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330 lines
11 KiB
330 lines
11 KiB
2 years ago
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{
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"cells": [
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{
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"cell_type": "markdown",
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"id": "36cee816",
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"metadata": {},
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"source": [
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"# Řešení 2. série"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"id": "efe16561",
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"metadata": {},
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"outputs": [],
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"source": [
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"from manim import *"
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]
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},
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{
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"cell_type": "markdown",
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"id": "36ec08cc",
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"metadata": {},
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"source": [
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"## Trojúhelník"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"id": "e7a3da39",
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"metadata": {},
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"outputs": [],
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"source": [
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"%%manim -v WARNING -qh Triangle\n",
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"\n",
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"from random import *\n",
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"\n",
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"\n",
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"class Triangle(Scene):\n",
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" def construct(self):\n",
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" seed(0xDEADBEEF)\n",
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"\n",
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" # vše trochu zvětšíme\n",
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" c = 2\n",
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"\n",
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" p1 = Dot().scale(c).shift(UP * c)\n",
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" p2 = Dot().scale(c).shift(DOWN * c + LEFT * c)\n",
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" p3 = Dot().scale(c).shift(DOWN * c + RIGHT * c)\n",
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"\n",
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" points = VGroup(p1, p2, p3)\n",
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" \n",
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" self.play(Write(points, lag_ratio=0.5), run_time=1.5)\n",
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"\n",
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" l1 = Line()\n",
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" l2 = Line()\n",
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" l3 = Line()\n",
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"\n",
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" lines = VGroup(l1, l2, l3)\n",
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"\n",
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" def create_line_updater(a, b):\n",
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" \"\"\"Vrátí funkci, která se chová jako updater nějaké úsečky.\"\"\"\n",
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" return lambda x: x.become(Line(start=a.get_center(), end=b.get_center()))\n",
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"\n",
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" l1.add_updater(create_line_updater(p1, p2))\n",
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" l2.add_updater(create_line_updater(p2, p3))\n",
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" l3.add_updater(create_line_updater(p3, p1))\n",
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"\n",
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" self.play(Write(lines, lag_ratio=0.5), run_time=1.5)\n",
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"\n",
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" x = Tex(\"x\")\n",
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" y = Tex(\"y\")\n",
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" z = Tex(\"z\")\n",
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"\n",
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" x.add_updater(lambda x: x.next_to(p1, UP))\n",
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" y.add_updater(lambda x: x.next_to(p2, DOWN + LEFT))\n",
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" z.add_updater(lambda x: x.next_to(p3, DOWN + RIGHT))\n",
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"\n",
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" labels = VGroup(x, y, z).scale(c * 0.8)\n",
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"\n",
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" self.play(FadeIn(labels, shift=UP * 0.2))\n",
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"\n",
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" circle = Circle()\n",
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" circle.add_updater(\n",
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" lambda c: c.become(\n",
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" Circle.from_three_points(\n",
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" p1.get_center(), p2.get_center(), p3.get_center()\n",
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" )\n",
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" )\n",
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" )\n",
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"\n",
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" self.play(Write(circle))\n",
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"\n",
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" self.play(\n",
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" p2.animate.shift(LEFT + UP),\n",
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" p1.animate.shift(RIGHT),\n",
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" )"
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]
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},
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{
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"cell_type": "markdown",
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"id": "171e8840",
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"metadata": {},
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"source": [
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"## Vlna"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"id": "252d64a3",
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"metadata": {},
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"outputs": [],
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"source": [
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"%%manim -v WARNING -qh Wave\n",
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"\n",
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"from random import *\n",
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"\n",
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"\n",
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"class Wave(Scene):\n",
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" def construct(self):\n",
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" seed(0xDEADBEEF)\n",
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"\n",
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" maze_string = \"\"\"\n",
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"#######################################################\n",
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"# ################# ## #\n",
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"# ################## #### #\n",
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"# ################# #### #\n",
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"# ############### ##### # ##\n",
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"# ######### ##### ####\n",
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"# ### ###### ######\n",
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"# ### ## ##### ### #####\n",
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"# #### ######## #### ##### ## #\n",
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"# ##### ########## ### ######## # #\n",
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"# ##### ########### ######## #\n",
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"# #### ########### ########## #\n",
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"# ## ########### ########## #\n",
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"# #### ############ ############# #\n",
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"# ###### ############ ############# #\n",
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"# ######### ## ########### ######### # #\n",
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"# ############### ######### ####### #\n",
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"# ############### ###### ###### #\n",
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"# ############### ##### #### #\n",
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"# ############# # ## #\n",
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"# # ####### ########### ####\n",
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"# ### # #################\n",
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"# ## #### #################\n",
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"##### ###### ##################\n",
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"###### ###### ##################\n",
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"# ### ### ####### ### ############### #\n",
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"# #### ############ #### ####### #\n",
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"# ##### ############ ### #\n",
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"# ### ########## #\n",
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"#######################################################\n",
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"\"\"\"\n",
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"\n",
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" maze = [] # 2D pole čtverců tak, jak ho vidíme\n",
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" maze_bool = [] # 2D pole True/False\n",
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" all_squares = VGroup()\n",
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"\n",
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" # parsujeme vstup, řádek po řádku\n",
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" for row in maze_string.strip().splitlines():\n",
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" maze.append([])\n",
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" maze_bool.append([])\n",
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"\n",
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" for char in row:\n",
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" square = Square(\n",
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" side_length=0.23,\n",
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" stroke_width=1,\n",
