last video for curvature

1 files changed, 56 insertions, 0 deletions

diff --git a/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/arc-length-and-curvature/file4_different_curvature_single_curve.py b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/arc-length-and-curvature/file4_different_curvature_single_curve.py
new file mode 100644
index 0000000..d71adda
--- /dev/null
+++ b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/arc-length-and-curvature/file4_different_curvature_single_curve.py
@@ -0,0 +1,56 @@
+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
+    }
+
+    def construct(self):
+
+        self.setup_axes()
+        def curve(x):
+            return 3 - (3653*x**2)/5292 + (2477*x**3)/31752 + (13*x**4)/784 - (17*x**5)/5292 + (17*x**6)/63504
+
+        graph = FunctionGraph(curve, x_min=-3, x_max=6, stroke_width = 2, color = BLUE)
+
+        tracker = ValueTracker(-3)
+
+        text = TextMobject(r'The curvature at point $P_{1}$ is \\ lesser than that at point $P_{2}$: \\ as $\kappa = \frac{1}{R}$').shift(3.2*RIGHT+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((4,-1, 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
+
+        line = always_redraw(get_tangent_line)
+
+        self.add(graph,line, dots, text)
+        self.wait(1.2)
+        self.play(tracker.set_value, 6, rate_func=smooth, run_time=13)
+        self.play(FadeOut(VGroup(*[graph, self.axes, line, dots, text])))
+        self.wait()