3e:null 3f:["$","title",null,{"children":"Force Edge Bundling | rolyhudson | Observable"}] 45:T4c7,function drawGraph({ nodes, links }) { const svg = d3 .create("svg") .attr("viewBox", [-10, -10, width + 20, height + 20]); const x = d3 .scaleLinear() .domain(d3.extent(nodes, (d) => d.x)) .range([0, width]) .nice(); const y = d3 .scaleLinear() .domain(d3.extent(nodes, (d) => d.y)) .range([0, height]) .nice(); const line = d3 .line() .x((d) => x(d.x)) .y((d) => y(d.y)); svg .selectAll("circle") .data(nodes) .join("circle") .attr("cx", (d) => x(d.x)) .attr("cy", (d) => y(d.y)) .attr("r", 2); if (useEdgeBundling) { svg .selectAll("path") .data(links) .join("path") .attr("d", (d) => line(d.path)) .attr("fill", "none") .attr("stroke", "#aaa3"); } else { const nodesMap = new Map(nodes.map(d => [d.id, d])) svg .selectAll("line") .data(links) .join("line") .attr("x1", (d) => x(nodesMap.get(d.source).x)) .attr("y1", (d) => y(nodesMap.get(d.source).y)) .attr("x2", (d) => x(nodesMap.get(d.target).x)) .attr("y2", (d) => y(nodesMap.get(d.target).y)) .attr("fill", "none") .attr("stroke", "#aaa3"); } return svg.node(); }46:T74c,// Given a network {nodes, links} computes the edge bundles and modifies the links // array adding a path attribute with the coordinates for each curve function edgeBundling( { nodes, // Array of nodes including x and y coords e.g. [{id: "a", x: 10, y:10}, {id: "b", x: 20, y: 20}, ...] links // Array of links in D3 forceSimulation format e.g. [{source: "a", target: "b"}, ... ] }, { id = (d) => d.id, pathAttr = "path", // name of the attribute to save the paths bundling_stiffness = 0.1, // global bundling constant controlling edge stiffness step_size = 0.1, // init. distance to move points subdivision_rate = 2, // subdivision rate increase cycles = 6, // number of cycles to perform iterations = 90, // init. number of iterations for cycle iterations_rate = 0.6666667, // rate at which iteration number decreases i.e. 2/3 compatibility_threshold = 0.6 // "which pairs of edges should be considered compatible (default is set to 0.6, 60% compatiblity)" } = {} ) { // The library wants the links as the index positions in the nodes array const dNodes = new Map(nodes.map((d, i) => [id(d), i])); const linksIs = links.map((l) => ({ source: dNodes.get(typeof l.source === "object" ? id(l.source) : l.source), target: dNodes.get(typeof l.source === "object" ? id(l.target) : l.target) })); const edgeBundling = ForceEdgeBundling() .nodes(nodes) .edges(linksIs) .bundling_stiffness(bundling_stiffness) .step_size(step_size) .subdivision_rate(subdivision_rate) .cycles(cycles) .iterations(iterations) .iterations_rate(iterations_rate) .compatibility_threshold(compatibility_threshold); edgeBundling.update = () => { const paths = edgeBundling(); links.map((l, i) => (l[pathAttr] = paths[i])); }; edgeBundling.update(); return edgeBundling; }47:T383d,// Adapted code from https://github.com/upphiminn/d3.ForceBundle // LICENSE: GPL V2 ForceEdgeBundling = function () { let data_nodes = {}, // {'nodeid':{'x':,'y':},..} data_edges = [], // [{'source':'nodeid1', 'target':'nodeid2'},..] compatibility_list_for_edge = [], subdivision_points_for_edge = [], K = 0.1, // global bundling constant controlling edge stiffness S_initial = 0.1, // init. distance to move points P_initial = 1, // init. subdivision number P_rate = 2, // subdivision rate increase C = 6, // number of cycles to perform I_initial = 90, // init. number of iterations for cycle I_rate = 0.6666667, // rate at which iteration number decreases i.e. 2/3 compatibility_threshold = 0.6, eps = 1e-6, P = null; /*** Geometry Helper Methods ***/ function vector_dot_product(p, q) { return p.x * q.x + p.y * q.y; } function edge_as_vector(P) { return { x: data_nodes[P.target].x - data_nodes[P.source].x, y: data_nodes[P.target].y - data_nodes[P.source].y }; } function edge_length(e) { // handling nodes that are on the same location, so that K/edge_length != Inf if ( Math.abs(data_nodes[e.source].x - data_nodes[e.target].x) < eps && Math.abs(data_nodes[e.source].y - data_nodes[e.target].y) < eps ) { return eps; } return Math.sqrt( Math.pow(data_nodes[e.source].x - data_nodes[e.target].x, 2) + Math.pow(data_nodes[e.source].y - data_nodes[e.target].y, 2) ); } function custom_edge_length(e) { return Math.sqrt( Math.pow(e.source.x - e.target.x, 2) + Math.pow(e.source.y - e.target.y, 2) ); } function edge_midpoint(e) { let middle_x = (data_nodes[e.source].x + data_nodes[e.target].x) / 2.0; let middle_y = (data_nodes[e.source].y + data_nodes[e.target].y) / 2.0; return { x: middle_x, y: middle_y }; } function compute_divided_edge_length(e_idx) { let length = 0; for (let i = 1; i < subdivision_points_for_edge[e_idx].length; i++) { let segment_length = euclidean_distance( subdivision_points_for_edge[e_idx][i], subdivision_points_for_edge[e_idx][i - 1] ); length += segment_length; } return length; } function euclidean_distance(p, q) { return Math.sqrt(Math.pow(p.x - q.x, 2) + Math.pow(p.y - q.y, 2)); } function project_point_on_line(p, Q) { let L = Math.sqrt( (Q.target.x - Q.source.x) * (Q.target.x - Q.source.x) + (Q.target.y - Q.source.y) * (Q.target.y - Q.source.y) ); let r = ((Q.source.y - p.y) * (Q.source.y - Q.target.y) - (Q.source.x - p.x) * (Q.target.x - Q.source.x)) / (L * L); return { x: Q.source.x + r * (Q.target.x - Q.source.x), y: Q.source.y + r * (Q.target.y - Q.source.y) }; } /*** ********************** ***/ /*** Initialization Methods ***/ function initialize_edge_subdivisions() { for (let i = 0; i < data_edges.length; i++) { if (P_initial === 1) { subdivision_points_for_edge[i] = []; //0 subdivisions } else { subdivision_points_for_edge[i] = []; subdivision_points_for_edge[i].push(data_nodes[data_edges[i].source]); subdivision_points_for_edge[i].push(data_nodes[data_edges[i].target]); } } } function initialize_compatibility_lists() { for (let i = 0; i < data_edges.length; i++) { compatibility_list_for_edge[i] = []; //0 compatible edges. } } function filter_self_loops(edgelist) { let filtered_edge_list = []; for (let e = 0; e < edgelist.length; e++) { if ( data_nodes[edgelist[e].source].x != data_nodes[edgelist[e].target].x || data_nodes[edgelist[e].source].y != data_nodes[edgelist[e].target].y ) { //or smaller than eps filtered_edge_list.push(edgelist[e]); } } return filtered_edge_list; } /*** ********************** ***/ /*** Force Calculation Methods ***/ function apply_spring_force(e_idx, i, kP) { let prev = subdivision_points_for_edge[e_idx][i - 1]; let next = subdivision_points_for_edge[e_idx][i + 1]; let crnt = subdivision_points_for_edge[e_idx][i]; let x = prev.x - crnt.x + next.x - crnt.x; let y = prev.y - crnt.y + next.y - crnt.y; x *= kP; y *= kP; return { x: x, y: y }; } function apply_electrostatic_force(e_idx, i) { let sum_of_forces = { x: 0, y: 0 }; let compatible_edges_list = compatibility_list_for_edge[e_idx]; for (let oe = 0; oe < compatible_edges_list.length; oe++) { let force = { x: subdivision_points_for_edge[compatible_edges_list[oe]][i].x - subdivision_points_for_edge[e_idx][i].x, y: subdivision_points_for_edge[compatible_edges_list[oe]][i].y - subdivision_points_for_edge[e_idx][i].y }; if (Math.abs(force.x) > eps || Math.abs(force.y) > eps) { let diff = 1 / Math.pow( custom_edge_length({ source: subdivision_points_for_edge[compatible_edges_list[oe]][i], target: subdivision_points_for_edge[e_idx][i] }), 1 ); sum_of_forces.x += force.x * diff; sum_of_forces.y += force.y * diff; } } return sum_of_forces; } function apply_resulting_forces_on_subdivision_points(e_idx, P, S) { let kP = K / (edge_length(data_edges[e_idx]) * (P + 1)); // kP=K/|P|(number of segments), where |P| is the initial length of edge P. // (length * (num of sub division pts - 1)) let resulting_forces_for_subdivision_points = [ { x: 0, y: 0 } ]; for (let i = 1; i < P + 1; i++) { // exclude initial end points of the edge 0 and P+1 let resulting_force = { x: 0, y: 0 }; let spring_force = apply_spring_force(e_idx, i, kP); let electrostatic_force = apply_electrostatic_force(e_idx, i, S); resulting_force.x = S * (spring_force.x + electrostatic_force.x); resulting_force.y = S * (spring_force.y + electrostatic_force.y); resulting_forces_for_subdivision_points.push(resulting_force); } resulting_forces_for_subdivision_points.push({ x: 0, y: 0 }); return resulting_forces_for_subdivision_points; } /*** ********************** ***/ /*** Edge Division Calculation Methods ***/ function update_edge_divisions(P) { for (let e_idx = 0; e_idx < data_edges.length; e_idx++) { if (P === 1) { subdivision_points_for_edge[e_idx].push( data_nodes[data_edges[e_idx].source] ); // source subdivision_points_for_edge[e_idx].push( edge_midpoint(data_edges[e_idx]) ); // mid point subdivision_points_for_edge[e_idx].push( data_nodes[data_edges[e_idx].target] ); // target } else { let divided_edge_length = compute_divided_edge_length(e_idx); let segment_length = divided_edge_length / (P + 1); let current_segment_length = segment_length; let new_subdivision_points = []; new_subdivision_points.push(data_nodes[data_edges[e_idx].source]); //source for (let i = 1; i < subdivision_points_for_edge[e_idx].length; i++) { let old_segment_length = euclidean_distance( subdivision_points_for_edge[e_idx][i], subdivision_points_for_edge[e_idx][i - 1] ); while (old_segment_length > current_segment_length) { let percent_position = current_segment_length / old_segment_length; let new_subdivision_point_x = subdivision_points_for_edge[e_idx][i - 1].x; let new_subdivision_point_y = subdivision_points_for_edge[e_idx][i - 1].y; new_subdivision_point_x += percent_position * (subdivision_points_for_edge[e_idx][i].x - subdivision_points_for_edge[e_idx][i - 1].x); new_subdivision_point_y += percent_position * (subdivision_points_for_edge[e_idx][i].y - subdivision_points_for_edge[e_idx][i - 1].y); new_subdivision_points.push({ x: new_subdivision_point_x, y: new_subdivision_point_y }); old_segment_length -= current_segment_length; current_segment_length = segment_length; } current_segment_length -= old_segment_length; } new_subdivision_points.push(data_nodes[data_edges[e_idx].target]); //target subdivision_points_for_edge[e_idx] = new_subdivision_points; } } } /*** ********************** ***/ /*** Edge compatibility measures ***/ function angle_compatibility(P, Q) { return Math.abs( vector_dot_product(edge_as_vector(P), edge_as_vector(Q)) / (edge_length(P) * edge_length(Q)) ); } function scale_compatibility(P, Q) { let lavg = (edge_length(P) + edge_length(Q)) / 2.0; return ( 2.0 / (lavg / Math.min(edge_length(P), edge_length(Q)) + Math.max(edge_length(P), edge_length(Q)) / lavg) ); } function position_compatibility(P, Q) { let lavg = (edge_length(P) + edge_length(Q)) / 2.0; let midP = { x: (data_nodes[P.source].x + data_nodes[P.target].x) / 2.0, y: (data_nodes[P.source].y + data_nodes[P.target].y) / 2.0 }; let midQ = { x: (data_nodes[Q.source].x + data_nodes[Q.target].x) / 2.0, y: (data_nodes[Q.source].y + data_nodes[Q.target].y) / 2.0 }; return lavg / (lavg + euclidean_distance(midP, midQ)); } function edge_visibility(P, Q) { let I0 = project_point_on_line(data_nodes[Q.source], { source: data_nodes[P.source], target: data_nodes[P.target] }); let I1 = project_point_on_line(data_nodes[Q.target], { source: data_nodes[P.source], target: data_nodes[P.target] }); //send actual edge points positions let midI = { x: (I0.x + I1.x) / 2.0, y: (I0.y + I1.y) / 2.0 }; let midP = { x: (data_nodes[P.source].x + data_nodes[P.target].x) / 2.0, y: (data_nodes[P.source].y + data_nodes[P.target].y) / 2.0 }; return Math.max( 0, 1 - (2 * euclidean_distance(midP, midI)) / euclidean_distance(I0, I1) ); } function visibility_compatibility(P, Q) { return Math.min(edge_visibility(P, Q), edge_visibility(Q, P)); } function compatibility_score(P, Q) { return ( angle_compatibility(P, Q) * scale_compatibility(P, Q) * position_compatibility(P, Q) * visibility_compatibility(P, Q) ); } function are_compatible(P, Q) { return compatibility_score(P, Q) >= compatibility_threshold; } function compute_compatibility_lists() { for (let e = 0; e < data_edges.length - 1; e++) { for (let oe = e + 1; oe < data_edges.length; oe++) { // don't want any duplicates if (are_compatible(data_edges[e], data_edges[oe])) { compatibility_list_for_edge[e].push(oe); compatibility_list_for_edge[oe].push(e); } } } } /*** ************************ ***/ /*** Main Bundling Loop Methods ***/ let forcebundle = function () { let S = S_initial; let I = I_initial; let P = P_initial; initialize_edge_subdivisions(); initialize_compatibility_lists(); update_edge_divisions(P); compute_compatibility_lists(); for (let cycle = 0; cycle < C; cycle++) { for (let iteration = 0; iteration < I; iteration++) { let forces = []; for (let edge = 0; edge < data_edges.length; edge++) { forces[edge] = apply_resulting_forces_on_subdivision_points( edge, P, S ); } for (let e = 0; e < data_edges.length; e++) { for (let i = 0; i < P + 1; i++) { subdivision_points_for_edge[e][i].x += forces[e][i].x; subdivision_points_for_edge[e][i].y += forces[e][i].y; } } } // prepare for next cycle S = S / 2; P = P * P_rate; I = I_rate * I; update_edge_divisions(P); //console.log('C' + cycle); //console.log('P' + P); //console.log('S' + S); } return subdivision_points_for_edge; }; /*** ************************ ***/ /*** Getters/Setters Methods ***/ forcebundle.nodes = function (nl) { if (arguments.length === 0) { return data_nodes; } else { data_nodes = nl; } return forcebundle; }; forcebundle.edges = function (ll) { if (arguments.length === 0) { return data_edges; } else { data_edges = filter_self_loops(ll); //remove edges to from to the same point } return forcebundle; }; forcebundle.bundling_stiffness = function (k) { if (arguments.length === 0) { return K; } else { K = k; } return forcebundle; }; forcebundle.step_size = function (step) { if (arguments.length === 0) { return S_initial; } else { S_initial = step; } return forcebundle; }; forcebundle.cycles = function (c) { if (arguments.length === 0) { return C; } else { C = c; } return forcebundle; }; forcebundle.iterations = function (i) { if (arguments.length === 0) { return I_initial; } else { I_initial = i; } return forcebundle; }; forcebundle.iterations_rate = function (i) { if (arguments.length === 0) { return I_rate; } else { I_rate = i; } return forcebundle; }; forcebundle.subdivision_points_seed = function (p) { if (arguments.length == 0) { return P; } else { P = p; } return forcebundle; }; forcebundle.subdivision_rate = function (r) { if (arguments.length === 0) { return P_rate; } else { P_rate = r; } return forcebundle; }; forcebundle.compatibility_threshold = function (t) { if (arguments.length === 0) { return compatibility_threshold; } else { compatibility_threshold = t; } return forcebundle; }; /*** ************************ ***/ return forcebundle; }48:T4675,## LICENSE GNU GENERAL PUBLIC LICENSE Version 2, June 1991 Copyright (C) 1989, 1991 Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA Everyone is permitted to copy and distribute verbatim copies of this license document, but changing it is not allowed. 