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" fill_color=WHITE if char == \"#\" else BLACK,\n",
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" fill_opacity=1,\n",
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" )\n",
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"\n",
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" maze[-1].append(square)\n",
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" maze_bool[-1].append(char == \" \")\n",
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" all_squares.add(square)\n",
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"\n",
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" # rozměry bludiště\n",
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" w = len(maze[0])\n",
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" h = len(maze)\n",
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"\n",
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" # rozmístění do gridu\n",
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" all_squares.arrange_in_grid(rows=h, buff=0)\n",
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"\n",
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" self.play(FadeIn(all_squares), run_time=2)\n",
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"\n",
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" # startovní pozice\n",
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" x, y = 1, 1\n",
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"\n",
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" colors = [\"#ef476f\", \"#ffd166\", \"#06d6a0\", \"#118ab2\"]\n",
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"\n",
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" # vytvoříme si slovník se vzdálenostmi od startu\n",
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" distances = {(x, y): 0}\n",
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" stack = [(x, y, 0)]\n",
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"\n",
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" while len(stack) != 0:\n",
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" x, y, d = stack.pop(0)\n",
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"\n",
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" for dx, dy in ((0, 1), (1, 0), (-1, 0), (0, -1)):\n",
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" nx, ny = dx + x, dy + y\n",
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"\n",
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" # není potřeba, jelikož vstup je ohraničený a nikde nevyběhneme :)\n",
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" #if nx < 0 or nx >= w or ny < 0 or ny >= h:\n",
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" # continue\n",
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"\n",
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" if maze_bool[ny][nx] and (nx, ny) not in distances:\n",
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" stack.append((nx, ny, d + 1))\n",
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" distances[(nx, ny)] = d + 1\n",
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"\n",
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" max_distance = max([d for d in distances.values()])\n",
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"\n",
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" all_colors = color_gradient(colors, max_distance + 1)\n",
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"\n",
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" # vytvoříme skupiny podle vzdálenosti od startu\n",
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" groups = []\n",
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" for d in range(max_distance + 1):\n",
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" groups.append(\n",
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" AnimationGroup(\n",
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" *[\n",
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" maze[y][x].animate.set_fill(all_colors[d])\n",
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" for x, y in distances\n",
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" if distances[x, y] == d\n",
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" ]\n",
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" )\n",
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" )\n",
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"\n",
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" self.play(AnimationGroup(*groups, lag_ratio=0.08))\n"
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]
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},
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{
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"cell_type": "markdown",
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"id": "e6f13b54",
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"metadata": {},
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"source": [
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"## Hilbert"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"id": "06ed2d5c",
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"metadata": {},
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"outputs": [],
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"source": [
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"%%manim -v WARNING -qh Hilbert\n",
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"\n",
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"\n",
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"class Path(VMobject):\n",
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" def __init__(self, points, *args, **kwargs):\n",
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" super().__init__(self, *args, **kwargs)\n",
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" self.set_points_as_corners(points)\n",
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"\n",
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" def get_important_points(self):\n",
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" \"\"\"Vrátí důležité body křivky.\"\"\"\n",
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" return list(self.get_start_anchors()) + [self.get_end_anchors()[-1]]\n",
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"\n",
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"\n",
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"class Hilbert(Scene):\n",
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" def construct(self):\n",
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" directions = [LEFT + DOWN, LEFT + UP, RIGHT + UP, RIGHT + DOWN]\n",
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"\n",
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" hilbert = Path(directions).scale(3)\n",
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"\n",
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" self.play(Write(hilbert, lag_ratio=0.5))\n",
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"\n",
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" for i in range(1, 4):\n",
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" # délka jedné úsečky\n",
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" new_segment_length = 1 / (2 ** (i + 1) - 1)\n",
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"\n",
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" # škálování částí křivky tak, aby byla vycentrovaná\n",
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" new_scale = (1 - new_segment_length) / 2\n",
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"\n",
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" # chceme si uchovat původní křivku, abychom pomocí ní vyrovnávali ostatní\n",
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" lu = hilbert.copy()\n",
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" lu, hilbert = hilbert, lu\n",
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"\n",
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" self.play(\n",
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" lu.animate.scale(new_scale)\n",
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" .set_color(DARK_GRAY)\n",
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" .align_to(hilbert, directions[1])\n",
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" )\n",
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"\n",
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" ru = lu.copy()\n",
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" self.play(ru.animate.align_to(hilbert, directions[2]))\n",
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"\n",
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" ld, rd = lu.copy(), ru.copy()\n",
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" self.play(\n",
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" ld.animate.align_to(hilbert, directions[0]).rotate(-PI / 2),\n",
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" rd.animate.align_to(hilbert, directions[3]).rotate(PI / 2),\n",
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" )\n",
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"\n",
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" new_hilbert = Path(\n",
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" list(ld.flip(LEFT).get_important_points())\n",
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" + list(lu.get_important_points())\n",
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" + list(ru.get_important_points())\n",
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" + list(rd.flip(LEFT).get_important_points())\n",
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" )\n",
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"\n",
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" self.play(Write(new_hilbert, run_time=2 ** i))\n",
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"\n",
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" self.remove(lu, ru, ld, rd)\n",
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"\n",
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" hilbert = new_hilbert"
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]
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}
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],
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"metadata": {
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"kernelspec": {
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"display_name": "Python 3 (ipykernel)",
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"language": "python",
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"name": "python3"
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},
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"language_info": {
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"codemirror_mode": {
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"name": "ipython",
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"version": 3
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},
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"file_extension": ".py",
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"mimetype": "text/x-python",
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"name": "python",
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"nbconvert_exporter": "python",
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"pygments_lexer": "ipython3",
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"version": "3.10.1"
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}
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},
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"nbformat": 4,
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"nbformat_minor": 5
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}
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