From 3b99e1259fea76103adc3c25b3af2da6d98635ed Mon Sep 17 00:00:00 2001
From: Nao Pross <np@0hm.ch>
Date: Wed, 14 Apr 2021 17:14:20 +0200
Subject: Add some animations

---
 vorlesungen/punktgruppen/crystals.py    | 269 +++++++++++++++
 vorlesungen/punktgruppen/poetry.lock    | 591 ++++++++++++++++++++++++++++++++
 vorlesungen/punktgruppen/pyproject.toml |  15 +
 3 files changed, 875 insertions(+)
 create mode 100644 vorlesungen/punktgruppen/crystals.py
 create mode 100644 vorlesungen/punktgruppen/poetry.lock
 create mode 100644 vorlesungen/punktgruppen/pyproject.toml

(limited to 'vorlesungen/punktgruppen')

diff --git a/vorlesungen/punktgruppen/crystals.py b/vorlesungen/punktgruppen/crystals.py
new file mode 100644
index 0000000..0f97a0f
--- /dev/null
+++ b/vorlesungen/punktgruppen/crystals.py
@@ -0,0 +1,269 @@
+from manim import *
+
+import math as m
+import numpy as np
+
+# configure style
+config.background_color = '#202020'
+config.tex_template.add_to_preamble(
+    r"\usepackage[p,osf]{scholax}"
+    r"\usepackage{amsmath}"
+    r"\usepackage[scaled=1.075,ncf,vvarbb]{newtxmath}"
+)
+
+# scenes
+class Geometric2DSymmetries(Scene):
+    def construct(self):
+        # title
+        title = Tex(r"Geometrische \\ Symmetrien")
+        title.scale(1.5)
+        self.play(Write(title))
+        self.wait()
+        self.play(FadeOut(title))
+        self.wait()
+
+        self.intro()
+        self.cyclic()
+        self.dihedral()
+
+    def intro(self):
+        # create square
+        square = Square()
+        square.set_fill(PINK, opacity=.5)
+        self.play(SpinInFromNothing(square))
+        self.wait()
+
+        # the action of doing nothing
+        action = MathTex(r"1")
+        self.play(Write(action))
+        self.play(ApplyMethod(square.scale, 1.2))
+        self.play(ApplyMethod(square.scale, 1/1.2))
+        self.play(FadeOut(action))
+
+        # show some reflections
+        axis = DashedLine(2 * LEFT, 2 * RIGHT)
+        sigma = MathTex(r"\sigma")
+        sigma.next_to(axis, RIGHT)
+
+        self.play(Create(axis))
+        self.play(Write(sigma))
+
+        self.play(ApplyMethod(square.flip, RIGHT))
+        self.wait()
+
+        for d in [UP + RIGHT, UP]:
+            self.play(
+                Rotate(axis, PI/4),
+                Rotate(sigma, PI/4, about_point=ORIGIN))
+
+            self.play(Rotate(sigma, -PI/4), run_time=.5)
+            self.play(ApplyMethod(square.flip, d))
+
+        self.play(
+            FadeOutAndShift(sigma),
+            Uncreate(axis))
+
+        # show some rotations
+        dot = Dot(UP + RIGHT)
+        figure = VGroup()
+        figure.add(square)
+        figure.add(dot)
+
+        rot = MathTex(r"r")
+        self.play(Write(rot), Create(dot))
+
+        last = rot
+        for newrot in map(MathTex, [r"r", r"r^2", r"r^3"]):
+            self.play(
+                ReplacementTransform(last, newrot),
+                Rotate(figure, PI/2, about_point=ORIGIN))
+            self.wait()
+            last = newrot
+
+        self.play(Uncreate(dot), FadeOut(square), FadeOut(last))
+
+
+    def cyclic(self):
+        # create symmetric figure
+        figure = VGroup()
+        prev = [1.5, 0, 0]
+        for i in range(1,6):
+            pos = [
+                1.5*m.cos(2 * PI/5 * i),
+                1.5*m.sin(2 * PI/5 * i),
+                0
+            ]
+
+            if prev:
+                line = Line(prev, pos)
+                figure.add(line)
+
+            dot = Dot(pos, radius=.1)
+            if i == 5:
+                dot.set_fill(RED)
