{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Mesh tutorial " ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": true }, "outputs": [], "source": [ "%load_ext autoreload\n", "%autoreload 2" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": true }, "outputs": [], "source": [ "import argiope as ag\n", "import numpy as np\n", "import pandas as pd\n", "import matplotlib.pyplot as plt\n", "import matplotlib as mpl\n", "from string import Template\n", "%matplotlib nbagg" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Geometry setup\n" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "725" ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" } ], "source": [ "geom_template = \"\"\"\n", "lc = $lc;\n", "Point(1) = {0,0,0,lc};\n", "Point(2) = {.5,0,0,lc};\n", "Point(3) = {.5,.5,0,lc};\n", "Point(4) = {1,.5,0,lc};\n", "Point(5) = {1,1,0,lc};\n", "Point(6) = {0,1,0,lc};\n", "Point(7) = {.5,.25,0,lc};\n", "Point(8) = {.5,.75,0,lc};\n", "Point(9) = {.125,.875,0,lc};\n", "Point(10) = {.125,.875-.05,0,lc};\n", "Point(11) = {.125,.875+.05,0,lc};\n", "\n", "Line(1) = {1,2};\n", "Circle(2) = {2,3,4};\n", "Line(3) = {4,5};\n", "Line(4) = {5,6};\n", "Line(5) = {6,1};\n", "Circle(6) = {7,3,8};\n", "Circle(7) = {8,3,7};\n", "Circle(8) = {10,9,11};\n", "Circle(9) = {11,9,10};\n", "\n", "Line Loop(1) = {6,7}; // interior loop\n", "Line Loop(2) = {1,2,3,4,5}; // exterior loop\n", "Line Loop(3) = {8,9};// hole\n", "Plane Surface(2) = {2,1,3}; // exterior surface (with a hole)\n", "Recombine Surface {2};\n", "Physical Surface(\"SURFACE\") = {2};\n", "\"\"\"\n", "open(\"./_workdir/mesh.geo\", \"w\").write(Template(geom_template).substitute(lc = 0.025))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Mesh creation\n", "\n", "GMSH can be run directly as a shell command." ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Info : Running 'gmsh -2 ./_workdir/mesh.geo -algo delquad' [Gmsh 3.0.6, 1 node, max. 1 thread]\n", "Info : Started on Fri Mar 2 16:03:33 2018\n", "Info : Reading './_workdir/mesh.geo'...\n", "Info : Done reading './_workdir/mesh.geo'\n", "Info : Finalized high order topology of periodic connections\n", "Info : Meshing 1D...\n", "Info : Meshing curve 1 (Line)\n", "Info : Meshing curve 2 (Circle)\n", "Info : Meshing curve 3 (Line)\n", "Info : Meshing curve 4 (Line)\n", "Info : Meshing curve 5 (Line)\n", "Info : Meshing curve 6 (Circle)\n", "Info : Meshing curve 7 (Circle)\n", "Info : Meshing curve 8 (Circle)\n", "Info : Meshing curve 9 (Circle)\n", "Info : Done meshing 1D (0.004 s)\n", "Info : Meshing 2D...\n", "Info : Meshing surface 2 (Plane, Frontal Quad)\n", "Info : Blossom: 3586 internal 232 closed\n", "Info : Blossom completed (0.08 s): 1227 quads 0 triangles 0 invalid quads 0 quads with Q < 0.1 Avg Q = 0.904 Min Q 0.451\n", "Info : Done meshing 2D (0.304 s)\n", "Info : 2856 vertices 1470 elements\n", "Info : Writing './_workdir/mesh.msh'...\n", "Info : Done writing './_workdir/mesh.msh'\n", "Info : Stopped on Fri Mar 2 16:03:34 2018\n" ] } ], "source": [ "!gmsh -2 ./_workdir/mesh.geo -algo 'delquad' " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "It is even simpler to use the dedicated function in *argiope.utils*. " ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": true }, "outputs": [], "source": [ "ag.utils.run_gmsh(gmsh_path = \"gmsh\", \n", " gmsh_space = 2, \n", " gmsh_options = \"-algo 'del2d'\", \n", " name = \"./_workdir/mesh.geo\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Mesh reading" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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" ], "text/plain": [ " conn materials sets type \n", " n0 n1 n2 n3 SURFACE all argiope solver\n", " \n", "element \n", "1 428 1689 767 766 True True quad4 \n", "2 344 743 693 1542 True True quad4 \n", "3 426 864 237 699 True True quad4 \n", "4 1392 815 254 1246 True True quad4 \n", "5 872 679 438 1479 True True quad4 " ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" } ], "source": [ "mesh.elements.head()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Putting it all together\n", "\n", "Let's now do all these operations in a single function and do fun stuff." ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" } ], "source": [ "def make_mesh(lc, algorithm = \"del2d\"):\n", " \"\"\"\n", " A mesh function that creates a mesh.\n", " \"\"\"\n", " open(\"./_workdir/mesh.geo\", \"w\").write(Template(geom_template).substitute(lc = lc))\n", " ag.utils.run_gmsh(gmsh_path = \"gmsh\", \n", " gmsh_space = 2, \n", " gmsh_options = \"-algo '{0}'\".format(algorithm), \n", " name = \"./_workdir/mesh.geo\")\n", " mesh = ag.mesh.read_msh(\"./_workdir/mesh.msh\")\n", " return mesh\n", "\n", "mesh = make_mesh(0.02, \"meshadapt\")\n", "mesh " ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "data": { "application/javascript": [ "/* Put everything inside the global mpl namespace */\n", "window.mpl = {};\n", "\n", "mpl.get_websocket_type = function() {\n", " if (typeof(WebSocket) !== 'undefined') {\n", " return WebSocket;\n", " } else if (typeof(MozWebSocket) !== 'undefined') {\n", " return MozWebSocket;\n", " } else {\n", " alert('Your browser does not have WebSocket support.' +\n", " 'Please try Chrome, Safari or Firefox ≥ 6. ' +\n", " 'Firefox 4 and 5 are also supported but you ' +\n", " 'have to enable WebSockets in about:config.');\n", " };\n", "}\n", "\n", "mpl.figure = function(figure_id, websocket, ondownload, parent_element) {\n", " this.id = figure_id;\n", "\n", " this.ws = websocket;\n", "\n", " this.supports_binary = (this.ws.binaryType != undefined);\n", "\n", " if (!this.supports_binary) {\n", " var warnings = document.getElementById(\"mpl-warnings\");\n", " if (warnings) {\n", " warnings.style.display = 'block';\n", " warnings.textContent = (\n", " \"This browser does not support binary websocket messages. \" +\n", " \"Performance may be slow.\");\n", " }\n", " }\n", "\n", " this.imageObj = new Image();\n", "\n", " this.context = undefined;\n", " this.message = undefined;\n", " this.canvas = undefined;\n", " this.rubberband_canvas = undefined;\n", " this.rubberband_context = undefined;\n", " this.format_dropdown = undefined;\n", "\n", " this.image_mode = 'full';\n", "\n", " this.root = $('
');\n", " this._root_extra_style(this.root)\n", " this.root.attr('style', 'display: inline-block');\n", "\n", " $(parent_element).append(this.root);\n", "\n", " this._init_header(this);\n", " this._init_canvas(this);\n", " this._init_toolbar(this);\n", "\n", " var fig = this;\n", "\n", " this.waiting = false;\n", "\n", " this.ws.onopen = function () {\n", " fig.send_message(\"supports_binary\", {value: fig.supports_binary});\n", " fig.send_message(\"send_image_mode\", {});\n", " fig.send_message(\"refresh\", {});\n", " }\n", "\n", " this.imageObj.onload = function() {\n", " if (fig.image_mode == 'full') {\n", " // Full images could contain transparency (where diff images\n", " // almost always do), so we need to clear the canvas so that\n", " // there is no ghosting.\n", " fig.context.clearRect(0, 0, fig.canvas.width, fig.canvas.height);\n", " }\n", " fig.context.drawImage(fig.imageObj, 0, 0);\n", " };\n", "\n", " this.imageObj.onunload = function() {\n", " this.ws.close();\n", " }\n", "\n", " this.ws.onmessage = this._make_on_message_function(this);\n", "\n", " this.ondownload = ondownload;\n", "}\n", "\n", "mpl.figure.prototype._init_header = function() {\n", " var titlebar = $(\n", " '
');\n", " var titletext = $(\n", " '
');\n", " titlebar.append(titletext)\n", " this.root.append(titlebar);\n", " this.header = titletext[0];\n", "}\n", "\n", "\n", "\n", "mpl.figure.prototype._canvas_extra_style = function(canvas_div) {\n", "\n", "}\n", "\n", "\n", "mpl.figure.prototype._root_extra_style = function(canvas_div) {\n", "\n", "}\n", "\n", "mpl.figure.prototype._init_canvas = function() {\n", " var fig = this;\n", "\n", " var canvas_div = $('
