1 files changed, 76 insertions, 0 deletions
diff --git a/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/arc-length-and-curvature/file5_different_curvature_single_curve.py b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/arc-length-and-curvature/file5_different_curvature_single_curve.py
new file mode 100644
index 0000000..0dc06bb
--- /dev/null
+++ b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/arc-length-and-curvature/file5_different_curvature_single_curve.py
@@ -0,0 +1,76 @@
+from manimlib.imports import *
+
+class GR(GraphScene):
+    CONFIG = {
+        "x_axis_label": "",
+        "y_axis_label": "",
+        "x_min": -4,
+        "x_max": 6,
+        "y_min": -6,
+        "y_max": 10,
+        "graph_origin": ORIGIN,
+        'x_tick_frequency': 20,
+        'y_tick_frequency': 20
+    }
+
+    def construct(self):
+
+        self.setup_axes()
+        def curve(x):
+            return 3 - (3653*x**2)/5292 + (277*x**3)/31752 + (13*x**4)/784 - (17*x**5)/5292 + (170*x**6)/63504
+
+        graph = FunctionGraph(curve, x_min=-2, x_max=6, stroke_width = 2, color = BLUE)
+
+        tracker = ValueTracker(-2)
+
+        text = TextMobject(r'$\because R_{1} > R_{2}$, the curvature at \\ point $P_{1}$ is less than that \\ at point $P_{2}$ as $\kappa = \frac{1}{R}$').shift(3.2*LEFT+3*UP).scale(0.6)
+
+        dot1 = Dot((0,3,0), color = YELLOW)
+        dot1label = TextMobject(r'$P_{1}$').next_to(dot1, UP+RIGHT, buff = 0.1)
+        dot2 = Dot((2.9,-0.47, 0), color = YELLOW)
+        dot2label = TextMobject(r'$P_{2}$').next_to(dot2, DOWN, buff = 0.1)
+        dots = VGroup(*[dot1, dot2, dot1label, dot2label])
+
+        def get_tangent_line():
+            line = Line(
+                ORIGIN, 2 * RIGHT,
+                color=RED,
+                stroke_width=4,
+            )
+            dx = 0.0001
+
+            x = tracker.get_value()
+            p0 = np.array([x-dx,curve(x-dx),0])
+            p1 = np.array([x, curve(x), 0])
+            p2 = np.array([x + dx, curve(x + dx), 0])
+
+            angle = angle_of_vector(p2 - p1)
+            line.rotate(angle)
+            line.move_to(p0)
+            return line
+
+        circle1 = Circle(radius = 0.8, color = GREY, opacity = 0.2).shift(2.2*UP)
+        tgt1 = Line((-2,3,0), (2,3,0), color = GREY, opacity = 0.2).scale(0.4)
+
+        r1 = Line(circle1.get_center(), circle1.get_center() + np.array([0,0.8,0]), color=GREEN_SCREEN)
+        r1label = TextMobject(r'$R_{1}$',color=WHITE).next_to(r1, RIGHT, buff = 0.1).scale(0.6)
+
+        curvature1 = VGroup(*[circle1, tgt1, r1, r1label])
+
+        circle2 = Circle(radius = 0.2, color = GREY, opacity = 0.2).shift(0.3*DOWN + 2.9*RIGHT)
+        tgt2 = Line((4,-2,0), (6, -2, 0), color = GREY, opacity = 0.2).scale(0.5).shift(2.1*LEFT + 1.5*UP)
+
+        r2 = Line(circle2.get_center(), circle2.get_center() - np.array([0,0.2,0]), color=GREEN_SCREEN)
+        r2label = TextMobject(r'$R_{2}$', color=WHITE).next_to(r2.get_start(), np.array([0,0,0]), buff = 0).scale(0.4)
+
+        curvature2 = VGroup(*[circle2, tgt2, r2, r2label])
+
+        line = always_redraw(get_tangent_line)
+
+        self.add(graph, line, dots, text)
+        self.wait(1.2)
+        self.play(tracker.set_value, 4, rate_func=smooth, run_time=10)
+        self.play(FadeIn(curvature1), FadeIn(curvature2))
+        self.wait(2)
+        self.play(FadeOut(VGroup(*[curvature1, curvature2, graph, self.axes, line, dots, text])))
+        self.wait()