+
+            prev = pos
+            figure.add(dot)
+
+        group = MathTex(r"G = \langle r \rangle")
+        self.play(Write(group), run_time = 2)
+        self.wait()
+        self.play(ApplyMethod(group.to_corner, UP))
+
+        actions = map(MathTex, [r"1", r"r", r"r^2", r"r^3", r"r^4", r"1"])
+        action = next(actions, MathTex(r"r"))
+        
+        self.play(Create(figure))
+        self.play(Write(action))
+        self.wait()
+
+        for i in range(5):
+            newaction = next(actions, MathTex(r"r"))
+            self.play(
+                ReplacementTransform(action, newaction),
+                Rotate(figure, 2*PI/5, about_point=ORIGIN))
+            action = newaction
+
+        self.play(Uncreate(figure), FadeOut(action))
+
+        whole_group = MathTex(
+            r"G = \langle r \rangle" 
+            r"= \left\{1, r, r^2, r^3, r^4 \right\}")
+
+        self.play(ApplyMethod(group.move_to, ORIGIN))
+        self.play(ReplacementTransform(group, whole_group))
+        self.wait()
+
+        cyclic = MathTex(
+            r"C_n = \langle r \rangle" 
+            r"= \left\{1, r, r^2, \dots, r^n \right\}")
+
+        cyclic_title = Tex(r"Zyklische Gruppe")
+        cyclic_title.next_to(cyclic, UP * 2)
+
+        cyclic.scale(1.2)
+        cyclic_title.scale(1.2)
+
+        self.play(ReplacementTransform(whole_group, cyclic))
+        self.play(FadeInFrom(cyclic_title, UP))
+
+        self.wait(5)
+        self.play(FadeOut(cyclic), FadeOut(cyclic_title))
+
+    def dihedral(self):
+        # create square
+        square = Square()
+        square.set_fill(PINK, opacity=.5)
+
+        # generator equation
+        group = MathTex(
+            r"G = \langle \sigma, r \,|\,",
+            r"\sigma^2 = 1,",
+            r"r^4 = 1,",
+            r"(\sigma r)^2 = 1 \rangle")
+
+        self.play(Write(group), run_time = 2)
+        self.wait()
+        self.play(ApplyMethod(group.to_corner, UP))
+        self.play(FadeIn(square))
+
+        axis = DashedLine(2 * LEFT, 2 * RIGHT)
+        sigma = MathTex(r"\sigma^2 = 1")
+        sigma.next_to(axis, RIGHT)
+        self.play(Create(axis), Write(sigma))
+        self.play(ApplyMethod(square.flip, RIGHT))
+        self.play(ApplyMethod(square.flip, RIGHT))
+        self.play(Uncreate(axis), FadeOut(sigma))
+
+        # rotations
+        dot = Dot(UP + RIGHT)
+        rot = MathTex(r"r^4 = 1")
+        rot.next_to(square, DOWN * 3)
+
+        figure = VGroup()
+        figure.add(dot)
+        figure.add(square)
+
+        self.play(Write(rot), Create(dot))
+        for i in range(4):
+            self.play(Rotate(figure, PI/2))
+        self.play(FadeOut(rot), Uncreate(dot))
+
+        # rotation and flip
+        action = MathTex(r"(\sigma r)^2 = 1")
+        action.next_to(square, DOWN * 5)
+
+        dot = Dot(UP + RIGHT)
+        axis = DashedLine(2 * LEFT, 2 * RIGHT)
+        self.play(Create(dot), Create(axis), Write(action))
+
+        figure = VGroup()
+        figure.add(dot)
+        figure.add(square)
+
+        for i in range(2):
+            self.play(Rotate(figure, PI/2))
+            self.play(ApplyMethod(figure.flip, RIGHT))
+            self.wait()
+
+        self.play(Uncreate(dot), Uncreate(axis), FadeOut(action))
+        self.play(FadeOut(square))
+
+        # equation for the whole
+        whole_group = MathTex(
+            r"G &= \langle \sigma, r \,|\,"
+            r"\sigma^2 = r^4 = (\sigma r)^2 = 1 \rangle \\"
+            r"&= \left\{"
+            r"1, r, r^2, r^3, \sigma, \sigma r, \sigma r^2, \sigma r^3"
