From ba7489873b87ab681ed58b2d9e1f3cb92dfd60e9 Mon Sep 17 00:00:00 2001 From: daustin305 Date: Mon, 14 Apr 2025 18:05:15 -0400 Subject: [PATCH 1/4] Created an animation for arrows approaching a limit --- .../limitsAnimation.cpython-310.pyc | Bin 0 -> 2408 bytes .../src/Animations/integralAnimations.py | 10 +-- .../src/Animations/limitsAnimation.py | 81 ++++++++++++++++++ .../Animations/media/Tex/66e1bc57a83e0f07.svg | 10 +++ .../Animations/media/Tex/66e1bc57a83e0f07.tex | 9 ++ .../Animations/media/Tex/70b3a8630e8c4922.svg | 16 ++++ .../Animations/media/Tex/70b3a8630e8c4922.tex | 9 ++ .../Animations/media/Tex/b330e3953bf029d7.svg | 10 +++ .../Animations/media/Tex/b330e3953bf029d7.tex | 9 ++ .../Animations/media/Tex/b47c9feb1c667bc8.svg | 10 +++ .../Animations/media/Tex/b47c9feb1c667bc8.tex | 9 ++ .../videos/limitsAnimation/1080p60/Limit.mp4 | Bin 0 -> 245328 bytes .../3040924799_1376512726_2967433267.mp4 | Bin 0 -> 55440 bytes .../3040924799_1541204567_3012000059.mp4 | Bin 0 -> 44403 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VGroup() area_sum = 0 - # Create rectangles using f(x) = 0.6 * x^2 for i in range(1, n + 1): x_right = a + i * dx height = 0.6 * x_right**2 @@ -48,18 +43,15 @@ def construct(self): rect.align_to(rect_corner, DOWN + LEFT) rectangles.add(rect) - # Animate rectangles fading in one-by-one (0.2s each) for rect in rectangles: self.play(FadeIn(rect, run_time=0.2)) - # Show area label in top-right corner 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) - - # Fade everything out + self.play( FadeOut(rectangles), FadeOut(area_text), diff --git a/calc-frontend/src/Animations/limitsAnimation.py b/calc-frontend/src/Animations/limitsAnimation.py index e69de29..a58f16a 100644 --- a/calc-frontend/src/Animations/limitsAnimation.py +++ b/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() diff --git a/calc-frontend/src/Animations/media/Tex/66e1bc57a83e0f07.svg b/calc-frontend/src/Animations/media/Tex/66e1bc57a83e0f07.svg new file mode 100644 index 0000000..56f9bee --- /dev/null +++ b/calc-frontend/src/Animations/media/Tex/66e1bc57a83e0f07.svg @@ -0,0 +1,10 @@ + + + + + + + + + + \ No newline at end of file diff --git a/calc-frontend/src/Animations/media/Tex/66e1bc57a83e0f07.tex b/calc-frontend/src/Animations/media/Tex/66e1bc57a83e0f07.tex new file mode 100644 index 0000000..7f5e239 --- /dev/null +++ b/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} \ No newline at end of file diff --git a/calc-frontend/src/Animations/media/Tex/70b3a8630e8c4922.svg b/calc-frontend/src/Animations/media/Tex/70b3a8630e8c4922.svg new file mode 100644 index 0000000..c446861 --- /dev/null +++ b/calc-frontend/src/Animations/media/Tex/70b3a8630e8c4922.svg @@ -0,0 +1,16 @@ + + + + + + + + + + + + + + + + \ No newline at end of file diff --git a/calc-frontend/src/Animations/media/Tex/70b3a8630e8c4922.tex b/calc-frontend/src/Animations/media/Tex/70b3a8630e8c4922.tex new file mode 100644 index 0000000..79bedbc --- /dev/null +++ b/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} \ No newline at end of file diff --git a/calc-frontend/src/Animations/media/Tex/b330e3953bf029d7.svg b/calc-frontend/src/Animations/media/Tex/b330e3953bf029d7.svg new file mode 100644 index 0000000..a4e8630 --- /dev/null +++ b/calc-frontend/src/Animations/media/Tex/b330e3953bf029d7.svg @@ -0,0 +1,10 @@ + + + + + + + + + + \ No newline at end of file diff --git a/calc-frontend/src/Animations/media/Tex/b330e3953bf029d7.tex b/calc-frontend/src/Animations/media/Tex/b330e3953bf029d7.tex new file mode 100644 index 0000000..7675c00 --- /dev/null +++ b/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} \ No newline at end of file diff --git a/calc-frontend/src/Animations/media/Tex/b47c9feb1c667bc8.svg b/calc-frontend/src/Animations/media/Tex/b47c9feb1c667bc8.svg new file mode 100644 index 0000000..b587f57 --- /dev/null +++ b/calc-frontend/src/Animations/media/Tex/b47c9feb1c667bc8.svg @@ -0,0 +1,10 @@ + + + + + + + + + + \ No newline at end of file diff --git a/calc-frontend/src/Animations/media/Tex/b47c9feb1c667bc8.tex b/calc-frontend/src/Animations/media/Tex/b47c9feb1c667bc8.tex new file mode 100644 index 0000000..b628b4c --- /dev/null +++ b/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} \ No newline at end of file diff --git a/calc-frontend/src/Animations/media/videos/limitsAnimation/1080p60/Limit.mp4 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