{
"cells": [
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [
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"data": {
"text/html": [
"Manim Community v0.18.0\n",
"\n",
"\n"
],
"text/plain": [
"Manim Community \u001b[32mv0.\u001b[0m\u001b[32m18.0\u001b[0m\n",
"\n"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"from manim import *\n",
"from manim_geometry import *\n",
"\n",
"config.media_embed = True\n",
"config.media_width = \"100%\"\n",
"_RV = \"-v WARNING -qm --progress_bar None --disable_caching\"\n",
"_RI = \"-v WARNING -s --progress_bar None --disable_caching\""
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Geos basics\n",
"\n",
"To start using ManimGeometry you have to instantiate the Geos class, and it receives the scene as a mandatory parameter.\n",
"\n",
"```py\n",
"class Example(Scene):\n",
" def construct(self):\n",
" geos = Geos(self)\n",
"```\n",
"\n",
"In addition to the scene you can receive these dictionaries:\n",
"\n",
"```py\n",
"DEFAULT_GEOS_STROKE_WIDTH = 3\n",
"DEFAULT_Z_INDEX_DOTS = 5\n",
"\n",
"class Geos:\n",
" DEFAULT_LINES_STYLE = {\n",
" \"stroke_width\": DEFAULT_GEOS_STROKE_WIDTH,\n",
" }\n",
" DEFAULT_CIRCLES_STYLE = {\n",
" \"stroke_width\": DEFAULT_GEOS_STROKE_WIDTH\n",
" }\n",
" DEFAULT_ARCS_STYLE = {\n",
" \"stroke_width\": DEFAULT_GEOS_STROKE_WIDTH\n",
" }\n",
" DEFAULT_DOTS_STYLE = {\n",
" \"stroke_width\": 0,\n",
" \"z_index\": DEFAULT_Z_INDEX_DOTS,\n",
" }\n",
" def __init__(self,\n",
" scene:Scene,\n",
" lines_style={},\n",
" dots_style={},\n",
" arcs_style={},\n",
" circles_style={},\n",
" ):\n",
" #........\n",
"```\n",
"\n",
"Dictionaries `lines_style`, `dots_style`, `arcs_style` and `circles_style` override the class variables you can see there.\n",
"\n",
".. note::\n",
" Example: `lines_style` override `DEFAULT_LINES_STYLE`.\n",
"\n",
"\n",
"Styles `DEFAULT_LINES_STYLE`, `DEFAULT_CIRCLES_STYLE`, `DEFAULT_ARCS_STYLE` and `DEFAULT_DOTS_STYLE` will apply to all objects created with this library, but can be changed individually.\n",
"\n",
"After defining geos you must use the `create_geos` method, here the construction process will be indicated, and it must have the following format:\n",
"\n",
"```py\n",
"geos = Geos(self)\n",
"geos.create_geos({\n",
" \"TN\": geos.some_method(),\n",
" #.....\n",
"})\n",
"```\n",
"\n",
"Where `T` is the type of object, it is important to respect the type since the library will use that information for some methods.\n",
"The `N` indicates a name, we give it that name, and it can have several letters, I recommend that they not be very long names, at most 3-4 letters.\n",
"\n",
"Example:\n",
"\n",
"```py\n",
"geos = Geos(self)\n",
"geos.create_geos({\n",
" \"dA\": geos.dot(...), # Dot with name A\n",
" \"dB\": geos.dot(...), # Dot with name B\n",
" \"lAB\": geos.line(\"dA\", \"dB\"), # Line from A to B\n",
"})\n",
"```\n",
"\n",
"In this example `dA` means that you are saving a Mobject of type `Dot`, and its name is `A`, the same for `dB`.\n",
"In the case of the line, it is not necessary to name it `AB`, it can be called anything, but it is important that it has the `l` or `b`at the beginning, that will be explained later.\n",
"\n",
"Once these elements are created, we can access them as an attribute:"
]
},
{
"cell_type": "code",
"execution_count": 27,
"metadata": {},
"outputs": [
{
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"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"class Example(Scene):\n",
" def construct(self):\n",
" geos = Geos(self)\n",
" geos.create_geos({\n",
" \"dA\": geos.dot(LEFT*2), # Dot with name A\n",
" \"dB\": geos.dot(RIGHT*2), # Dot with name B\n",
" \"lAB\": geos.line(\"dA\", \"dB\"), # Line from A to B\n",
" })\n",
" self.add(\n",
" geos.dA.set_color(RED),\n",
" geos.dB.set_color(GREEN),\n",
" geos.lAB.set_color(BLUE)\n",
" )\n",
"\n",
"%manim $_RV Example"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Here are all the types of objects, please use the recommended letter.\n",
"The differences between `l`, `b` and similar will be explained later.\n",
"\n",
"Object types:\n",
"```py\n",
"class _GeosTypes:\n",
" DOT = \"d\" # Dot\n",
" LINE = \"l\" # Line\n",
" BISECTOR = \"b\" # Same as line\n",
" CIRCLE = \"c\" # ICircle\n",
" ARC = \"a\" # Arc or IAngle\n",
" POINT = \"p\" # np.ndarray\n",
" VECTOR = \"v\" # np.ndarray\n",
" LABEL = \"_\" # MathTex or Tex\n",
" NUMBER = \"n\" # Int or Float\n",
" ANGLE = \"o\" # Int or Float\n",
" DISTANCE = \"x\" # Int or Float\n",
" MOBJECT = \"m\" # Any VMobject\n",
" VGROUP = \"g\" # Any VGroup\n",
" INTERSECTION = \"i\" # Dot\n",
"```\n",
"\n",
".. hint::\n",
" Most methods can receive a vector/object/string referencing previous values, with these examples you can learn how to use them.\n",
"\n",
"## Coordinates"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"class Example(Scene):\n",
" def construct(self):\n",
" self.add(NumberPlane().fade(0.7))\n",
"\n",
" geos = Geos(self)\n",
" init_geos = {\n",
" \"pA\": LEFT,\n",
" \"pB\": geos.shift(\"pA\", RIGHT), # LEFT + RIGHT = ORIGIN\n",
" \"pC\": geos.shift(RIGHT, DOWN), # RIGHT + DOWN\n",
" \"pD\": geos.shift(RIGHT, \"pC\"), # RIGHT + (RIGHT + DOWN)\n",
" }\n",
" geos.create_geos(init_geos)\n",
"\n",
" dA = Dot(geos.pA, color=RED)\n",
" dB = Dot(geos.pB, color=BLUE)\n",
" dC = Dot(geos.pC, color=GREEN)\n",
" dD = Dot(geos.pD, color=YELLOW)\n",
"\n",
" self.add(dA, dB, dC, dD)\n",
"\n",
"%manim $_RV Example"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Mobjects"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"class Example(Scene):\n",
" def construct(self):\n",
" self.add(NumberPlane().fade(0.7))\n",
"\n",
" geos = Geos(self)\n",
" init_geos = {\n",
" \"dA\": Dot(LEFT*2, color=RED),\n",
" \"mA\": Square(color=BLUE),\n",
" \"lA\": Line(LEFT, RIGHT, color=GREEN),\n",
" \"_A\": MathTex(\"A\"),\n",
" }\n",
" geos.create_geos(init_geos)\n",
"\n",
" self.add(geos.get_all_mobs_as_grp())\n",
"\n",
"\n",
"%manim $_RV Example"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Dots\n",
"\n",
"Points are intended to be used as coordinates, and vectors are used to obtain other coordinates, using the \"shift\" method."