+            r"\right\}")
+
+        self.play(ApplyMethod(group.move_to, ORIGIN))
+        self.play(ReplacementTransform(group, whole_group))
+        self.wait(2)
+
+        dihedral = MathTex(
+            r"D_n &= \langle \sigma, r \,|\,"
+            r"\sigma^2 = r^n = (\sigma r)^2 = 1 \rangle \\"
+            r"&= \left\{"
+            r"1, r, r^2, \dots, \sigma, \sigma r, \sigma r^2, \dots"
+            r"\right\}")
+
+        dihedral_title = Tex(r"Diedergruppe: Symmetrien eines \(n\)-gons")
+        dihedral_title.next_to(dihedral, UP * 2)
+
+        dihedral.scale(1.2)
+        dihedral_title.scale(1.2)
+
+        self.play(ReplacementTransform(whole_group, dihedral))
+        self.play(FadeInFrom(dihedral_title, UP))
+
+        self.wait(5)
+        self.play(FadeOut(dihedral), FadeOut(dihedral_title))
+
+
+class Geometric3DSymmetries(ThreeDScene):
+    def construct(self):
+        self.symmetric()
+
+    def symmetric(self):
+        self.renderer.camera.light_source.move_to(3*IN) # changes the source of the light
+        self.set_camera_orientation(phi=60 * DEGREES, theta=-20 * DEGREES)
+
+        cube = Cube()
+        axes = ThreeDAxes()
+
+        axis = np.array([2,2,2])
+        line = DashedLine(-axis, axis)
+
+        self.play(Create(axes), Create(cube))
+        self.play(Create(line))
+
+        self.play(ApplyMethod(cube.rotate, PI, axis / abs(axis)))
+
+        self.begin_ambient_camera_rotation(rate=0.1)
+        self.wait(7)
+
+
+class AlgebraicSymmetries(Scene):
+    def construct(self):
+        pass
diff --git a/vorlesungen/punktgruppen/poetry.lock b/vorlesungen/punktgruppen/poetry.lock
new file mode 100644
index 0000000..13c5100
--- /dev/null
+++ b/vorlesungen/punktgruppen/poetry.lock
@@ -0,0 +1,591 @@
+[[package]]
+name = "colorama"
+version = "0.4.4"
+description = "Cross-platform colored terminal text."
+category = "main"
+optional = false
+python-versions = ">=2.7, !=3.0.*, !=3.1.*, !=3.2.*, !=3.3.*, !=3.4.*"
+
+[[package]]
+name = "colour"
+version = "0.1.5"
+description = "converts and manipulates various color representation (HSL, RVB, web, X11, ...)"
+category = "main"
+optional = false
+python-versions = "*"
+
+[package.extras]
+test = ["nose"]
+
+[[package]]
+name = "commonmark"
+version = "0.9.1"
+description = "Python parser for the CommonMark Markdown spec"
+category = "main"
+optional = false
+python-versions = "*"
+
+[package.extras]
+test = ["flake8 (==3.7.8)", "hypothesis (==3.55.3)"]
+
+[[package]]
+name = "decorator"
+version = "4.4.2"
+description = "Decorators for Humans"
+category = "main"
+optional = false
+python-versions = ">=2.6, !=3.0.*, !=3.1.*"
+
+[[package]]
+name = "glcontext"
+version = "2.3.3"
+description = "Portable OpenGL Context"
+category = "main"
+optional = false
+python-versions = "*"
+
+[[package]]
+name = "importlib-metadata"
+version = "3.10.0"
+description = "Read metadata from Python packages"
+category = "main"
+optional = false
+python-versions = ">=3.6"
+
+[package.dependencies]
+typing-extensions = {version = ">=3.6.4", markers = "python_version < \"3.8\""}
+zipp = ">=0.5"
+
+[package.extras]
+docs = ["sphinx", "jaraco.packaging (>=8.2)", "rst.linker (>=1.9)"]
+testing = ["pytest (>=4.6)", "pytest-checkdocs (>=2.4)", "pytest-flake8", "pytest-cov", "pytest-enabler (>=1.0.1)", "packaging", "pep517", "pyfakefs", "flufl.flake8", "pytest-black (>=0.3.7)", "pytest-mypy", "importlib-resources (>=1.3)"]
+
+[[package]]
+name = "manim"
+version = "0.5.0"
+description = "Animation engine for explanatory math videos."
