{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# 3-dimensional plots with SageMath"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"\n",
"\n"
],
"text/plain": [
"Graphics3d Object"
]
},
"execution_count": 1,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"x, y = var('x y')\n",
"plot3d(sin(x*y), (x,-pi,pi), (y,-pi,pi), color='green')"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"\n",
"\n"
],
"text/plain": [
"Graphics3d Object"
]
},
"execution_count": 2,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"g1 = plot3d(sin(x*y), (x,-pi,pi), (y,-pi,pi), color='green', plot_points=100)\n",
"g1"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"\n",
"\n"
],
"text/plain": [
"Graphics3d Object"
]
},
"execution_count": 3,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"g2 = sphere()\n",
"g1 + g2"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"SageMath's default 3D viewer is `threejs`; it has many options, which are listed [here](https://doc.sagemath.org/html/en/reference/plot3d/threejs.html).\n",
"\n",
"Another 3D viewer is `tachyon`, which produces static images:"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"Graphics3d Object"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"show(g1 + g2, viewer='tachyon', aspect_ratio=1, figsize=10)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Parametric plots"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"\n",
"\n"
],
"text/plain": [
"Graphics3d Object"
]
},
"execution_count": 5,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"u, v = var('u v')\n",
"f1 = (4+(3+cos(v))*sin(u), 4+(3+cos(v))*cos(u), 4+sin(v))\n",
"f2 = (8+(3+cos(v))*cos(u), 3+sin(v), 4+(3+cos(v))*sin(u))\n",
"g1 = parametric_plot3d(f1, (u,0,2*pi), (v,0,2*pi), color=\"red\")\n",
"g2 = parametric_plot3d(f2, (u,0,2*pi), (v,0,2*pi), color=\"gold\")\n",
"g1 + g2"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Implicit plots"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"\n",
"\n"
],
"text/plain": [
"Graphics3d Object"
]
},
"execution_count": 6,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"phi = golden_ratio()\n",
"z = var('z')\n",
"F = 2 - (cos(x+phi*y) + cos(x-phi*y) + cos(y+phi*z) + cos(y-phi*z) + cos(z-phi*x) \n",
" + cos(z+phi*x))\n",
"r = 4.77\n",
"implicit_plot3d(F, (x,-r,r), (y,-r,r), (z,-r,r), plot_points=40, color='darkkhaki')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Animated 3D plots"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"\n",
"\n"
],
"text/plain": [
"Graphics3d Object"
]
},
"execution_count": 7,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"n = 20\n",
"animate([plot3d(sin((x - k*pi/(n-1))*y), (x, -pi, pi), (y, -pi, pi))\n",
" for k in range(n)]).interactive(delay=10)"
]
}
],
"metadata": {
"kernelspec": {
"display_name": "SageMath 9.6.beta4",
"language": "sage",
"name": "sagemath"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.8.10"
}
},
"nbformat": 4,
"nbformat_minor": 4
}