Manim animation delay between repetitions

calc-frontend/package.json

@@ -17,7 +17,7 @@
     "@radix-ui/react-tooltip": "^1.2.0",
     "@tailwindcss/vite": "^4.0.4",
     "axios": "^1.8.1",
-    "better-auth": "^1.2.4",
+    "better-auth": "^1.2.7",
     "class-variance-authority": "^0.7.1",
     "clsx": "^2.1.1",
     "jsdom": "^26.0.0",

calc-frontend/src/Animations/derivativeAnimation.py

@@ -18,7 +18,7 @@ def construct(self):
 
         func = axes.plot(
             lambda x: .5 * x * (x-3) * (x-4) + .6, 
-            x_range = (0,10)
+            x_range = (0,5)
         )
 
         x = ValueTracker(7)
@@ -38,7 +38,7 @@ def construct(self):
             )
         )
 
-        dot1 =always_redraw(
+        dot1 = always_redraw(
             lambda: Dot()
             .scale(0.7)
             .move_to(axes.c2p(x.get_value(), func.underlying_function(x.get_value())))
@@ -55,12 +55,18 @@ def construct(self):
             )
         )
 
+        tangent_label = always_redraw(
+            lambda: MathTex("y = f'(x)")
+            .scale(0.6)
+            .next_to(secant, UP, buff=0.1)
+            .set_color(GREEN)
+        )
+
         self.add(axes, axes_labels,func)
-        self.play(Create(VGroup(dot1,dot2,secant)))
+        self.add(dot1,dot2,secant,tangent_label)
         self.play(dx.animate.set_value(.001), run_time=1)
-        self.wait(2)
         self.play(x.animate.set_value(1), run_time = 4)
         self.play(x.animate.set_value(7), run_time = 4)
-        self.wait()
-        self.play(dx.animate.set_value(2), run_time = 4)
-        self.wait()
+        self.play(dx.animate.set_value(2), run_time = 1)
+
+        self.wait(3)

calc-frontend/src/Animations/integralAnimations.py

@@ -0,0 +1,65 @@
+from manim import *
+
+class RightRiemannSum(Scene):
+    def construct(self):
+        axes = Axes(
+            x_range=[0, 2.5, 1],
+            y_range=[0, 5, 1],
+            x_length=10,
+            y_length=5,
+            axis_config={"include_numbers": True}
+        ).to_edge(LEFT)
+
+        x_label = axes.get_x_axis_label("x")
+        y_label = axes.get_y_axis_label("y")
+
+        self.play(Create(axes), Write(x_label), Write(y_label))
+
+        graph = axes.plot(lambda x: 0.6 * x**2, x_range=[0, 2.3], color=WHITE)
+        self.play(Create(graph), run_time=2)
+
+        a, b = 0, 2
+        n = 10
+        dx = (b - a) / n
+        rectangles = VGroup()
+        area_sum = 0
+
+        for i in range(1, n + 1):
+            x_right = a + i * dx
+            height = 0.6 * x_right**2
+            area_sum += height * dx
+
+            rect_corner = axes.c2p(x_right - dx, 0)
+            rect_width = axes.c2p(dx, 0)[0] - axes.c2p(0, 0)[0]
+            rect_height = axes.c2p(0, height)[1] - axes.c2p(0, 0)[1]
+
+            rect = Rectangle(
+                width=rect_width,
+                height=rect_height,
+                fill_color=YELLOW,
+                fill_opacity=0.8,
+                stroke_width=0.5
+            )
+            rect.align_to(rect_corner, DOWN + LEFT)
+            rectangles.add(rect)
+
+        for rect in rectangles:
+            self.play(FadeIn(rect, run_time=0.2))
+
+        area_text = Text(f"Area ≈ {area_sum:.2f}", font_size=36)
+        area_text.to_edge(UP).shift(DOWN*2.4 + LEFT * 3.5)
+        self.play(Write(area_text))
+
+        self.wait(1.5)
+
+        self.play(
+            FadeOut(rectangles),
+            FadeOut(area_text),
+            FadeOut(graph),
+            FadeOut(axes),
+            FadeOut(x_label),
+            FadeOut(y_label),
+            run_time=1
+        )
+
+        self.wait(3)

