2e:null 2f:["$","title",null,{"children":"k-d trees Nearest Neighbour Iterative Algorithm | Chathura Jayalath | Observable"}] 34:T546,function kdNeighborsInRange(root, searchPoint, searchRadius){ if(root == null){ return []; } const retVal = []; const stack = [ [root, 0] ]; const squaredSearchDist = searchRadius * searchRadius; while(0 < stack.length){ //console.log(squaredSearchDist, stack.map(d => (d[0] == null)? "x" : d[0].point) ) const [current, depth] = stack.pop(); const curSquaredDist = calcSquaredDistance(searchPoint, current.point); if(curSquaredDist <= squaredSearchDist){ retVal.push(current.point); } const dim = depth % 2; let goodSide = null; let badSide = null; if(searchPoint[dim] < current.point[dim]){ goodSide = current.left; badSide = current.right; }else{ goodSide = current.right; badSide = current.left; } //console.log(dim, current.point, curSquaredDist); if(badSide != null){ const squaredBadSideDist = (searchPoint[dim] - current.point[dim]) * (searchPoint[dim] - current.point[dim]); //console.log("badDist : " + squaredBadSideDist); if(squaredBadSideDist < squaredSearchDist){ stack.push([badSide, depth + 1]); //console.log("badside pushed"); } } if(goodSide != null){ stack.push([goodSide, depth + 1]); } } //console.log(retVal); return retVal; }35:T624,function kdAllNearestNeighbors(root, searchPoint){ if(root == null){ return [Infinity, []]; } const retVal = []; const stack = [ [root, 0] ]; let minDistPoint = null; let minSquaredDist = Infinity; while(0 < stack.length){ //console.log(minSquaredDist, minDistPoint, stack.map(d => (d[0] == null)? "x" : d[0].point) ) const [current, depth] = stack.pop(); const curSquaredDist = calcSquaredDistance(searchPoint, current.point); if(curSquaredDist < minSquaredDist){ minSquaredDist = curSquaredDist; minDistPoint = current.point; retVal.length = 0; retVal.push(minDistPoint); } else if(curSquaredDist == minSquaredDist){ retVal.push(current.point); } const dim = depth % 2; let goodSide = null; let badSide = null; if(searchPoint[dim] < current.point[dim]){ goodSide = current.left; badSide = current.right; }else{ goodSide = current.right; badSide = current.left; } //console.log(dim, current.point, curSquaredDist, minSquaredDist); if(badSide != null){ const squaredBadSideDist = (searchPoint[dim] - current.point[dim]) * (searchPoint[dim] - current.point[dim]); //console.log("badDist : " + squaredBadSideDist); if(squaredBadSideDist < minSquaredDist){ stack.push([badSide, depth + 1]); //console.log("badside pushed"); } } if(goodSide != null){ stack.push([goodSide, depth + 1]); } } //console.log(minSquaredDist, retVal); return retVal; }36:T583,function kdNearestNeighbor(root, searchPoint){ if(root == null){ return null; } const stack = [ [root, 0] ]; let minDistPoint = null; let minSquaredDist = Infinity; while(0 < stack.length){ //console.log(minSquaredDist, minDistPoint, stack.map(d => (d[0] == null)? "x" : d[0].point) ) const [current, depth] = stack.pop(); const curSquaredDist = calcSquaredDistance(searchPoint, current.point); if(curSquaredDist < minSquaredDist){ minSquaredDist = curSquaredDist; minDistPoint = current.point; } const dim = depth % 2; let goodSide = null; let badSide = null; if(searchPoint[dim] < current.point[dim]){ goodSide = current.left; badSide = current.right; }else{ goodSide = current.right; badSide = current.left; } //console.log(dim, current.point, curSquaredDist, minSquaredDist); if(badSide != null){ const squaredBadSideDist = (searchPoint[dim] - current.point[dim]) * (searchPoint[dim] - current.point[dim]); //console.log("badDist : " + squaredBadSideDist); if(squaredBadSideDist < minSquaredDist){ stack.push([badSide, depth + 1]); //console.log("badside pushed"); } } if(goodSide != null){ stack.push([goodSide, depth + 1]); } } //console.log(minSquaredDist, minDistPoint); return minDistPoint; }37:T1015,function drawSpacialMap(array, searchPoint, searchRadius, padding = 50) { const kdroot = generateKdTreeFromArray(array); const [svgElement, svg] = getSVG(); const xdomain = d3.extent(array, d => d[0]); const ydomain = d3.extent(array, d => d[1]); const comDomain = [Math.min(xdomain[0],ydomain[0]), Math.max(xdomain[1],ydomain[1])]; const xScale = d3.scaleLinear() .domain([comDomain[0] * 0.9, comDomain[1] * 1.1]) .range([padding, xyWH - padding]) .nice(); const yScale = d3.scaleLinear() .domain([comDomain[0] * 0.9, comDomain[1] * 1.1]) .range([xyWH - padding, padding]) .nice(); const radiDomain = (array[0].length > 2)? [0, comDomain[1] * 1.1] : [0,array.length]; const radiusScale = (array[0].length > 2)? d3.scaleLinear().domain([0, comDomain[1] * 1.1]).range([0, (xyWH - padding - padding)]) : d3.scaleLinear().domain(radiDomain).range([padding * 0.1, padding]); // draw xAxis and ticks svg .append("g") .attr("transform", `translate(${0},${xyMargin})`) .call(d3.axisBottom(xScale).tickSize(xyWH - xyMargin - xyMargin)) .style("opacity",0.2) .attr("stroke-dasharray", "2,2") // draw yAxis and ticks svg .append("g") .attr("transform", `translate(${xyWH},${0})`) .call(d3.axisLeft(yScale).tickSize(xyWH - xyMargin - xyMargin)) .style("opacity",0.2) .attr("stroke-dasharray", "2,2") // draw query point if(searchPoint != null){ const searchArea = svg.append("g") searchArea .append("circle") .attr("r", 10) .attr("cx", xScale(searchPoint[0])) .attr("cy", yScale(searchPoint[1])) .style("fill","red") .style("stroke", "black") .style("stroke-width", 2) if(searchRadius != null){ // draw search radius searchArea .append("circle") .attr("r", radiusScale(searchRadius)) .attr("cx", xScale(searchPoint[0])) .attr("cy", yScale(searchPoint[1])) .style("fill","yellow") .style("stroke", "none") .style("opacity", 0.1) } } // draw the actual points const container = svg.append("g") const allCircles = container .selectAll("circle") .data(array) .join("circle") .attr("cx", d => xScale(d[0])) .attr("cy", d => yScale(d[1])) .attr("r", (d,i) => (d.length > 2)? radiusScale(d[2]) : radiusScale(i)) .style("fill", (d,i) => d3.schemeCategory10[i]) .style("opacity", 0.8) // add hovering text to points allCircles .append("title") .text((d,i) => "x : " + d[0] + " y : " + d[1] + "\n" + ( (d.length > 3) ? d[3] : String.fromCharCode(65 + i) ) ) // draw divisor lines const stack = [ [kdroot,0,[xScale.invert(padding),xScale.invert(xyWH - padding)], [yScale.invert(xyWH - padding),yScale.invert(padding)]] ]; while(0 < stack.length){ const [current, depth, xrange, yrange] = stack.pop(); const dim = depth % 2; if(current != null){ // Draw hyper-plane svg .append("line") .attr("x1", xScale( (dim == 0)? current.point[0] : xrange[0]) ) .attr("y1", yScale( (dim == 0)? yrange[0] : current.point[1]) ) .attr("x2", xScale( (dim == 0)? current.point[0] : xrange[1]) ) .attr("y2", yScale( (dim == 0)? yrange[1] : current.point[1]) ) .style("stroke", d3.schemeCategory10[depth]) .style("stroke-width", Math.max(padding * 0.04, 0.5)) .style("opacity", 1) stack.push([ current.left, depth + 1, [xrange[0], (dim==0)? current.point[0] : xrange[1] ], [yrange[0], (dim==0)? yrange[1] : current.point[1] ] ]); stack.push([ current.right, depth + 1, [(dim==0)? current.point[0] : xrange[0], xrange[1] ], [(dim==0)? yrange[0] : current.point[1], yrange[1] ] ]); } } return svgElement; }38:[{"id":"85644ef109d7a408c2d3ceb61dd5a647df6975ea0f66dfd1f581e0cc29b76202c1fbcd621a0470a899db25abcae889996003795af314d376b2599f3c48928848","href":"https://static.observableusercontent.com/files/85644ef109d7a408c2d3ceb61dd5a647df6975ea0f66dfd1f581e0cc29b76202c1fbcd621a0470a899db25abcae889996003795af314d376b2599f3c48928848","name":"airports.csv","type":"text/csv","lastModified":1619568702035.119,"size":1127366}] 32:{"id":"c1ff9213928b9da0","slug":"k-d-trees","title":"k-d trees Nearest Neighbour Iterative Algorithm","thumbnail":"ddef95e3389c58220b74ea37e4c7ef125ce4161da1fea53fb47fee9b5422573f","access_level":"public","create_time":"$D2021-04-27T03:26:55.538Z","update_time":"$D2021-05-08T16:58:36.254Z","view_time":null,"first_public_time":"$D2021-04-27T19:09:44.511Z","has_unpublished_edits":null,"fork":false,"stars":2,"starred":false,"owner":{"type":"team","id":"faa67bfd1359f951","login":"deamonpog","name":"Chathura 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Algorithm`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":960,"value":"md`Currently only works for 2D (k = 2)`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":28,"value":"knownArray = [[3, 