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It is safest to attach them to the start of each source file to most effectively convey the exclusion of warranty; and each file should have at least the "copyright" line and a pointer to where the full notice is found. {description} Copyright (C) {year} {fullname} This program is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with this program; if not, write to the Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA. Also add information on how to contact you by electronic and paper mail. If the program is interactive, make it output a short notice like this when it starts in an interactive mode: Gnomovision version 69, Copyright (C) year name of author Gnomovision comes with ABSOLUTELY NO WARRANTY; for details type `show w'. This is free software, and you are welcome to redistribute it under certain conditions; type `show c' for details. The hypothetical commands `show w' and `show c' should show the appropriate parts of the General Public License. Of course, the commands you use may be called something other than `show w' and `show c'; they could even be mouse-clicks or menu items--whatever suits your program. You should also get your employer (if you work as a programmer) or your school, if any, to sign a "copyright disclaimer" for the program, if necessary. Here is a sample; alter the names: Yoyodyne, Inc., hereby disclaims all copyright interest in the program `Gnomovision' (which makes passes at compilers) written by James Hacker. {signature of Ty Coon}, 1 April 1989 Ty Coon, President of Vice This General Public License does not permit incorporating your program into proprietary programs. If your program is a subroutine library, you may consider it more useful to permit linking proprietary applications with the library. If this is what you want to do, use the GNU Lesser General Public License instead of this License.49:[{"id":"8c4c24c2789793540bd1c9dd52996cd55fc1e1916bd1c9f8fcc460594e8e8e7ca2552954b00aa48ceb724f8bdb4cf14257c9f7fdcb5470ee43470f17dce7a0c3","href":"https://static.observableusercontent.com/files/8c4c24c2789793540bd1c9dd52996cd55fc1e1916bd1c9f8fcc460594e8e8e7ca2552954b00aa48ceb724f8bdb4cf14257c9f7fdcb5470ee43470f17dce7a0c3","name":"airlines@1.json","type":"application/json","lastModified":1705944526582.958,"size":78580}] 43:{"id":"7c6edad451124623","slug":null,"title":"Force Edge Bundling","thumbnail":"4e0f93fbca75958a3bff15eab044111c6fa1d449491da2cf0fe1b55b2cc6ca4c","access_level":"public","create_time":"$D2024-01-22T17:28:46.582Z","update_time":"$D2024-01-22T17:28:46.582Z","view_time":null,"first_public_time":"$D2024-01-22T17:28:46.582Z","has_unpublished_edits":null,"fork":{"id":"67def5cb48f2f6c4","slug":"force-edge-bundling","title":"Force Edge Bundling","owner":{"id":"cd3c1e49fc84d010","login":"john-guerra","name":"John Alexis Guerra Gómez"}},"stars":0,"starred":false,"owner":{"type":"team","id":"39eb8dd4c906cd6c","login":"rolyhudson","name":"","avatar_url":"https://avatars-next.observableusercontent.com/11a061b4eb5bd17787fef60475aac7edb528a33327c9914e5ddcd149493e8cb7","tier":"starter_2024","bio":"","following":false},"version":198,"publish_version":null,"role":null,"authored":false,"authors":[{"type":"individual","id":"cd83edde98ad3724","login":"rolyhudson","name":"","avatar_url":"https://avatars-next.observableusercontent.com/11a061b4eb5bd17787fef60475aac7edb528a33327c9914e5ddcd149493e8cb7","tier":null,"bio":"","following":false}],"members":[{"type":"individual","id":"cd83edde98ad3724","login":"rolyhudson","name":"","avatar_url":"https://avatars-next.observableusercontent.com/11a061b4eb5bd17787fef60475aac7edb528a33327c9914e5ddcd149493e8cb7","tier":null,"role":"editor"}],"comments":[],"custom_thumbnail":false,"trashed":false,"lapsed":null,"subscribed":null,"forks":0,"collection":null,"type":"notebook","body":{"titling":"auto","title":"Force