+category = "main"
+optional = false
+python-versions = ">=3.6.2,<4.0.0"
+
+[package.dependencies]
+colour = "*"
+importlib-metadata = {version = "*", markers = "python_version < \"3.8\""}
+manimpango = ">=0.2.4,<0.3.0"
+mapbox-earcut = ">=0.12.10,<0.13.0"
+moderngl = ">=5.6.3,<6.0.0"
+moderngl-window = ">=2.3.0,<3.0.0"
+networkx = ">=2.5,<3.0"
+numpy = ">=1.9,<2.0"
+Pillow = "*"
+pycairo = ">=1.19,<2.0"
+pydub = "*"
+pygments = "*"
+rich = ">=6.0,<7.0"
+scipy = "*"
+tqdm = "*"
+
+[package.extras]
+webgl_renderer = ["grpcio (>=1.33.0,<1.34.0)", "grpcio-tools (>=1.33.0,<1.34.0)", "watchdog"]
+jupyterlab = ["jupyterlab (>=3.0,<4.0)"]
+
+[[package]]
+name = "manimpango"
+version = "0.2.5.post0"
+description = "Bindings for Pango for using with Manim."
+category = "main"
+optional = false
+python-versions = ">=3.6"
+
+[[package]]
+name = "mapbox-earcut"
+version = "0.12.10"
+description = "Python bindings for the mapbox earcut C++ polygon triangulation library."
+category = "main"
+optional = false
+python-versions = "*"
+
+[package.dependencies]
+numpy = "*"
+
+[[package]]
+name = "moderngl"
+version = "5.6.4"
+description = "ModernGL: High performance rendering for Python 3"
+category = "main"
+optional = false
+python-versions = "*"
+
+[package.dependencies]
+glcontext = ">=2,<3"
+
+[[package]]
+name = "moderngl-window"
+version = "2.3.0"
+description = "A cross platform helper library for ModernGL making window creation and resource loading simple"
+category = "main"
+optional = false
+python-versions = ">=3.5"
+
+[package.dependencies]
+moderngl = "<6"
+numpy = ">=1.16,<2"
+Pillow = ">=5"
+pyglet = ">=1.5.8,<2"
+pyrr = ">=0.10.3,<1"
+
+[package.extras]
+pysdl2 = ["pysdl2"]
+pyside2 = ["PySide2 (<6)"]
+glfw = ["glfw"]
+pygame = ["pygame (==2.0.0.dev10)"]
+pyqt5 = ["pyqt5"]
+pywavefront = ["pywavefront (>=1.2.0,<2)"]
+tk = ["pyopengltk (>=0.0.3)"]
+trimesh = ["trimesh (>=3.2.6,<4)", "scipy (>=1.3.2)"]
+
+[[package]]
+name = "multipledispatch"
+version = "0.6.0"
+description = "Multiple dispatch"
+category = "main"
+optional = false
+python-versions = "*"
+
+[package.dependencies]
+six = "*"
+
+[[package]]
+name = "networkx"
+version = "2.5.1"
+description = "Python package for creating and manipulating graphs and networks"
+category = "main"
+optional = false
+python-versions = ">=3.6"
+
+[package.dependencies]
+decorator = ">=4.3,<5"
+
+[package.extras]
+all = ["numpy", "scipy", "pandas", "matplotlib", "pygraphviz", "pydot", "pyyaml", "lxml", "pytest"]
+gdal = ["gdal"]
+lxml = ["lxml"]
+matplotlib = ["matplotlib"]
+numpy = ["numpy"]
+pandas = ["pandas"]
+pydot = ["pydot"]
+pygraphviz = ["pygraphviz"]
+pytest = ["pytest"]
+pyyaml = ["pyyaml"]
+scipy = ["scipy"]
+
+[[package]]
+name = "numpy"
+version = "1.20.2"
+description = "NumPy is the fundamental package for array computing with Python."