6], [17, 15], [13, 15], [6, 12], [9, 1], [2, 7], [10, 19]]","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":116,"value":"knownArray2 = [[2,3], [4,2], [4,5],[3,3], [1,5], [4,4] ]","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":188,"value":"drawSpacialMap(knownArray,searchPoint1, searchRadius1)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":435,"value":"searchPoint1 = [10,12]","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":437,"value":"searchRadius1 = 5","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":430,"value":"kdNearestNeighbor(root1, searchPoint1)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":190,"value":"drawSpacialMap(knownArray2, searchPoint2, searchRadius2)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":337,"value":"searchPoint2 = [2.5, 4]","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":339,"value":"searchRadius2 = 1.3","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":802,"value":"root3 = generateKdTreeFromArray(knownArray_withRadius)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":776,"value":"drawSpacialMap(knownArray_withRadius, searchPoint_3_withRadius, searchRadius_3_withRadius)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":822,"value":"kdNeighborsInRangeWithRadius(root3, maxRadius_3, searchPoint_3_withRadius, searchRadius_3_withRadius)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":765,"value":"knownArray_withRadius = [[3, 6, 1], [17, 15, 2], [13, 15, 1], [6, 12, 1], [9, 1, 1], [2, 7, 1], [10, 19, 1]]","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":792,"value":"searchPoint_3_withRadius = [16,10]","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":790,"value":"searchRadius_3_withRadius = 3.5","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":810,"value":"maxRadius_3 = d3.max(knownArray_withRadius, d => d[2])","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":844,"value":"md`### Find All Neighbor circles that collide with a given range of a given point`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":799,"value":"function kdNeighborsInRangeWithRadius(root, maxNbrRadius, searchPoint, searchRadius){\n const retVal = kdNeighborsInRange(root, searchPoint, searchRadius + maxNbrRadius);\n return retVal.filter(d => \n calcSquaredDistance(searchPoint, [d[0],d[1]]) <= (searchRadius + d[2]) * (searchRadius + d[2]) );\n}","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":484,"value":"md`### Find All Neighbors in a given range of a given point`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":500,"value":"kdNeighborsInRange(root2, searchPoint2, searchRadius2)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":468,"value":"$34","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":475,"value":"md`### Find All Nearest Neighbors to a given point`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":462,"value":"kdAllNearestNeighbors(root2, searchPoint2)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":448,"value":"$35","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":471,"value":"md`### Find the Nearest Neighbor to a given point (returns only one resulting point)`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":320,"value":"kdNearestNeighbor(root2, searchPoint2)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":310,"value":"$36","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":605,"value":"md`### Drawing the k-d tree map`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":18,"value":"$37","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":118,"value":"root1 = generateKdTreeFromArray(knownArray)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":121,"value":"root2 = generateKdTreeFromArray(knownArray2)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":520,"value":"md`### Generate k-d Tree from an array of points`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":738,"value":"md`#### By iterating the items on recursive Insertion`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":149,"value":"function generateKdTreeFromArray(array){\n let r = null;\n const divs = [];\n for(let i = 0; i < array.length; i++){\n r = kdInsert(array[i], r);\n }\n return r;\n}","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":4,"value":"function kdNewNode(in_point){\n return ({ point: in_point, left: null, right: null });\n}","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":742,"value":"md`#### Recursive Insertion`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":5,"value":"function kdInsertRec(point, root, depth){\n if(root == null){\n return kdNewNode(point);\n }\n \n const cur_dim = depth % 2;\n \n if(point[cur_dim] < root.point[cur_dim]){\n root.left = kdInsertRec(point, root.left, depth + 1);\n }else{\n root.right = kdInsertRec(point, root.right, depth + 1);\n }\n \n return root\n}","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":7,"value":"function kdInsert(point, root){\n return kdInsertRec(point, root, 0);\n}","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":9,"value":"function kdSearchRec(point, root, depth){\n if(root == null){\n return false;\n }\n if(point[0] == root.point[0] && point[1] == root.point[1]){\n return true;\n }\n \n const cur_dim = depth % 2;\n \n if(point[cur_dim] < root.point[cur_dim]){\n return kdSearchRec(point, root.left, depth + 1);\n }else{\n return kdSearchRec(point, root.right, depth + 1);\n }\n}","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":11,"value":"function kdSearch(point, root){\n return kdSearchRec(point, root, 0);\n}","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":14,"value":"function calcDistance(p,q){\n return Math.sqrt( ((p[0] - q[0]) * (p[0] - q[0])) + ((p[1] - q[1]) * (p[1] - q[1])) );\n}","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":15,"value":"function calcSquaredDistance(p,q){\n return ((p[0] - q[0]) * (p[0] - q[0])) + ((p[1] - q[1]) * (p[1] - q[1]));\n}","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":131,"value":"md`## Helpers`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":401,"value":"xyLength = 700","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":403,"value":"xyMargin = 10","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":883,"value":"xyWH = xyLength - xyMargin - xyMargin","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":22,"value":"function getSVG(useBorder) {\n const svgElement = DOM.svg(xyLength, xyLength);\n const svg = d3.select(svgElement);\n \n const chart = svg.append(\"g\").attr(\"transform\",`translate(${xyMargin},${xyMargin})`);\n \n if(useBorder){ svg.append(\"rect\").attr(\"width\",xyLength).attr(\"height\",xyLength).attr(\"fill\",\"none\").attr(\"stroke\",\"black\");\n }\n \n return [svgElement, chart];\n}","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":526,"value":"md`## Data based test`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":559,"value":"drawSpacialMap(airport_locations, null, null, 3)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":697,"value":"kdNeighborsInRange(airport_kdtree_root, [80,8], 10)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":694,"value":"airport_kdtree_root = generateKdTreeFromArray(\n airports.map(d => [d.Longitude, -d.Latitude, d.Name])\n);","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":535,"value":"airport_locations = airports.map(d => [d.Longitude, d.Latitude, scaleAltitude(d.Altitude), d.Name])","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":968,"value":"scaleAltitude = d3.scaleLinear().domain(d3.extent(airports,d => d.Altitude)).range([0,2]);","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":532,"value":"airports_csv_file = FileAttachment(\"airports.csv\").url();","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":529,"value":"airports = {\n const data = await d3.csv(airports_csv_file,d3.autoType);\n data.splice(data.findIndex(d => d.Latitude == -90), 1, -89.999999); // fix inifinity problem\n return data;\n}","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":128,"value":"md`## Import Libraries`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":20,"value":"d3 = require(\"d3@6\")","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":546,"value":"import {select} from \"@jashkenas/inputs\"","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"}],"files":"$W38","stdlib":"1","titling":"auto"}} 33:"$32:body"