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-rw-r--r--vorlesungen/punktgruppen/crystals.py269
-rw-r--r--vorlesungen/punktgruppen/poetry.lock591
-rw-r--r--vorlesungen/punktgruppen/pyproject.toml15
3 files changed, 875 insertions, 0 deletions
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"
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+python-versions = ">=3.6"
+
+[[package]]
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+category = "main"
+optional = false
+python-versions = ">=3.6, <4"
+
+[[package]]
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+description = "Manipulate audio with an simple and easy high level interface"
+category = "main"
+optional = false
+python-versions = "*"
+
+[[package]]
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+[[package]]
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+optional = false
+python-versions = ">=3.5"
+
+[[package]]
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+category = "main"
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+
+[package.dependencies]
+multipledispatch = "*"
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+
+[[package]]
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+category = "main"
+optional = false
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+
+[package.dependencies]
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+
+[package.extras]
+jupyter = ["ipywidgets (>=7.5.1,<8.0.0)"]
+
+[[package]]
+name = "scipy"
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+description = "SciPy: Scientific Library for Python"
+category = "main"
+optional = false
+python-versions = ">=3.7"
+
+[package.dependencies]
+numpy = ">=1.16.5"
+
+[[package]]
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+description = "Python 2 and 3 compatibility utilities"
+category = "main"
+optional = false
+python-versions = ">=2.7, !=3.0.*, !=3.1.*, !=3.2.*"
+
+[[package]]
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+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]]
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+version = "3.4.1"
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+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"
+
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+ {file = "typing_extensions-3.7.4.3-py2-none-any.whl", hash = "sha256:dafc7639cde7f1b6e1acc0f457842a83e722ccca8eef5270af2d74792619a89f"},
+ {file = "typing_extensions-3.7.4.3-py3-none-any.whl", hash = "sha256:7cb407020f00f7bfc3cb3e7881628838e69d8f3fcab2f64742a5e76b2f841918"},
+ {file = "typing_extensions-3.7.4.3.tar.gz", hash = "sha256:99d4073b617d30288f569d3f13d2bd7548c3a7e4c8de87db09a9d29bb3a4a60c"},
+]
+zipp = [
+ {file = "zipp-3.4.1-py3-none-any.whl", hash = "sha256:51cb66cc54621609dd593d1787f286ee42a5c0adbb4b29abea5a63edc3e03098"},
+ {file = "zipp-3.4.1.tar.gz", hash = "sha256:3607921face881ba3e026887d8150cca609d517579abe052ac81fc5aeffdbd76"},
+]
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"
generated by cgit v1.2.1 (git 2.18.0) at 2024-11-21 23:31:50 +0100