+category = "main"
+optional = false
+python-versions = ">=3.7"
+
+[[package]]
+name = "pillow"
+version = "8.2.0"
+description = "Python Imaging Library (Fork)"
+category = "main"
+optional = false
+python-versions = ">=3.6"
+
+[[package]]
+name = "pycairo"
+version = "1.20.0"
+description = "Python interface for cairo"
+category = "main"
+optional = false
+python-versions = ">=3.6, <4"
+
+[[package]]
+name = "pydub"
+version = "0.25.1"
+description = "Manipulate audio with an simple and easy high level interface"
+category = "main"
+optional = false
+python-versions = "*"
+
+[[package]]
+name = "pyglet"
+version = "1.5.15"
+description = "Cross-platform windowing and multimedia library"
+category = "main"
+optional = false
+python-versions = "*"
+
+[[package]]
+name = "pygments"
+version = "2.8.1"
+description = "Pygments is a syntax highlighting package written in Python."
+category = "main"
+optional = false
+python-versions = ">=3.5"
+
+[[package]]
+name = "pyrr"
+version = "0.10.3"
+description = "3D mathematical functions using NumPy"
+category = "main"
+optional = false
+python-versions = "*"
+
+[package.dependencies]
+multipledispatch = "*"
+numpy = "*"
+
+[[package]]
+name = "rich"
+version = "6.2.0"
+description = "Render rich text, tables, progress bars, syntax highlighting, markdown and more to the terminal"
+category = "main"
+optional = false
+python-versions = ">=3.6,<4.0"
+
+[package.dependencies]
+colorama = ">=0.4.0,<0.5.0"
+commonmark = ">=0.9.0,<0.10.0"
+pygments = ">=2.6.0,<3.0.0"
+typing-extensions = ">=3.7.4,<4.0.0"
+
+[package.extras]
+jupyter = ["ipywidgets (>=7.5.1,<8.0.0)"]
+
+[[package]]
+name = "scipy"
+version = "1.6.1"
+description = "SciPy: Scientific Library for Python"
+category = "main"
+optional = false
+python-versions = ">=3.7"
+
+[package.dependencies]
+numpy = ">=1.16.5"
+
+[[package]]
+name = "six"
+version = "1.15.0"
+description = "Python 2 and 3 compatibility utilities"
+category = "main"
+optional = false
+python-versions = ">=2.7, !=3.0.*, !=3.1.*, !=3.2.*"
+
+[[package]]
+name = "tqdm"
+version = "4.60.0"
+description = "Fast, Extensible Progress Meter"
+category = "main"
+optional = false
+python-versions = "!=3.0.*,!=3.1.*,!=3.2.*,!=3.3.*,>=2.7"
+
+[package.extras]
+dev = ["py-make (>=0.1.0)", "twine", "wheel"]
+notebook = ["ipywidgets (>=6)"]
+telegram = ["requests"]
+
+[[package]]
+name = "typing-extensions"
+version = "3.7.4.3"
+description = "Backported and Experimental Type Hints for Python 3.5+"
+category = "main"
+optional = false
+python-versions = "*"
+
+[[package]]
+name = "zipp"
+version = "3.4.1"
+description = "Backport of pathlib-compatible object wrapper for zip files"
+category = "main"
+optional = false
+python-versions = ">=3.6"
+