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"class Example(Scene):\n",
" def construct(self):\n",
" self.add(NumberPlane().fade(0.7))\n",
"\n",
" geos = Geos(self)\n",
" init_geos = {\n",
" \"pA\": UR*2,\n",
" \"v1\": DOWN*2, # Vectors\n",
" \"pC\": geos.shift(\"pA\", \"v1\"),\n",
" \"dA\": geos.dot(\"pA\", color=RED),\n",
" \"dB\": geos.dot(UL*2, color=BLUE),\n",
" # You can use all Dot kwargs\n",
" \"dC\": geos.dot(\"pC\", color=YELLOW, radius=0.2),\n",
" }\n",
" geos.create_geos(init_geos)\n",
"\n",
" self.add(geos.get_all_mobs_as_grp())\n",
"\n",
"\n",
"%manim $_RV Example"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"class Example(Scene):\n",
" def construct(self):\n",
" self.add(NumberPlane().fade(0.7))\n",
"\n",
" geos = Geos(self)\n",
" init_geos = {\n",
" \"m1\": Line(DL*2, UR*2),\n",
" \"dStart\": geos.point_from_proportion(\"m1\", 0, color=PINK), # as Line.get_start()\n",
" \"dA\": geos.point_from_proportion(\"m1\", 0.2, color=RED),\n",
" # .pfp == .point_from_proportion\n",
" \"dB\": geos.pfp(\"m1\", 0.5, color=GREEN),\n",
" \"dC\": geos.pfp(\"m1\", 0.9, color=BLUE),\n",
" \"dEnd\": geos.pfp(\"m1\", 1, color=YELLOW), # as Line.get_end()\n",
" }\n",
" geos.create_geos(init_geos)\n",
"\n",
" self.add(geos.get_all_mobs_as_grp())\n",
"\n",
"\n",
"%manim $_RV Example"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
".. note::\n",
" Most methods have a shorthand so you don't have to write so many parameters, instead of using something like `geos.some_method(\"A\", \"B\")` you can use `geos.some_method(\"A,B\")`."
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"class Example(Scene):\n",
" def construct(self):\n",
" self.add(NumberPlane().fade(0.7))\n",
"\n",
" geos = Geos(self)\n",
" init_geos = {\n",
" \"dA\": geos.dot(UP*3+LEFT*3, color=RED),\n",
" \"dB\": geos.dot(DOWN*2+LEFT*2, color=BLUE),\n",
" \"dC\": geos.dot(UR*2, color=GREEN),\n",
" \"dD\": geos.parallel_dot(\"dC\", \"dA,dB\", color=YELLOW),\n",
" \"pE\": UR*3.5,\n",
" \"dF\": geos.parallel_dot(\"pE\", \"dA,dB\", color=PINK),\n",
" }\n",
" geos.create_geos(init_geos)\n",
"\n",
" self.add(geos.get_all_mobs_as_grp())\n",
" self.add(\n",
" Arrow(geos.dA, geos.dB, buff=0),\n",
" Arrow(geos.dC, geos.dD, buff=0),\n",
" Arrow(geos.pE, geos.dF, buff=0),\n",
" )\n",
"\n",
"%manim $_RV Example"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Dot from method"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"class Example(Scene):\n",
" def construct(self):\n",
" self.add(NumberPlane().fade(0.7))\n",
"\n",
" geos = Geos(self)\n",
" init_geos = {\n",
" \"m1\": Square().scale(2),\n",
" \"d1\": geos.dot_from_method(lambda n: n(\"m1\").get_corner(UR), color=RED)\n",
" }\n",
" geos.create_geos(init_geos)\n",
"\n",
" self.add(geos.get_all_mobs_as_grp())\n",
"\n",
"\n",
"%manim $_RV Example"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Labels"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"class Example(Scene):\n",
" def construct(self):\n",
" self.add(NumberPlane().fade(0.7))\n",
"\n",
" geos = Geos(self)\n",
" init_geos = {\n",
" \"pA\": UR*2,\n",
" \"v1\": DOWN*2,\n",
" \"pC\": geos.shift(\"pA\", \"v1\"),\n",
" \"dA\": geos.dot(\"pA\", color=RED),\n",
" \"dB\": geos.dot(UL*2, color=BLUE),\n",
" \"dC\": geos.dot(\"pC\", color=YELLOW, radius=0.2),\n",
" \"_A\": geos.label(\"pA\", \"A\"), # Can receive coords\n",
" \"_B\": geos.label(\"dB\", \"B\", direction=LEFT, color=ORANGE), # Can receive dots\n",
" \"_C\": geos.label(\"dC\", MathTex(\"C\", color=RED), buff=0.5),\n",
" }\n",
" geos.create_geos(init_geos)\n",
"\n",
" self.add(geos.get_all_mobs_as_grp())\n",
"\n",
"\n",
"%manim $_RV Example"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"class Example(Scene):\n",
" def construct(self):\n",
" self.add(NumberPlane().fade(0.7))\n",
"\n",
" geos = Geos(self)\n",
" init_geos = {\n",
" \"pA\": UR*2,\n",
" \"v1\": DOWN*2, # <-- Ignored\n",
" \"pX\": DOWN*5, # <-- Ignored\n",
" \"pC\": geos.shift(\"pA\", \"v1\"),\n",
