Merge pull request #67 from stayaryan/patch-13

Create RiemannRectanglesAnimation.py

1 files changed, 64 insertions, 0 deletions

diff --git a/FSF-2020/calculus/intro-to-calculus/riemannintegrals/RiemannRectanglesAnimation.py b/FSF-2020/calculus/intro-to-calculus/riemannintegrals/RiemannRectanglesAnimation.py
new file mode 100644
index 0000000..a278c9d
--- /dev/null
+++ b/FSF-2020/calculus/intro-to-calculus/riemannintegrals/RiemannRectanglesAnimation.py
@@ -0,0 +1,64 @@
+from manimlib.imports import *
+class RiemannRectanglesAnimation(GraphScene):
+    CONFIG = {
+        "y_max": 5,
+        "x_max": 6,
+        "x_min": 0,
+        "y_min": 0,
+        "x_axis_width": 5,
+        "y_axis_height": 5,
+        "init_dx":0.5,
+        "graph_origin": ORIGIN+2*DOWN+6*LEFT,
+    }
+    def construct(self):
+        self.setup_axes()
+        def func(x):
+            return  0.1*(x)*(x-3)*(x-7)+3
+
+        graph1=self.get_graph(func,x_min=0,x_max=6)
+        kwargs = {
+            "x_min" : 1.5,
+            "x_max" : 5.5,
+            "fill_opacity" : 0.75,
+            "stroke_width" : 0.25,
+            "input_sample_type": "right",
+        }
+        flat_rectangles1 = self.get_riemann_rectangles(self.get_graph(lambda x : 0),dx=self.init_dx,start_color=invert_color(PURPLE),end_color=invert_color(ORANGE),**kwargs)
+        riemann_rectangles_list1 = self.get_riemann_rectangles_list(graph1,8,max_dx=self.init_dx,power_base=2,start_color=PURPLE,end_color=ORANGE,**kwargs)
+        self.add(graph1)
+        self.graph_origin = ORIGIN+2*DOWN+1*RIGHT
+        self.setup_axes()
+        graph2=self.get_graph(func,x_min=0,x_max=6)
+        kwargs = {
+            "x_min" : 1.5,
+            "x_max" : 5.5,
+            "fill_opacity" : 0.75,
+            "stroke_width" : 0.25,
+            "input_sample_type": "left",
+        }
+        flat_rectangles2 = self.get_riemann_rectangles(self.get_graph(lambda x : 0),dx=self.init_dx,start_color=invert_color(PURPLE),end_color=invert_color(ORANGE),**kwargs)
+        riemann_rectangles_list2 = self.get_riemann_rectangles_list(graph2,8,max_dx=self.init_dx,power_base=2,start_color=PURPLE,end_color=ORANGE,**kwargs)
+        self.add(graph2)
+        text1 = TextMobject("Left Riemann sum").move_to(np.array([-3,-2.5,0]))
+        text2 = TextMobject("Right Riemann sum").move_to(np.array([4,-2.5,0]))
+        grp1 = VGroup(text1, text2)
+        text3 = TexMobject(r"n \rightarrow \infty").move_to(np.array([0, -3, 0]))
+        text4 = TextMobject("Left and Right Riemann sums are equal").move_to(np.array([0, -3, 0]))
+        text5 = TextMobject("Hence function is Riemann integrable and value of integral equals area covered").move_to(np.array([0, -3, 0])).scale(0.6)
+        grp2 = VGroup(text1, text2, text3)
+        # Show Riemann rectangles
+        self.play(ReplacementTransform(flat_rectangles1,riemann_rectangles_list1[0]), ReplacementTransform(flat_rectangles2, riemann_rectangles_list2[0]))
+        self.wait()
+        self.play(ShowCreation(grp1))
+        for r in range(1,len(riemann_rectangles_list1)-5):
+            self.transform_between_riemann_rects(riemann_rectangles_list1[r-1],riemann_rectangles_list1[r],replace_mobject_with_target_in_scene = True,)
+            self.transform_between_riemann_rects(riemann_rectangles_list2[r-1],riemann_rectangles_list2[r],replace_mobject_with_target_in_scene = True,)
+        self.play(ShowCreation(text3))
+        for r in range(len(riemann_rectangles_list1)-5,len(riemann_rectangles_list1)):
+            self.transform_between_riemann_rects(riemann_rectangles_list1[r-1],riemann_rectangles_list1[r],replace_mobject_with_target_in_scene = True,)
+            self.transform_between_riemann_rects(riemann_rectangles_list2[r-1],riemann_rectangles_list2[r],replace_mobject_with_target_in_scene = True,)
+        self.wait(2)
+        self.play(ReplacementTransform(grp2, text4))
+        self.wait(2)
+        self.play(ReplacementTransform(text4, text5))
+        self.wait(4)