calc-frontend/src/Animations/limitsAnimation.py

@@ -0,0 +1,81 @@
+import numpy as np 
+from manim import *
+
+class Limit(Scene):
+    def construct(self):
+
+        axes = Axes(
+            x_range=[0.1, 4, 1],
+            y_range=[0, 10, 2],
+            axis_config={"include_numbers": True},
+            x_length=8,
+            y_length=5
+        )
+        labels = axes.get_axis_labels(x_label="x", y_label="y")
+        self.play(Create(axes), Write(labels))
+
+        def func(x):
+            if x == 2:
+                return np.nan  # removable discontinuity
+            return (x**2 + 4*x - 12)/(x**2 - 2*x)
+
+        graph = axes.plot(
+            func, 
+            color=WHITE, 
+            discontinuities=[2], 
+            dt=0.01,
+            x_range=[.7,3.9]
+        )
+
+        hole_point = Circle(
+            radius=0.04,
+            color=WHITE,
+            fill_opacity=0,
+            stroke_width=4
+        ).move_to(axes.c2p(2, func(2.01)))
+
+        self.play(Create(graph), FadeIn(hole_point), run_time=2)
+
+        def get_tangent_angle(x):
+            dx = 0.001
+            dy = func(x + dx) - func(x)
+            return np.arctan2(dy, dx)
+
+        t_left = ValueTracker(0.7)
+        t_right = ValueTracker(3.5)
+
+        left_arrow = Triangle(color=GREEN, fill_opacity=1).scale(0.2)
+        left_arrow.rotate(PI/2)
+        left_updater = always_redraw(
+            lambda: left_arrow.move_to(axes.c2p(t_left.get_value(), func(t_left.get_value())))
+                                 .set_angle(get_tangent_angle(t_left.get_value()))
+        )
+
+        right_arrow = Triangle(color=YELLOW, fill_opacity=1).scale(0.2)
+        right_arrow.rotate(PI/2)
+        right_updater = always_redraw(
+            lambda: right_arrow.move_to(axes.c2p(t_right.get_value(), func(t_right.get_value())))
+                                  .set_angle(get_tangent_angle(t_right.get_value()))
+        )
+
+        self.add(left_updater, right_updater)
+
+        self.play(
+            t_left.animate.set_value(1.99),
+            t_right.animate.set_value(2.01),
+            run_time=2,
+            rate_func=linear
+        )
+
+        self.wait(.5)
+
+        self.play(
+            FadeOut(axes),
+            FadeOut(labels),
+            FadeOut(graph),
+            FadeOut(hole_point),
+            FadeOut(left_arrow),
+            FadeOut(right_arrow)
+        )
+
+        self.wait(3)

calc-frontend/src/Animations/media/Tex/66e1bc57a83e0f07.tex

@@ -0,0 +1,9 @@
+\documentclass[preview]{standalone}
+\usepackage[english]{babel}
+\usepackage{amsmath}
+\usepackage{amssymb}
+\begin{document}
+\begin{align*}
+0
+\end{align*}
+\end{document}

calc-frontend/src/Animations/media/Tex/70b3a8630e8c4922.tex

@@ -0,0 +1,9 @@
+\documentclass[preview]{standalone}
+\usepackage[english]{babel}
+\usepackage{amsmath}
+\usepackage{amssymb}
+\begin{document}
+\begin{align*}
+f(x)
+\end{align*}
+\end{document}

calc-frontend/src/Animations/media/Tex/b330e3953bf029d7.tex

@@ -0,0 +1,9 @@
+\documentclass[preview]{standalone}
+\usepackage[english]{babel}
+\usepackage{amsmath}
+\usepackage{amssymb}
+\begin{document}
+\begin{align*}
+6
+\end{align*}
+\end{document}

calc-frontend/src/Animations/media/Tex/b47c9feb1c667bc8.tex

@@ -0,0 +1,9 @@
+\documentclass[preview]{standalone}
+\usepackage[english]{babel}
+\usepackage{amsmath}
+\usepackage{amssymb}
+\begin{document}
+\begin{align*}
+8
+\end{align*}
+\end{document}