(TAU*t),
+                np.sin(TAU*t),
+                0.4*t
+                ]), t_min = -1.33*np.pi/3, t_max = -np.pi/3, color = WHITE
+                )
+
+        helix4 = ParametricFunction(
+                lambda t: np.array([
+                np.cos(TAU*t),
+                np.sin(TAU*t),
+                0.4*t
+                ]), t_min = -np.pi/3, t_max = -1.3*np.pi/6, color = WHITE
+                )
+
+        helix5 = ParametricFunction(
+                lambda t: np.array([
+                np.cos(TAU*t),
+                np.sin(TAU*t),
+                0.4*t
+                ]), t_min = -1.3*np.pi/6, t_max = 0, color = WHITE
+                )
+
+        helix_dot = Dot(radius = 0.16, color = RED)
+
+        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]))
+        bnm0 = Arrow((0,0,0), (0,2,0), color = GREEN_E).shift(6.1*LEFT + 3*DOWN)
+        plane0 = Square(color = DARK_BROWN, fill_color = WHITE, fill_opacity=0.3).shift(dot0.get_center() + np.array([-0.35, 0.85, 0])).scale(1.2).rotate(65*DEGREES)
+        point0 = VGroup(*[dot0, tgt0, nm0, bnm0, plane0]).scale(0.8).shift(np.array([1,0,0]))
+
+        dot1 = Dot(np.array([np.cos(-np.pi/3), np.sin(-np.pi/3), -0.4*np.pi/3]) + np.array([0,0.2,0]), radius = 0.16, color=RED)
+        tgt1 = Arrow((0,0,0), (-2,-0.55,0), color = YELLOW).shift(dot1.get_center() + np.array([0.18,0.04,0]))
+        nm1 = Arrow((0,0,0), (0.4,-2,0), color = BLUE).shift(dot1.get_center() + np.array([0,0.26,0]))
+        bnm1 = Arrow((0,0,0), (0,2,0), color=GREEN_E).shift(3.68*RIGHT+2.48*DOWN)
+        plane1 = Square(color = DARK_BROWN, fill_color = WHITE, fill_opacity=0.3).shift(dot1.get_center() + np.array([-0.4, -0.6, 0])).rotate(13*DEGREES).scale(1.2)
+        point1 = VGroup(*[dot1, tgt1, nm1, plane1]).scale(0.8).shift(np.array([1,6.25,0]))
+
+        dot2 = Dot(np.array([np.cos(-np.pi/6), np.sin(-np.pi/6), -0.2*np.pi/3]) - np.array([1.9,0,0]), radius=0.16,color=RED)
+        tgt2 = Arrow((0,0,0), (1,-2,0), color = YELLOW).shift(dot2.get_center() + np.array([-0.2,0.2,0]))
+        nm2 = Arrow((0,0,0), (2,1,0), color = BLUE).shift(dot2.get_center() + np.array([-0.2,-0.06,0]))
+        bnm2 = Arrow((0,0,0), (0,2,0), color=GREEN_E).shift(0.4*RIGHT + 0.16*DOWN)
+        plane2 = Square(color = DARK_BROWN, fill_color = WHITE, fill_opacity=0.3).shift(dot2.get_center() + np.array([0.92, -0.5, 0])).rotate(23*DEGREES).scale(1.2)
+        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.play(ApplyMethod(helix.scale, 4))
+        self.add_fixed_in_frame_mobjects(bnm0)
+        self.play(FadeIn(point0), MoveAlongPath(helix_dot, helix1, run_time=5))
+
+        self.add_fixed_in_frame_mobjects(bnm1)
+        self.play(ApplyMethod(point0.set_color, GRAY), FadeIn(point1))
+        self.play(MoveAlongPath(helix_dot, helix2, run_time = 5))
+
+        self.add_fixed_in_frame_mobjects(bnm2)
+        self.play(ApplyMethod(point1.set_color, GRAY), ApplyMethod(bnm1.set_color, GRAY), FadeIn(point2))
+        self.play(MoveAlongPath(helix_dot, helix3, 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]))
+        nm3 = Arrow((0,0,0), (-2,0,0), color = BLUE).shift(helix_dot.get_center() + np.array([0.25,0,0]))
+        bnm3 = Arrow((0,0,0), (0,2,0), color = GREEN_E).shift(3.87*LEFT + 1.24*DOWN)
+        plane3 = Square(color = DARK_BROWN, fill_color = WHITE, fill_opacity=0.3).shift(helix_dot.get_center() + np.array([-0.5, 0.62, 0]))
+        point3 = VGroup(*[dot3, tgt3, nm3, bnm3, plane3]).shift(np.array([0,0,0]))
+
+        dot4 = Dot(np.array([np.cos(-np.pi/12), np.sin(-np.pi/12), -0.1*np.pi/3]) + np.array([-3.4,3.4,0]), radius = 0.16, color=RED)
+        tgt4 = Arrow((0,0,0), (-2,-0.85,0), color = YELLOW).shift(dot4.get_center() - np.array([-0.05,0,0]))
+        nm4 = Arrow((0,0,0), (0.8,-2,0), color = BLUE).shift(dot4.get_center() + np.array([-0.1,0.25,0]))
+        bnm4 = Arrow((0,0,0), (0,2,0), color = GREEN_E).shift(4.03*RIGHT + 0.5*DOWN)
+        plane4 = Square(color = DARK_BROWN, fill_color = WHITE, fill_opacity=0.3).shift(dot4.get_center() + np.array([-0.4,-1,0])).rotate(22*DEGREES).scale(1.2)
+        point4 = VGroup(*[dot4, tgt4, nm4, bnm4, plane4])
+
+        dot5 = Dot((1,0,0) + np.array([2.3,-1,1]))
+        tgt5 = Arrow((0,0,0), (0,2,0), color = YELLOW).shift(dot5.get_center() - np.array([-0.05,0.2,0]))
+        nm5 = Arrow((0,0,0), (-2,0,0), color = BLUE).shift(dot5.get_center() + np.array([0.25,0,0]))
+        bnm5 = Arrow((0,0,0), (0,2,0), color = GREEN_E).shift(3.34*LEFT+0.3*UP)
+        plane5 = Square(color = DARK_BROWN, fill_color = WHITE, fill_opacity=0.3).shift(dot5.get_center() + np.array([-0.5,0.5,0]))
+        point5 = VGroup(*[tgt5, nm5, bnm5, plane5])
+
+        self.add_fixed_in_frame_mobjects(bnm3)
+        self.play(ApplyMethod(point2.set_color, GRAY), FadeIn(point3))
+        self.play(MoveAlongPath(helix_dot, helix4, run_time=5))
+
+        self.add_fixed_in_frame_mobjects(bnm4)
+        self.play(ApplyMethod(point3.set_color, GRAY), FadeIn(point4))
+        self.play(MoveAlongPath(helix_dot, helix5, run_time=5))
+
+        self.add_fixed_in_frame_mobjects(bnm5)
+        self.play(ApplyMethod(point4.set_color, GRAY), FadeIn(point5))
+        self.wait(2)
+
+        self.play(FadeOut(VGroup(*[helix, bnm1, point0, point1, point2, point3, point4, point5, helix_dot])))