{
"nbformat": 4,
"nbformat_minor": 0,
"metadata": {
"anaconda-cloud": {},
"hide_input": false,
"kernelspec": {
"display_name": "Python 3",
"language": "python",
"name": "python3"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.7.4"
},
"latex_envs": {
"bibliofile": "biblio.bib",
"cite_by": "apalike",
"current_citInitial": 1,
"eqLabelWithNumbers": true,
"eqNumInitial": 0
},
"name": "3D.ipynb",
"colab": {
"name": "kl_py_diagramok_3D.ipynb",
"provenance": [],
"collapsed_sections": [],
"include_colab_link": true
}
},
"cells": [
{
"cell_type": "markdown",
"metadata": {
"id": "view-in-github",
"colab_type": "text"
},
"source": [
""
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "s9ijd0MWaINt",
"colab_type": "text"
},
"source": [
"# Adatdiagrammok következő szintje a 3D ábrák\n",
"\n",
"A `matplotlib` csomag elsősorban 2D ábrák gyártására lett kialakítva. \n",
"\n",
"Ennek ellenére rendelkezik néhány 3D-s ábrakészítési függvénnyel is. \n",
"\n",
"Ahhoz, hogy a 3D-s ábrázolási függvényeket el tudjuk érni, be kell tölteni a `matplotlib` csomag `mpl_toolkits.mplot3d` alcsomagját. "
]
},
{
"cell_type": "code",
"metadata": {
"id": "itlVKV0vaINv",
"colab_type": "code",
"colab": {},
"outputId": "14fae72c-73bc-4a72-af5e-d3a4e90cab6f"
},
"source": [
"%pylab inline \n",
"from mpl_toolkits.mplot3d import * #3D-s ábrák alcsomagja\n",
"from ipywidgets import * #interaktivitáshoz szükséges függvények"
],
"execution_count": 0,
"outputs": [
{
"output_type": "stream",
"text": [
"Populating the interactive namespace from numpy and matplotlib\n"
],
"name": "stdout"
}
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "GeNaJXUjaINy",
"colab_type": "text"
},
"source": [
"## Térbeli görbék, adathalmazok\n",
"\n",
"Ahhoz hogy egy ábrát térben tudjunk megjeleníteni, fel kell készíteni a környezetet. A térbeli ábrák megjelenítése és azok tulajdonságainak beállítása kicsit körülményesebb a 2D-s ábráknál.\n",
"\n",
"A legszembetűnőbb különbség, hogy az ábrák úgynevezett `axes` (körül belül itt a koordinátatengelyekre kell gondolni...) objektumok köré csoportosulnak, s ezek tulajdonságaiként, illetve ezeken alkalmazott függvényekként jönnek létre maguk az ábrák. \n",
"\n",
"Egy egszerű paraméteres térbeli görbe megjelenítése : spirális függvény:\n",
"\n",
"\\begin{equation}\n",
"\\mathbf{r}(t)=\\left(\\begin{array}{c}\n",
"\\cos(3t)\\\\\n",
"\\sin(3t)\\\\\n",
"t\n",
"\\end{array}\\right)\n",
"\\end{equation}"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "AcHuvRs3aINz",
"colab_type": "text"
},
"source": [
"Először is gyártsuk let a $t$ paraméter mintavételezési pontjait a $[0,2\\pi]$ intervallumban:"
]
},
{
"cell_type": "code",
"metadata": {
"id": "n1QtLqIoaIN0",
"colab_type": "code",
"colab": {}
},
"source": [
"t=linspace(0,2*pi,100) # 100 pont 0 és 2*pi között"
],
"execution_count": 0,
"outputs": []
},
{
"cell_type": "markdown",
"metadata": {
"id": "rRu2razLaIN2",
"colab_type": "text"
},
"source": [
"A következő kódcellában két dolog fog történni. Előszöris létrehozzuk az `ax` nevű `axes` objektumot, amelynek expliciten megadjuk, hogy 3D-s koordinátarendszer legyen. Illetve erre az objektumra hatva a `plot` függvénnyel létrehozzuk magát az ábrát. Figyeljük meg, hogy most a `plot` függvény háruom bemenő paramétert vár! "
]
},
{
"cell_type": "code",
"metadata": {
"id": "H2rvXIRoaIN2",
"colab_type": "code",
"colab": {},
"outputId": "4931a376-03cc-4059-e62a-32dfe185b8d8"
},
"source": [
"ax=subplot(1,1,1,projection='3d') #térbeli koordináta tengely létrehozása\n",
"ax.plot(cos(3*t),sin(3*t),t)"
],
"execution_count": 0,
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": [
"[]"
]
},
"metadata": {
"tags": []
},
"execution_count": 3
},
{
"output_type": "display_data",
"data": {
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\n",
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