{ "cells": [ { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": false, "jupyter": { "outputs_hidden": false } }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "(s, t)" ] }, "execution_count": 1, "metadata": {}, "output_type": "execute_result" } ], "source": [ "%display typeset\n", "var('s,t')" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": false, "jupyter": { "outputs_hidden": false } }, "outputs": [], "source": [ "R=2\n", "def x(s,t):\n", " return (R+s*cos(t/2))*cos(t)\n", "\n", "def y(s,t):\n", "\treturn (R+s*cos(t/2))*sin(t)\n", "\n", "def z(s,t):\n", "\treturn s*sin(t/2)" ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "collapsed": false, "jupyter": { "outputs_hidden": false } }, "outputs": [ { "data": { "text/html": [ "\n", "\n" ], "text/plain": [ "Graphics3d Object" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "cm = colormaps.Greens\n", "def c(s,t):\n", "\treturn 0.5+0.5*sin(t)**2\n", "\n", "S=parametric_plot3d((x(s,t), y(s,t), z(s,t)), (s,-1,1), (t,0,2*pi), color = (c,cm))\n", "show(S)" ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "collapsed": false, "jupyter": { "outputs_hidden": false } }, "outputs": [ { "data": { "text/html": [ "\n", "\n" ], "text/plain": [ "Graphics3d Object" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "Bord = parametric_plot3d((x(-1,t), y(-1,t), z(-1,t)), (t,0,2*pi), color=\"red\", thickness =3)\n", "show(S+Bord)" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false, "jupyter": { "outputs_hidden": false } }, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "SageMath 9.0", "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": "3.7.3" } }, "nbformat": 4, "nbformat_minor": 4 }