1 files changed, 91 insertions, 0 deletions
diff --git a/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file4_fs1.py b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file4_fs1.py
new file mode 100644
index 0000000..f3f5a9c
--- /dev/null
+++ b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file4_fs1.py
@@ -0,0 +1,91 @@
+from manimlib.imports import *
+class fs1(GraphScene):
+    CONFIG = {
+        "x_min": -2,
+        "x_max": 2,
+        "y_min": -6,
+        "y_max": 6,
+        "graph_origin": ORIGIN
+    }
+    def construct(self):
+
+        text = TextMobject(r'$\frac{dT}{ds} = \kappa N$ \\ $\frac{dT}{ds}$ gives the direction of N, \\ while $\kappa$ gives its magnitude.').scale(0.7).shift(3*UP + 3*LEFT)
+
+        self.setup_axes()
+        def curve_(x):
+            return x**3 - 2*x
+
+        def nm(x):
+            return abs(6 * x / ((9*(x**4) - 6*(x**2) + 5)**1.5))
+
+        figure = self.get_graph(curve_)
+
+
+        dot = Dot().rotate(PI/2)
+        alpha = ValueTracker(0)
+        t2_ = ValueTracker(-2)
+        t2 = t2_.get_value
+        t = alpha.get_value
+        vector_x = self.get_tangent_vector(t(),figure,scale=2)
+        vector_y = self.get_normal_vector(t(),figure,scale=2)
+
+        kappa = TextMobject(r'$\kappa = $').scale(0.7).shift(3*DOWN + 3*RIGHT)
+
+        t_text = always_redraw(
+            lambda: DecimalNumber(
+                nm(t2()),
+                color=WHITE,
+            ).scale(0.7).next_to(kappa)
+        ).scale(0.6)
+
+        self.play(
+            ShowCreation(figure),
+            GrowFromCenter(dot),
+            GrowArrow(vector_x),
+            GrowArrow(vector_y)
+            )
+        vector_x.add_updater(
+            lambda m: m.become(
+                    self.get_tangent_vector(t(),figure,scale=2)
+                )
+            )
+        vector_y.add_updater(
+            lambda m: m.become(
+                    self.get_normal_vector(t(),figure,scale=2)
+                )
+            )
+        dot.add_updater(lambda m: m.move_to(vector_x.get_start()))
+        circle = Circle(radius = 2, color = GREEN_SCREEN). shift(2.63*RIGHT + 2.8*UP)
+        dot2 = Dot(np.array([2, curve_(2), 0]), color = WHITE).shift(2*DOWN + 2.5*RIGHT)
+
+        self.add(vector_x, vector_y,dot, t_text, kappa, text)
+        self.play(t2_.set_value, 2, alpha.set_value, 1, run_time=18, rate_func=smooth)
+        self.play(FadeIn(dot2), FadeIn(circle))
+        self.wait(2)
+        self.play(FadeOut(VGroup(*[self.axes, dot2, figure, circle, text, kappa, t_text])))
+
+
+    def get_tangent_vector(self, proportion, curve, dx=0.001, scale=0.5):
+        coord_i = curve.point_from_proportion(proportion)
+        coord_f = curve.point_from_proportion(proportion + dx)
+        reference_line = Line(coord_i,coord_f)
+        unit_vector = reference_line.get_unit_vector() * 0.7
+        vector = Arrow(coord_i , coord_i + unit_vector, color = YELLOW, buff=0)
+        return vector
+
+    def get_normal_vector(self, proportion, curve, dx=0.001, scale=1):
+        t = proportion.copy()/6
+        coord_i = curve.point_from_proportion(proportion)
+        coord_f = curve.point_from_proportion(proportion + dx)
+        length = 6 * t / ((9*(t**4) - 6*(t**2) + 5)**1.5)
+        if coord_i[0] <=  0 and coord_i[0] >  -0.5:
+            reference_line = Line(coord_i,coord_f).rotate(PI/2).set_width(0).scale(2)
+        elif coord_i[0] >  0 and (coord_i[0] < 0.5 or coord_i[0] > 2.7):
+            reference_line = Line(coord_i,coord_f).rotate(PI/2).set_width(0).scale(2)
+        elif coord_i[0] >  0:
+            reference_line = Line(coord_i,coord_f).rotate(PI/2).set_width(length).scale(2)
+        else:
+            reference_line = Line(coord_i,coord_f).rotate(-PI/2).set_width(length).scale(2)
+        unit_vector = reference_line.get_vector() * scale
+        vector = Arrow(coord_i , coord_i + unit_vector, color = RED_C, buff=0)
+        return vector