" \"dA\": geos.dot(\"pA\", color=RED),\n",
" \"dB\": geos.dot(UL*2, color=BLUE),\n",
" \"dC\": geos.dot(\"pC\", color=YELLOW, radius=0.2),\n",
" }\n",
" # Labels will only be applied to Dots (Mobjects), \n",
" # not to points or vectors (np.ndarrays).\n",
" geos.create_geos(\n",
" init_geos,\n",
" set_all_labels=True, # <-- Create all labels automatically\n",
" label_direction=LEFT,\n",
" label_buff=0.1,\n",
" label_kwargs={\"font_size\":100, \"color\": ORANGE}\n",
" ) \n",
"\n",
" self.add(geos.get_all_mobs_as_grp())\n",
"\n",
"\n",
"%manim $_RV Example"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"class Example(Scene):\n",
" def construct(self):\n",
" self.add(NumberPlane().fade(0.7))\n",
"\n",
" geos = Geos(self)\n",
" init_geos = {\n",
" \"pA\": UR*2,\n",
" \"v1\": DOWN*2, \n",
" \"pX\": DOWN*5, \n",
" \"pC\": geos.shift(\"pA\", \"v1\"),\n",
" \"dA\": geos.dot(\"pA\", color=RED),\n",
" \"dB\": geos.dot(UL*2, color=BLUE),\n",
" \"dC\": geos.dot(\"pC\", color=YELLOW, radius=0.2),\n",
" \"dD\": geos.dot(DOWN*2, color=ORANGE, radius=0.2),\n",
" }\n",
" geos.create_geos(init_geos) \n",
" geos.set_labels([\n",
" (\"dA\", \"X\"),\n",
" (\"dB\", \"Y\"),\n",
" (\"dC\", \"P_1\"),\n",
" ])\n",
"\n",
" geos._A.set_color(RED)\n",
" self.add(geos.get_all_mobs_as_grp())\n",
"\n",
"\n",
"%manim $_RV Example"
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"class Example(Scene):\n",
" def construct(self):\n",
" self.add(NumberPlane().fade(0.7))\n",
"\n",
" geos = Geos(self)\n",
" init_geos = {\n",
" \"pA\": UR*2,\n",
" \"v1\": DOWN*2, \n",
" \"pX\": DOWN*5, \n",
" \"pC\": geos.shift(\"pA\", \"v1\"),\n",
" \"dA\": geos.dot(\"pA\", color=RED),\n",
" \"dB\": geos.dot(UL*2, color=BLUE),\n",
" \"dC\": geos.dot(\"pC\", color=YELLOW, radius=0.2),\n",
" \"dD\": geos.dot(DOWN*2, color=ORANGE, radius=0.2),\n",
" }\n",
" geos.create_geos(init_geos) \n",
" geos.set_labels([\"dA,X\", \"dB,Y\", \"dD,P_2\"])\n",
"\n",
" geos._A.set_color(RED)\n",
" self.add(geos.get_all_mobs_as_grp())\n",
"\n",
"\n",
"%manim $_RV Example"
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"class Example(Scene):\n",
" def construct(self):\n",
" self.add(NumberPlane().fade(0.7))\n",
"\n",
" geos = Geos(self)\n",
" init_geos = {\n",
" \"pA\": UR*2,\n",
" \"v1\": DOWN*2, \n",
" \"pX\": DOWN*5, \n",
" \"pC\": geos.shift(\"pA\", \"v1\"),\n",
" \"dA\": geos.dot(\"pA\", color=RED),\n",
" \"dB\": geos.dot(UL*2, color=BLUE),\n",
" \"dC\": geos.dot(\"pC\", color=YELLOW, radius=0.2),\n",
" \"dD\": geos.dot(DOWN*2, color=ORANGE, radius=0.2),\n",
" }\n",
" geos.create_geos(init_geos) \n",
" geos.set_auto_labels_dots(\"dA,dB,dC\", direction=LEFT, buff=0)\n",
"\n",
" geos._A.set_color(RED)\n",
" geos._B.set_color(PINK)\n",
" self.add(geos.get_all_mobs_as_grp())\n",
"\n",
"\n",
"%manim $_RV Example"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Lines"
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"class Example(Scene):\n",
" def construct(self):\n",
" self.add(NumberPlane().fade(0.7))\n",
"\n",
" geos = Geos(self)\n",
" init_geos = {\n",
" \"pA\": UR*3,\n",
" \"dB\": geos.dot(DOWN*3, color=RED),\n",
" \"dC\": geos.dot(LEFT*3+UP*2, color=BLUE),\n",
" \"lAB\": geos.line(\"pA\", \"dB\", color=GREEN),\n",
" \"lAC\": geos.segment(\"pA,dC\", color=PURPLE),\n",
" \"lBC\": geos.segment(\"dB,dC\", color=YELLOW),\n",
" }\n",
" geos.create_geos(init_geos)\n",
"\n",
" self.add(geos.get_all_mobs_as_grp())\n",
"\n",
"%manim $_RV Example"
]
},
{
"cell_type": "code",