+[package.extras]
+docs = ["sphinx", "jaraco.packaging (>=8.2)", "rst.linker (>=1.9)"]
+testing = ["pytest (>=4.6)", "pytest-checkdocs (>=1.2.3)", "pytest-flake8", "pytest-cov", "pytest-enabler", "jaraco.itertools", "func-timeout", "pytest-black (>=0.3.7)", "pytest-mypy"]
+
+[metadata]
+lock-version = "1.1"
+python-versions = "^3.7"
+content-hash = "f990b445406f5bbce3e53cd28ef3362be09615b40062f11233a62f99bcd59a79"
+
+[metadata.files]
+colorama = [
+    {file = "colorama-0.4.4-py2.py3-none-any.whl", hash = "sha256:9f47eda37229f68eee03b24b9748937c7dc3868f906e8ba69fbcbdd3bc5dc3e2"},
+    {file = "colorama-0.4.4.tar.gz", hash = "sha256:5941b2b48a20143d2267e95b1c2a7603ce057ee39fd88e7329b0c292aa16869b"},
+]
+colour = [
+    {file = "colour-0.1.5-py2.py3-none-any.whl", hash = "sha256:33f6db9d564fadc16e59921a56999b79571160ce09916303d35346dddc17978c"},
+    {file = "colour-0.1.5.tar.gz", hash = "sha256:af20120fefd2afede8b001fbef2ea9da70ad7d49fafdb6489025dae8745c3aee"},
+]
+commonmark = [
+    {file = "commonmark-0.9.1-py2.py3-none-any.whl", hash = "sha256:da2f38c92590f83de410ba1a3cbceafbc74fee9def35f9251ba9a971d6d66fd9"},
+    {file = "commonmark-0.9.1.tar.gz", hash = "sha256:452f9dc859be7f06631ddcb328b6919c67984aca654e5fefb3914d54691aed60"},
+]
+decorator = [
+    {file = "decorator-4.4.2-py2.py3-none-any.whl", hash = "sha256:41fa54c2a0cc4ba648be4fd43cff00aedf5b9465c9bf18d64325bc225f08f760"},
+    {file = "decorator-4.4.2.tar.gz", hash = "sha256:e3a62f0520172440ca0dcc823749319382e377f37f140a0b99ef45fecb84bfe7"},
+]
+glcontext = [
+    {file = "glcontext-2.3.3-cp35-cp35m-macosx_10_9_x86_64.whl", hash = "sha256:f518379551a2b60d45c1eec23759cb1ee85517d4b943fc31530b6ab13e304fe4"},
+    {file = "glcontext-2.3.3-cp35-cp35m-manylinux1_i686.whl", hash = "sha256:d3a8fbc27f43766d168bae02474790459f4050adeb25832ff0a227cc5006c933"},
+    {file = "glcontext-2.3.3-cp35-cp35m-manylinux1_x86_64.whl", hash = "sha256:aa1d9e4f9bd6eda3d195f39c47c849b3721caf65813a4ad1e006a20fa02d33e4"},
+    {file = "glcontext-2.3.3-cp35-cp35m-win32.whl", hash = "sha256:8b4ee9cb5573e2ae313e1681fdfe2c5ac5b8780b20e857daf8f95e318c36aa2f"},
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diff --git a/vorlesungen/punktgruppen/pyproject.toml b/vorlesungen/punktgruppen/pyproject.toml
new file mode 100644
index 0000000..92c06e2
--- /dev/null
+++ b/vorlesungen/punktgruppen/pyproject.toml
@@ -0,0 +1,15 @@
+[tool.poetry]
+name = "presentation"
+version = "0.1.0"
+description = ""
+authors = ["Nao Pross <np@0hm.ch>"]
+
+[tool.poetry.dependencies]
+python = "^3.7"
+manim = "^0.5.0"
+
+[tool.poetry.dev-dependencies]
+
+[build-system]
+requires = ["poetry-core>=1.0.0"]
+build-backend = "poetry.core.masonry.api"
-- 
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