');\n", "\n", " canvas_div.attr('style', 'position: relative; clear: both; outline: 0');\n", "\n", " function canvas_keyboard_event(event) {\n", " return fig.key_event(event, event['data']);\n", " }\n", "\n", " canvas_div.keydown('key_press', canvas_keyboard_event);\n", " canvas_div.keyup('key_release', canvas_keyboard_event);\n", " this.canvas_div = canvas_div\n", " this._canvas_extra_style(canvas_div)\n", " this.root.append(canvas_div);\n", "\n", " var canvas = $('');\n", " canvas.addClass('mpl-canvas');\n", " canvas.attr('style', \"left: 0; top: 0; z-index: 0; outline: 0\")\n", "\n", " this.canvas = canvas[0];\n", " this.context = canvas[0].getContext(\"2d\");\n", "\n", " var rubberband = $('');\n", " rubberband.attr('style', \"position: absolute; left: 0; top: 0; z-index: 1;\")\n", "\n", " var pass_mouse_events = true;\n", "\n", " canvas_div.resizable({\n", " start: function(event, ui) {\n", " pass_mouse_events = false;\n", " },\n", " resize: function(event, ui) {\n", " fig.request_resize(ui.size.width, ui.size.height);\n", " },\n", " stop: function(event, ui) {\n", " pass_mouse_events = true;\n", " fig.request_resize(ui.size.width, ui.size.height);\n", " },\n", " });\n", "\n", " function mouse_event_fn(event) {\n", " if (pass_mouse_events)\n", " return fig.mouse_event(event, event['data']);\n", " }\n", "\n", " rubberband.mousedown('button_press', mouse_event_fn);\n", " rubberband.mouseup('button_release', mouse_event_fn);\n", " // Throttle sequential mouse events to 1 every 20ms.\n", " rubberband.mousemove('motion_notify', mouse_event_fn);\n", "\n", " rubberband.mouseenter('figure_enter', mouse_event_fn);\n", " rubberband.mouseleave('figure_leave', mouse_event_fn);\n", "\n", " canvas_div.on(\"wheel\", function (event) {\n", " event = event.originalEvent;\n", " event['data'] = 'scroll'\n", " if (event.deltaY < 0) {\n", " event.step = 1;\n", " } else {\n", " event.step = -1;\n", " }\n", " mouse_event_fn(event);\n", " });\n", "\n", " canvas_div.append(canvas);\n", " canvas_div.append(rubberband);\n", "\n", " this.rubberband = rubberband;\n", " this.rubberband_canvas = rubberband[0];\n", " this.rubberband_context = rubberband[0].getContext(\"2d\");\n", " this.rubberband_context.strokeStyle = \"#000000\";\n", "\n", " this._resize_canvas = function(width, height) {\n", " // Keep the size of the canvas, canvas container, and rubber band\n", " // canvas in synch.\n", " canvas_div.css('width', width)\n", " canvas_div.css('height', height)\n", "\n", " canvas.attr('width', width);\n", " canvas.attr('height', height);\n", "\n", " rubberband.attr('width', width);\n", " rubberband.attr('height', height);\n", " }\n", "\n", " // Set the figure to an initial 600x600px, this will subsequently be updated\n", " // upon first draw.\n", " this._resize_canvas(600, 600);\n", "\n", " // Disable right mouse context menu.\n", " $(this.rubberband_canvas).bind(\"contextmenu\",function(e){\n", " return false;\n", " });\n", "\n", " function set_focus () {\n", " canvas.focus();\n", " canvas_div.focus();\n", " }\n", "\n", " window.setTimeout(set_focus, 100);\n", "}\n", "\n", "mpl.figure.prototype._init_toolbar = function() {\n", " var fig = this;\n", "\n", " var nav_element = $('
')\n", " nav_element.attr('style', 'width: 100%');\n", " this.root.append(nav_element);\n", "\n", " // Define a callback function for later on.\n", " function toolbar_event(event) {\n", " return fig.toolbar_button_onclick(event['data']);\n", " }\n", " function toolbar_mouse_event(event) {\n", " return fig.toolbar_button_onmouseover(event['data']);\n", " }\n", "\n", " for(var toolbar_ind in mpl.toolbar_items) {\n", " var name = mpl.toolbar_items[toolbar_ind][0];\n", " var tooltip = mpl.toolbar_items[toolbar_ind][1];\n", " var image = mpl.toolbar_items[toolbar_ind][2];\n", " var method_name = mpl.toolbar_items[toolbar_ind][3];\n", "\n", " if (!name) {\n", " // put a spacer in here.\n", " continue;\n", " }\n", " var button = $('