"execution_count": 14,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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A0JwtX748rr/++jjqqKPiS1/6UgwZMiRmzJgRERFt2rSJY489tsQTAuTXpUuXuq//8Ic/lHASANg6CYAA0ABdunSJn/70p3Haaadt8PZnnnkm/umf/imefPLJiIjo1KlTkeMBtEhr1qyp+/q1114r4SQAsHXyEmAAqKeKior4/e9/H1/5ylci4pOXAP/nf/7nesfV1tbGU089FV/72td8EAhAAd544426r1euXFmv+1RVVUX//v3jmWeeaaqxAGCr4QpAAKinvn371sW/v/zlL7FkyZKNHrvbbrvF6tWr46677ipqPIAW65FHHqn7+tMvB96YVq1axZ133hn77rtvU44FAFsNARCAFquqqqru68rKyk0ev2rVqvj4449j2rRpMWLEiFi2bNkGj9tzzz1jxIgR8dOf/jSWLl3aaPMCtBR/e36uz3NzRMSLL74Yc+bMiYiIESNGfO6xHTt2jAceeCAWLlwY11577ZYNCgDNhAAIQIvQqlWr6NChQ3Tr1i369u0bxx9/fBx22GF1t1944YWx9957R69evaJjx47Rvn379X7Gm2++GbNmzYo333xzoy8ZGzx4cMycOTN++9vfxhVXXNFkvw9AFm3atIkOHTrEzjvvHP3794/x48dHnz59IiKidevWceWVV8aAAQOiZ8+e0aFDh2jbtu0Gf86pp54af/7zn2Ps2LHRsWPH9W6vrKyMk08+OZ588sm4995747zzzova2tom/d0AYGvhPQABaBFGjhwZDzzwwEZvHzNmTIwZM6bu++effz4GDhy43nHf+c53YvLkybFo0aK45557YtGiRVFWVhZdu3aNAw88MHr27BkTJkyI22+/3X9YAtTDuHHj4tJLL93o7RMmTIgJEybUfX/jjTfGSSedtN5xr732Wuy///5x8803xzPPPBPXX399LFmyJLp16xZDhgyJvfbaK+6///446KCD4r//+7+b5HcBgK2VAAhAizB79uz44he/GBERy5cvj+rq6g0e1759+9hmm23i448/3uDtK1asiJNPPjk6deoUQ4YMiZ133jkqKyvjnXfeiQkTJsSCBQua7HcAyOjnP/95XHfddRHxyfur1tTUbPC4Dh06RMRnP/H37y1atCiGDBkSgwcPjsGDB0f37t1j6dKlcfXVV8ezzz670ed2AMhOAASgRaiurt7oe/Z92ocfflivn7d06dKYOXPmlo4F0OKtXr06Vq9evcnj6vMcHvHJJ7HPnz8/5s+fv6WjAUAa3gMQAAAAABITAAEAAAAgMQEQAAAAABITAAEAAAAgMQEQAAAAABITAAEAAAAgMQEQAAAAABITAAEAAAAgMQEQAAAAABITAAEAAAAgMQEQAAAAABITAAEAAAAgMQEQAAAAABITAAEAAAAgMQEQAAAAABITAAEAAAAgMQEQAAAAABITAAEAAAAgMQEQAAAAABITAAEAAAAgMQEQAAAAABITAAEAAAAgMQEQAAAAABITAAEAAAAgMQEQAAAAABITAAEAAAAgMQEQAAAAABITAAEAAAAgMQEQAAAAABITAAEAAAAgMQEQAAAAABITAAEAAAAgMQEQAAAAABITAAEAAAAgMQEQAAAAABITAAEAAAAgMQEQAAAAABKraNt/0CYPquzRNyIiamtqmnqeFs2ei2HPxbDnYthzMey5GPZcjFadd4qIiPqcA7L5PJ6LYc/FsOdi2HMx7LkY9lyMhuzZFYAAAAAAkFjFyoXPbvKgsvJPOmF9jmXz2XMx7LkY9lwMey6GPRfDnotRve/eEWHPTc3juRj2XAx7LoY9F8Oei2HPxWjInl0BCAAAAACJCYAAAAAAkJgACAAAAACJCYAAAAAAkJgACAAAAACJCYAAAAAAkJgACAAAAACJCYAAAAAAkJgACAAAAACJCYAAAAAAkJgACAAAAACJCYAAAAAAkJgACAAAAACJCYAAAAAAkJgACAAAAACJCYAAAAAAkJgACAAAAACJCYAAAAAAkJgACAAAAACJCYAAAAAAkJgACAAAAACJCYAAAAAAkJgACAAAAACJCYAAAAAAkJgACAAAAACJCYAAAAAAkJgACAAAAACJCYAAAAAAkJgACAAAAACJCYAAAAAAkJgACAAAAACJCYAAAAAAkJgACAAAAACJCYAAAAAAkJgACAAAAACJCYAAAAAAkJgACAAAAACJCYAAAAAAkJgACAAAAACJCYAAAAAAkJgACAAAAACJCYAAAAAAkJgACAAAAACJCYAAAAAAkJgACAAAAACJCYAAAAAAkJgACAAAAACJCYAAAAAAkJgACAAAAACJCYAAAAAAkJgACAAAAACJCYAAAAAAkJgACAAAAACJCYAAAAAAkJgACAAAAACJCYAAAAAAkJgACAAAAACJCYAAAAAAkJgACAAAAACJCYAAAAAAkJgACAAAAACJCYAAAAAAkJgACAAAAACJCYAAAAAAkJgACAAAAACJCYAAAAAAkJgACAAAAACJCYAAAAAAkJgACAAAAACJCYAAAAAAkJgACAAAAACJCYAAAAAAkJgACAAAAACJCYAAAAAAkJgACAAAAACJCYAAAAAAkJgACAAAAACJCYAAAAAAkJgACAAAAACJCYAAAAAAkJgACAAAAACJCYAAAAAAkJgACAAAAACJCYAAAAAAkJgACAAAAACJCYAAAAAAkJgACAAAAACJlR120r/Ubuqg1l3+ISIi1r77dpMP1JLZczHsuRj2XAx7LoY9F8OeizF4v69HRMQz//ZEiSfJzeO5GPZcDHsuhj0Xw56LYc/FaMieXQEIAAAAAIlVzPrN/9vkQe0GDImIiBUL5jf1PC2aPRfDnothz8Ww52LYczHsuRjbbLNNRETU5xyQzefxXAx7LoY9F8Oei2HPxbDnYjRkz64ABAAAAIDEBEAAAAAASEwABAAAAIDEBEAAAAAASEwABAAAAIDEBEAAAAAASEwABAAAAIDEBEAAAAAASEwABAAAAIDEBEAAAAAASEwABAAAAIDEBEAAAAAASEwABAAAAIDEBEAAAAAASEwABAAAAIDEBEAAAAAASEwABAAAAIDEBEAAAAAASEwABAAAAIDEBEAAAAAASEwABAAAAIDEBEAAAAAASEwABAAAAIDEBEAAAAAASEwABAAAAIDEBEAAAAAASEwABAAAAIDEBEAAAAAASEwABAAAAIDEBEAAAAAASEwABAAAAIDEBEAAAAAASEwABAAAAIDEBEAAAAAASEwABAAAAIDEBEAAAAAASEwABAAAAIDEBEAAAAAASEwABAAAAIDEBEAAAAAASEwABAAAAIDEBEAAAAAASEwABAAAAIDEBEAAAAAASEwABAAAAIDEBEAAAAAASEwABAAAAIDEBEAAAAAASEwABAAAAIDEBEAAAAAASEwABAAAAIDEBEAAAAAASEwABAAAAIDEBEAAAAAASEwABAAAAIDEBEAAAAAASEwABAAAAIDEBEAAAAAASEwABAAAAIDEBEAAAAAASEwABAAAAIDEBEAAAAAASEwABAAAAIDEBEAAAAAASEwABAAAAIDEBEAAAAAASEwABAAAAIDEBEAAAAAASEwABAAAAIDEBEAAAAAASEwABAAAAIDEBEAAAAAASEwABAAAAIDEBEAAAAAASEwABAAAAIDEBEAAAAAASEwABAAAAIDEBEAAAAAASEwABAAAAIDEBEAAAAAASEwABAAAAIDEBEAAAAAASEwABAAAAIDEBEAAAAAASEwABAAAAIDEBEAAAAAASEwABAAAAIDEKtr2H7TJgyp79I2IiNqamqaep0Wz52LYczHsuRj2XAx7LoY9F6NV550iIqI+54BsPo/nYthzMey5GPZcDHsuhj0XoyF7dgUgAAAAACRWsXLhs5s8qKz8k05Yn2PZfPZcDHsuhj0Xw56LYc/FsOdiVO+7d0TYc1PzeC6GPRfDnothz8Ww52LYczEasmdXAAIAAABAYgIgAAAAACQmAAIAAABAYgIgAAAAACQmAAIAAABAYgIgAAAAACQmAAIAAABAYgIgAAAAACQmAAIAAABAYgIgAAAAACQmAAIAAABAYgIgAAAAACQmAAIAAABAYgIgAAAAACQmAAIAAABAYgIgAAAAACQmAAIAAABAYgIgAAAAACQmAAIAAABAYgIgAAAAACQmAAIAAABAYgIgAAAAACQmAAIAAABAYgIgAAAAACQmAAIAAABAYgIgAAAAACQmAAIAAABAYgIgAAAAACQmAAIAAABAYgIgAAAAACQmAAIAAABAYgIgAAAAACQmAAIAAABAYgIgAAAAACQmAAIAAABAYgIgAAAAACQmAAIAAABAYgIgAAAAACQmAAIAAABAYgIgAAAAACQmAAIAAABAYgIgAAAAACQmAAIAAABAYgIgAAAAACQmAAIAAABAYgIgAAAAACQmAAIAAABAYgIgAAAAACQmAAIAAABAYgIgAAAAACQmAAIAAABAYgIgAAAAACQmAAIAAABAYgIgAAAAACQmAAIAAABAYgIgAAAAACQmAAIAAABAYgIgAAAAACQmAAIAAABAYgIgAAAAACQmAAIAAABAYgIgAAAAACQmAAIAAABAYgIgAAAAACQmAAIAAABAYgIgAAAAACQmAAIAAABAYgIgAAAAACQmAAIAAABAYgIgAAAAACQmAAIAAABAYgIgAAAAACQmAAIAAABAYgIgAAAAACQmAAIAAABAYgIgAAAAACQmAAIAAABAYgIgAAAAACQmAAIAAABAYgIgAAAAACQmAAI0U1VVVdG3Z4/o27NHVFVVlXocACAh5xsAOQiAAM3M8OHDY/bs2fHBBx/E8/dNj+fvmx4ffPBBzJo1K4YNG1bq8QCABJxvAOQiAAI0ExUVFTFlypSYM2dOjBgxIlq3bl13W+vWrWPkyJExd+7cuPbaa6OioqKEkwIAzZXzDYCcPGMDNBPXXHNNnHbaaZs8buzYsRERccYZZzT1SABAMs43AHJyBSBAM7D//vvX62T8b8aOHRsHHnhgE04EAGTjfAMgLwEQoBn48Y9/3OD7jB8/vgkmAQCycr4BkJeXAANs5dq2bRvDhw9v8P0OOuTQOGLqzFjz8cdNMFXLUl7VLiIialatKPEkudlzMap26BQREYcOPaTEk+Tm8VwMe248lRXbxEGHNPx5Yfjw4VFVVRWrVq1qgqkAaCwVbfsP2uRBlT36RkREbU1NU8/TotlzMey5GPbcePr02Pkzb8BdX622KY/euw+Id1dVN8FUQHP3xY6dSj0CsBXpWtUqKsob/gKxysrK6HvgYbF4yR+bYKqWxflzMey5GPZcjIbs2UuAAbZ2tbWbf9dGHAMAyGtLzhlqnXEAbPUqVi58dpMHlf31b4Lqcyybz56LYc/FsOfGs/iNRbF27doGXwVY/XFNvP7iAi8BbgReYlYMey7G9n99CfBf/rS0xJPk5vFcDHtuPCsqtol1e+7U4KsA16xZE4vnzPYS4Ebg/LkY9lwMey5GQ/bsPQABtnIrV66MOXPmxMiRIxt0v0d/96/x4P83uommalnaDRgSERErFswv8SS52XMxRn/v9IiI+N0NvyzxJLl5PBfDnhvXo51mNfh8Y86cOeIfQDPgJcAAzcDll1/e4PtcddVVTTAJAJCV8w2AvARAgGbgiSeeiClTptT7+MmTJ8fcuXObcCIAIBvnGwB5CYAAzcQ555xTr5Pya6+9NsaNG1fARABANs43AHISAAGaiXXr1sUZZ5wRw4cPj9mzZ8eaNWvqbluzZk3MmjUrDjjggDjzzDNj3bp1JZwUAGiunG8A5ORDQACamXnz5sW8efOiTZs28eVDj4iIiJd/92CsXr26xJMBAFk43wDIRQAEaKZWr14di99aUvc1AEBjc74BkIOXAAMAAABAYgIgAAAAACQmAAIAAABAYgIgAAAAACQmAAIAAABAYgIgAAAAACQmAAIAAABAYgIgAAAAACQmAAIAAABAYgIgAAAAACQmAAIAAABAYgIgAAAAACQmAAIAAABAYgIgAAAAACQmAAIAAABAYgIgAAAAACRWUeoBAPg/HTt2jKOPPjqGDRsWXbp0idWrV8eSJUviscceixkzZsRHH31U6hEBgGauZ8+eccwxx8TQoUOjU6dOsWzZsnjjjTfi0UcfjZkzZ0Z1dXWpRwSgkbkCEGArceKJJ8bixYvj8MMPj+eeey5uvvnmeO655+LQQw+NqVOnxpIlS+LMM8+MsrKyUo8KADRD5eXlcdlll8WLL74Y/fr1i8ceeyxuvvnmeOutt+LYY4+NGTNmxOLFi+PII48s9agANDJXAAJsBcaPHx/jxo2L0aNHx1NPPfWZ2y6++OK46aab4lvf+lZcc801MXDgwPjud78btbW1JZoWAGhuysrK4uabb44BAwbEHnvsEa+//vpnbr/00kvj/vvvj0GDBsV9990XEyZMiJ///OclmhaAxuYKQIAS23fffePCCy+Mgw8+eL34FxGxYsWKOO644+KFF16IiIjjjz8+xo0bV/SYAEAzdsopp8R+++0XBx988HrxLyLinXfeidGjR8eyZcuirKwsfvazn8Whhx5agkkBaAoCIECJXXTRRfGrX/0qXnzxxY0es3bt2rj44ovrvp84cWJ06NChiPEAgGauoqIiLrroorjgggvif//3fzd63P/8z//EtddeGxGfXDE4adKkokYEoIkJgAAl1KFDhxg+fHiMGTMmpk+fHh07dtzosQ899FCsXr06IiK22267OOKII4oaEwBoxvbZZ5/o0qVLTJw4MSZPnhwVFRt/J6h77rmn7uv+/fvHgAEDihgRgCYmAAKU0C677BIVFRXRrVu3GDNmTPzwhz/c6LFr166NV155pe77r371q0WMCAA0c7vuumtERPTp0yfOOOOM+Pa3v73RYxctWhQff/xx3ffONwByEAABSuhvV/T9TZs2bT73+I8++qju68+7WhAA4G8acr7x8ccfx8qVK+u+d74BkINPAQYooYULF8Yvf/nL+P73vx+LFy+Oa6655nOP//RJ+Pvvv1/vf84OO+wQ++yzT3Tq1Ck+/PDDeOWVV2LBggWbOzYA0IzMmDEjjj766Bg1alT8/ve/jzvvvHOjx1ZWVsa2225b931Dzje233772GeffaJr167x0UcfxYIFCz7z6gUASscVgAAlNnbs2GjXrl3069cv3njjjY0et/3220ffvn3rvn/66ac3+bO7du0ad9xxRzz99NNxwAEHRJs2baJ79+5xySWXxLx586Jnz56N8jsAAFuvlStXxuGHHx6VlZVx8MEHf+YVBX9v0KBBUVZWVvd9fc439t5773jwwQfjrbfeimOPPTa+8IUvxK677hp333133HrrrdG6detG+T0A2HyuAATYCqxdu3aTxxxzzDGxzTbbRETEn//855g5c2ZEz69s9Pidd945nnjiifj3f//36NevX6xZs6butkmTJsXo0aPjwQcfjD333DPWrVu35b8EALBVq8/5xvHHH1/39X/8x3/ESy+9FO0GDNngsVVVVTF58uQ45ZRT4uGHH45+/frFu+++W3f7lVdeGY8//nhceOGFcf7552/5LwDAZnMFIEAzccopp9R9ff7553/u395HREydOjXatGkT3/ve9z4T/yIiOnfuHKeeemr07ds39txzz6YYFwBoZrbbbrs45phjIuKT9wI899xzN3ps+/bt47HHHotTTjkl7rnnnjjiiCM+E/8iIqqrq2PatGkxatSoJp0bgE0TAAGagWOPPbbuU/imT58eN9xww+cev9dee8WwYcPi3/7t3+Ivf/nLerePHz8+Ro8eHRUVFbF06dImmRkAaF4mTpwY2223Xd3XTz311AaPq6ioiPvvvz8GDx4cb7/9dnz3u9+NmpqaDR7buXPn+PDDD5tsZgDqRwAE2Mp16NAhJk2aFBERDz30UJxwwglRW1v7ufcZOnRoRETssssuUV6+/lP9448/HgsXLowf/ehH8cc//rHxhwYAmpUBAwbE2WefHRERV111VVxxxRUbPfYHP/hBDBs2LCIiLrzwwlixYsUGj+vYsWP88z//c9x0002NPi8ADSMAAmzFysvL47e//W107tw55s6dG9/61rfq9f49bdu2jYhPTubvvffeGDZsWFRWVtbd/sADD8Tuu+8eP/vZz5psdgCgedhuu+3i9ttvj4qKirjxxhvjhz/84UaP3XbbbeOSSy6JiIjly5fHHXfcsd4x5eXlMWLEiHjqqadizpw5MXXq1KYaHYB68iEgAFuxiy66KEaPHh0PPfRQjBkzJlatWlWv+z366KNRU1MT5eXlceSRR8aRRx4Zq1atiqeffjoeffTR+NWvfhV/+tOfmnh6AGBrV15eHrfcckv069cvrr766hg3btznvtLgiCOOiO233z4iIpYsWVL3oSFlZWXRo0eP6NevX+y5557x9ttvx6WXXhq33nprIb8HAJ/PFYAAW6njjjsufvKTn8Qtt9wS//iP/xgrV66s931feOGFOPfccz/z6b5VVVUxbNiwuOyyy2LBggXRv3//phgbAGhGJk2aFEceeWRcfPHFce65527ybUaOOOKIuq//8Ic/RIcOHWLbbbeN2traeP755+OKK66IAQMGxH777RfTpk3b5M8DoBiuAATYCh1++OFx0003xZQpU+Kss87arJPna665JmbMmBEnnnhiDB8+PAYOHBjt2rWLiIguXbrE9OnTY8CAAfHxxx839vgAQDPwox/9KE4//fQ45ZRT4je/+U297tOzZ8+6r6+88spYuHBhU40HQCNyBSDAVmbo0KExffr0mDBhQpx55pkbjH89evSIAw44YJM/649//GNcdNFFccABB0SHDh3iG9/4Rt2Jer9+/WLfffdt9PkBgK3fCSecEBMnToyjjjpqo/Fv0KBB671i4Etf+lJERKxatSpefvnlJp8TgMYhAAJsRXr37h33339/nHfeefGLX/xio8d985vfjAMPPHC9P997771j0qRJccghh6x3W3V1ddx///1x0EEH1b2cuFOnTo03PADQLBx00EExefLkOOqoo+Lhhx/e6HFnnnlm9OnT5zN/9rcPI3vrrbc+81YjAGzdBECArUSXLl1i9uzZcf7558eUKVM+99iBAweu97fuu+66a8ybNy/OOeecmDZt2kbvu3Tp0nj11VcjIrxsBwBamEGDBsUtt9wSRx11VDz66KOfe+yGzjfeeOONiIh6fzBZRESvXr1ip512aviwADQaARBgK9C+fft48MEH46KLLtrke/C0bds2Ro0aFYsWLfrMn48YMSIqKysjIuLFF1/c6P0rKyujd+/e8fTTT8crr7yy5cMDAM1C796947bbbotvfvOb8fjjj3/usbvttlv07t07Xnvttc/8+SOPPBIR//dS4E3p3r17/Ou//mt07Nhx84YGoFH4EBCAEmvdunXce++90adPnzjrrLPirLPO2uix7du3j27dukVlZWW8+uqrUd5n97rbVq9eHe+9917ceeedccUVV2z0Z5x22mlRVVUV55xzTmP+GgDAVqxz584xe/bs2HbbbTf5SoOOHTvGTjvtFK+99lpUV1dH60/dNnXq1Jg4cWJ07do1dt9998/9S8evfvWrccstt8TZZ58dCxYsaKTfBIDNIQAClFBZWVlMnTq17v38Bg4cWK/7vf7667Fq1apo96k/u/vuu+O8886Lhx9+ON57770N/rNOPPHEuOyyy+Lkk0+Op556qjF+BQBgK9e2bdt46KGHYpdddomIT2Jgffz9qw0iIt5///34l3/5l7j11lvjwgsvjDFjxkRNTc1njtlxxx1j3LhxMWrUqDjppJPi6aef3vJfAoAtIgAClNBee+0VRx99dIPv99JLL633Z++//36MGDEifvOb38R5550Xs2bNijfffDPatWsXvXv3jlGjRsUHH3wQX//61+O5555rjPEBgGbg6KOPrvdfMn7ahs43IiLuuOOOqK6ujuuuuy7mzJkTt99+eyxfvjz69OkT++yzT3Tt2jVuuOGGGDx4cKxevXpLxwegEQiAACX0wgsvxBe/+MUG32/NmjUb/PNXX301vv71r8eXv/zl2G233aJ79+6xbt26eP755+O6666Ld955Z0tHBgCamWnTpsWMGTMafL+VK1du9LZ77rknZs6cGQcffHD06dMnqqqq4pVXXolp06at976BAJSeAAhQQuvWrYtly5Y1+s99+eWX1/vUPgCgZVqzZs1G//JwS3/uQw891Og/F4DG51OAAQAAACAxARAAAAAAEhMAAQAAACAxARAAAAAAEhMAAQAAACAxARAAAAAAEhMAAQAAACAxARAAAAAAEhMAAQAAACAxARAAAAAAEhMAAQAAACAxARAAAAAAEhMAAQAAACAxARAAAAAAEhMAAQAAACAxARAAAAAAEhMAAQAAACAxARAAAAAAEhMAAQAAACAxARAAAAAAEhMAAQAAACAxARAAAAAAEhMAAQAAACAxARAAAAAAEhMAAQAAACAxARAAAAAAEhMAAQAAACAxARAAAAAAEhMAAQAAACAxARAAAAAAEhMAAQAAACAxARAAAAAAEhMAAQAAACAxARAAAAAAEhMAAQAAACAxARAAAAAAEhMAAQAAACCxirb9B23yoMoefSMiorampqnnadHsuRj2XAx7LoY9F8Oei2HPxWjVeaeIiKjPOSCbz+O5GPZcDHsuhj0Xw56LYc/FaMieXQEIAAAAAIlVrFz47CYPKiv/pBPW51g2nz0Xw56LYc/FsOdi2HMx7LkY1fvuHRH23NQ8nothz8Ww52LYczHsuRj2XIyG7NkVgAAAAACQmAAIAAAAAIkJgAAAAACQmAAIAAAAAIkJgAAAAACQmAAIAAAAAIkJgAAAAACQmAAIAAAAAIkJgAAAAACQmAAIAAAAAIkJgAAAAACQmAAIAAAAAIkJgAAAAACQmAAIAAAAAIkJgAAAAACQmAAIAAAAAIkJgAAAAACQmAAIAAAAAIkJgAAAAACQmAAIAAAAAIkJgAAAAACQmAAIAAAAAIkJgAAAAACQmAAIAAAAAIkJgAAAAACQmAAIAAAAAIkJgAAAAACQmAAIAAAAAIkJgAAAAACQmAAIAAAAAIkJgAAAAACQmAAIAAAAAIkJgAAAAACQmAAIAAAAAIkJgAAAAACQmAAIAAAAAIkJgAAAAACQmAAIAAAAAIkJgAAAAACQmAAIAAAAAIkJgAAAAACQmAAIAAAAAIkJgAAAAACQmAAIAAAAAIkJgAAAAACQmAAIAAAAAIkJgAAAAACQmAAIAAAAAIkJgAAAAACQmAAIAAAAAIkJgAAAAACQmAAIAAAAAIkJgAAAAACQmAAIAAAAAIkJgAAAAACQmAAIAAAAAIkJgAAAAACQmAAIAAAAAIkJgAAAAACQmAAIAAAAAIkJgAAAAACQmAAIAAAAAIkJgAAAAACQmAAIAAAAAIkJgAAAAACQmAAIAAAAAIkJgAAAAACQmAAIAAAAAIkJgAAAAACQmAAIAAAAAIkJgAAAAACQmAAIAAAAAIkJgAAAAACQmAAIAAAAAIkJgAAAAACQmAAIAAAAAIkJgAAAAACQmAAIAAAAAIkJgAAAAACQmAAIAAAAAIkJgAAAAACQmAAIAAAAAIkJgAAAAACQmAAIAAAAAIkJgAAAAACQmAAIAAAAAIkJgAAAAACQmAAIAAAAAIn9/zyLhCu3aALzAAAAAElFTkSuQmCC",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"class Example(Scene):\n",
" def construct(self):\n",
" self.add(NumberPlane().fade(0.7))\n",
"\n",
" geos = Geos(self)\n",
" init_geos = {\n",
" \"l1\": Line(LEFT*2, RIGHT*2, color=RED).shift(UP*2),\n",
" \"l2\": Line(LEFT*3, RIGHT*3, color=BLUE).shift(DOWN*2),\n",
" \"d1s\": geos.dot_at_start_line(\"l1\"),\n",
" \"d1e\": geos.dot_at_end_line(\"l1\"),\n",
" \"d2s,d2e\": geos.dots_at_start_end_line(\"l2\"),\n",
" }\n",
" geos.create_geos(init_geos, set_all_labels=True)\n",
"\n",
" self.add(geos.get_all_mobs_as_grp())\n",
"\n",
"%manim $_RV Example"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Circles"