Edge Bundling","cells":[{"id":0,"value":"# Force Edge Bundling\n\nBundles edges together using a force simulation. Adaptation of the [Force Directed Edge Bundling d3 plugin](https://github.com/upphiminn/d3.ForceBundle) to make it work with ES6 and in Observable, while also fixing [some bugs](https://github.com/upphiminn/d3.ForceBundle/pull/11). Compare with the [hierarchical edge bundling](https://observablehq.com/@d3/hierarchical-edge-bundling).\n\nMake sure no two points have the same x,y coordinates\n\n## Usage\n\n```js\nimport {edgeBundling} from \"@john-guerra/force-edge-bundling\"\n\n// or if you want the original d3.forceBundle \nimport {ForceEdgeBundling} from \"@john-guerra/force-edge-bundling\"\n```\n\nSeems a bit slow for larger networks. Here is the original example with airline data\n\nInspired by the experiment by [Stuart Thompson](https://observablehq.com/@stuartathompson/force-edge-bundling)","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"","database":"$undefined"},{"id":183,"value":"viewof useEdgeBundling = Inputs.toggle({\n label: \"Use Edge Bundling\",\n value: true\n})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":75,"value":"viewof compatibility_threshold = Inputs.range([0, 1], {\n label: \"Compatibility threshold\",\n value: 0.6,\n step: 0.01\n})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":76,"value":"viewof bundling_stiffness = Inputs.range([0, 60], {\n label: \"Bundling Stiffness\",\n value: 0.1,\n step: 0.01\n})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":77,"value":"viewof step_size = Inputs.range([0, 1], {\n label: \"Step Size\",\n value: 0.2,\n step: 0.01\n})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":62,"value":"{\n // run the edgeBundling, resulting paths stored in airlinesGraph.links[i].path\n const bundling = edgeBundling(airlinesGraph, {\n compatibility_threshold,\n bundling_stiffness,\n step_size\n });\n \n // use bundling.update() to recompute, useful inside the tick function of a forceSimulation\n\n return drawGraph(airlinesGraph);\n}","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":110,"value":"// Toy example\n{\n const nodes = [\n { id: \"a\", x: 5, y: 15 },\n { id: \"b\", x: 17, y: 14 },\n { id: \"c\", x: 17, y: 15 },\n { id: \"d\", x: 17, y: 20 }\n ],\n links = [\n { source: \"a\", target: \"b\" },\n { source: \"a\", target: \"c\" },\n { source: \"a\", target: \"d\" },\n ];\n const bundling = edgeBundling(\n { nodes, links },\n {\n compatibility_threshold,\n bundling_stiffness,\n step_size\n }\n );\n // then links will contain the bundles in the path attribute\n\n return drawGraph({ nodes, links });\n\n // (Optional) To update the bundling call, useful for force simulations\n bundling.update();\n}","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":53,"value":"$45","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":22,"value":"$46","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":5,"value":"$47","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":54,"value":"height = 500;","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":39,"value":"airlinesGraph = FileAttachment(\"airlines@1.json\").json()","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":13,"value":"$48","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"","database":"$undefined"}],"files":"$W49","stdlib":"1"}} 44:"$43:body"