]
},
{
"cell_type": "code",
"execution_count": 15,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"class Example(Scene):\n",
" def construct(self):\n",
" self.add(NumberPlane().fade(0.7))\n",
"\n",
" geos = Geos(self)\n",
" init_geos = {\n",
" \"pA\": UR*3,\n",
" \"n1\": 3,\n",
" \"dB\": geos.dot(DOWN*3, color=RED),\n",
" \"cA\": geos.circle(\"pA\", \"n1\"),\n",
" \"cB\": geos.circle(\"dB\", 2),\n",
" }\n",
" geos.create_geos(init_geos)\n",
"\n",
" self.add(geos.get_all_mobs_as_grp())\n",
"\n",
"%manim $_RV Example"
]
},
{
"cell_type": "code",
"execution_count": 16,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"geos.AB=2.23606797749979\n",
"geos.AC=3.3541019662496847\n"
]
},
{
"data": {
"image/png": 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",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"class Example(Scene):\n",
" def construct(self):\n",
" self.add(NumberPlane().fade(0.7))\n",
"\n",
" geos = Geos(self)\n",
" init_geos = {\n",
" \"dA\": geos.dot(LEFT*3),\n",
" \"dB\": geos.dot(LEFT*2+UP*2, color=RED),\n",
" \"dC\": geos.dot(DOWN*1.5, color=BLUE),\n",
" \"AB\": geos.distance(\"dA\", \"dB\"),\n",
" \"AC\": geos.distance(\"dA,dC\"),\n",
" \"cA1\": geos.circle(\"dA\", \"AB\", color=RED),\n",
" \"cA2\": geos.circle(\"dA\", \"AC\", color=BLUE),\n",
" }\n",
" geos.create_geos(init_geos)\n",
"\n",
" print(f\"{geos.AB=}\")\n",
" print(f\"{geos.AC=}\")\n",
"\n",
" self.add(geos.get_all_mobs_as_grp())\n",
"\n",
"%manim $_RV Example"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Arcs"
]
},
{
"cell_type": "code",
"execution_count": 17,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"class Example(Scene):\n",
" def construct(self):\n",
" self.add(NumberPlane().fade(0.7))\n",
"\n",
" geos = Geos(self)\n",
" init_geos = {\n",
" # geos.arc(center, radius, start_angle, angle, **kwargs)\n",
" \"a1\": geos.arc(ORIGIN, 1, 0, PI/2, color=RED),\n",
" \"a2\": geos.arc(ORIGIN, 2, PI/2, PI, color=BLUE),\n",
" }\n",
" geos.create_geos(init_geos)\n",
"\n",
" self.add(geos.get_all_mobs_as_grp())\n",
"\n",
"%manim $_RV Example"
]
},
{
"cell_type": "code",
"execution_count": 18,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"class Example(Scene):\n",
" def construct(self):\n",
" self.add(NumberPlane().fade(0.7))\n",
"\n",
" geos = Geos(self)\n",
" init_geos = {\n",
" \"dA\": geos.dot(ORIGIN),\n",
" \"dB\": geos.dot(RIGHT+UP*2),\n",
" \"dC\": geos.dot(DOWN*1.5+RIGHT*3),\n",
" \"lAB\": geos.segment(\"dA,dB\"),\n",
" \"lAC\": geos.segment(\"dA,dC\"),\n",
" \"aA1\": geos.arc_three_points(\"dC,dA,dB\", 1, color=RED),\n",
" \"aA2\": geos.arc3p(\"dB,dA,dC\", 1.2, color=BLUE),\n",
" \"aA3\": geos.arc3p(\"dB,dA,dC\", 1.4, color=GREEN, other_angle=True),\n",
" }\n",
" geos.create_geos(init_geos, set_all_labels=True)\n",
"\n",
" self.add(geos.get_all_mobs_as_grp())\n",
"\n",
"%manim $_RV Example"
]
},
{
"cell_type": "code",
"execution_count": 19,
"metadata": {},
"outputs": [
{
"data": {
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",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"class Example(Scene):\n",
" def construct(self):\n",
" self.add(NumberPlane().fade(0.7))\n",
"\n",
" geos = Geos(self)\n",
" init_geos = {\n",
" \"dA\": geos.dot(LEFT*3),\n",
" \"dB\": geos.dot(LEFT*2+UP*2),\n",
" \"dC\": geos.dot(DOWN*1.5),\n",
" \"dX\": geos.dot(RIGHT*3),\n",
" \"dY\": geos.dot(RIGHT*2+UP*2),\n",
" \"lAB\": geos.segment(\"dA,dB\"),\n",
" \"lAC\": geos.segment(\"dA,dC\"),\n",
" \"lXC\": geos.segment(\"dX,dC\"),\n",
" \"lXY\": geos.segment(\"dX,dY\"),\n",
" # Arcs\n",
" \"aA1\": geos.arc_three_points(\"dC,dA,dB\", 1, overshot_ang=0, color=BLUE),\n",
" \"aA2\": geos.arc3p(\"dC,dA,dB\", 1, overshot_ang=0, other_angle=True, color=RED),\n",
" \"aX1\": geos.arc3p(\"dY,dX,dC\", 1, overshot_ang=0, color=TEAL),\n",
" \"aX2\": geos.arc3p(\"dY,dX,dC\", 1.2, overshot_ang=10*DEGREES, color=RED),\n",
" \"aX3\": geos.arc3p(\"dY,dX,dC\", 1.5, overshot_ang=20*DEGREES, color=GREEN),\n",
" \"aX4\": geos.arc3p(\"dC,dX,dY\", 0.5, overshot_ang=20*DEGREES, color=ORANGE)\n",
" }\n",
" geos.create_geos(init_geos, set_all_labels=True)\n",
"\n",
" self.add(geos.get_all_mobs_as_grp())\n",
"\n",
"%manim $_RV Example"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Multiple inputs\n",
"\n",
"For objects to be automatically assigned, the `GeosVGroup` object must be used. If you want to create a group without assigning multiple objects, use the normal `VGroup`."
]
},
{
"cell_type": "code",
"execution_count": 29,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"class Example(Scene):\n",
" def construct(self):\n",
" self.add(NumberPlane().fade(0.7))\n",
"\n",
" geos = Geos(self)\n",
" init_geos = {\n",
" \"d1,d2,l1,c1,m1\": GeosVGroup(\n",
" Dot(LEFT*2), Dot(RIGHT*2), Line(UP, DOWN), Circle(), Square()\n",
" ).rotate(30*DEGREES).scale(2),\n",
" \"g1\": VGroup(Triangle(), MathTex(\"X\").scale(2)).rotate(-PI/2)\n",
" }\n",
" geos.create_geos(init_geos, set_all_labels=True)\n",
"\n",
" geos.d2.set_color(PINK)\n",
" geos.l1.set_color(TEAL)\n",
" geos.c1.set_color(ORANGE)\n",
" geos.m1.set_color(GREEN)\n",
" geos.g1.set_color(YELLOW)\n",
" self.add(geos.get_all_mobs_as_grp())\n",
"\n",
"%manim $_RV Example"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Copies"
]
},
{
"cell_type": "code",
"execution_count": 21,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"class Example(Scene):\n",
" def construct(self):\n",
" geos = Geos(self)\n",
" geos.create_geos({\n",
" \"dA\": Dot(LEFT+UP*2),\n",
" \"dB\": Dot(-LEFT-UP*2),\n",
" \"dC\": Dot(DOWN*2),\n",
" \"dD\": geos.geos_copy(\"dC\", lambda m,n: m.next_to(n(\"dA\"), DOWN, buff=1)),\n",
" \"dE\": geos.geos_copy(\"dD\", lambda m: m.shift(LEFT)),\n",
" },\n",
" set_all_labels=True\n",
" )\n",
" self.add(NumberPlane().fade(0.7))\n",
" self.add(geos.get_all_mobs_as_grp())\n",
"\n",
"%manim $_RV Example"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Getters"
]
},
{
"cell_type": "code",
"execution_count": 22,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"class Example(Scene):\n",
" def construct(self):\n",
" self.add(NumberPlane().fade(0.7))\n",
"\n",
" geos = Geos(self)\n",
" geos.create_geos({\n",
" \"l1\": Line(LEFT*3, RIGHT*3),\n",
" \"l2\": Line(LEFT*3, RIGHT*3).rotate(30*DEGREES),\n",
" \"dA\": Dot(LEFT*2),\n",
" \"dB\": Dot(RIGHT*2),\n",
" \"dC\": Dot(DOWN*2),\n",
" \"cA\": geos.circle(\"dA\", 1),\n",
" \"cB\": geos.circle(\"dB\", 2),\n",
" \"aAB1\": geos.arc(ORIGIN, 1, 0, 30*DEGREES, color=RED),\n",
" \"aAB2\": geos.arc(ORIGIN, 0.5, -PI, 30*DEGREES, color=GREEN),\n",
" },\n",
" set_all_labels=True\n",
" )\n",
"\n",
" self.add(geos.get_all_mobs_as_grp())\n",
" geos.get_as_grp(\"dA\", \"dB\").set_color(ORANGE)\n",
" geos.get_all_lines().set_color(BLUE)\n",
" geos.get_all_circles().set_color(YELLOW)\n",
" geos.get_all_dots().shift(DOWN)\n",
" geos.get_all_arcs().set_color(PINK)\n",
" geos.get_all_arcs().set_color(PINK)\n",
" geos.get_all_labels().set_color(RED)\n",
"\n",
"%manim $_RV Example"
]
},
{
"cell_type": "code",
"execution_count": 23,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"class Example(Scene):\n",
" def construct(self):\n",
" self.add(NumberPlane().fade(0.7))\n",
"\n",
" geos = Geos(self)\n",
" geos.create_geos({\n",
" \"d1,d2,d3,d4,d5\": GeosVGroup(*[\n",
" Dot() for _ in range(5)]\n",
" ).arrange(RIGHT, buff=1).shift(UP*2),\n",
" \"l1,l2,l3,l4,l5\": GeosVGroup(*[\n",
" Line() for _ in range(5)]\n",
" ).arrange(DOWN, buff=0.5).to_edge(DOWN),\n",
" \"c1,c2,c3,c4,c5\": GeosVGroup(*[\n",
" Circle(0.5) for _ in range(5)]\n",
" ).arrange(DOWN, buff=0.5).to_edge(LEFT),\n",
" },\n",
" set_all_labels=True \n",
" )\n",
"\n",
" self.add(geos.get_all_dots(exclude=\"3,5\"))\n",
" self.add(geos.get_all_labels(exclude=\"1,4\"))\n",
" self.add(geos.get_all_lines(exclude=\"2,3\"))\n",
" self.add(geos.get_all_circles(exclude=\"3,4\"))\n",
"\n",
"%manim $_RV Example"
]
},
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