2b:null 2c:["$","title",null,{"children":"Leaf Auto Generation | Chuncheng | Observable"}] 31:T698,/** * 计算二维Gabor小波在指定位置的值 * @param {number} x - x坐标（相对于中心） * @param {number} y - y坐标（相对于中心） * @param {Object} params - Gabor参数 * @param {number} params.sigma - 高斯包络的标准差 * @param {number} params.theta - 方向角度（弧度） * @param {number} params.lambda - 波长（空间频率的倒数） * @param {number} params.psi - 相位偏移（默认0） * @param {number} params.gamma - 空间纵横比（默认1.0） * @returns {Object} 包含实部和虚部值的对象 */ function gabor2D(x, y, fixTheta = false) { // 默认参数 let { sigma = 4.0, theta = 0, lambda = 8.0, psi = 0, gamma = 1.0 } = gaborParams; if (!fixTheta) theta = Math.random() * Math.PI * 2; // 计算旋转后的坐标 const cosTheta = Math.cos(theta); const sinTheta = Math.sin(theta); const xPrime = x * cosTheta + y * sinTheta; const yPrime = -x * sinTheta + y * cosTheta; // 计算sigma_x和sigma_y const sigma_x = sigma; const sigma_y = sigma / gamma; // 高斯包络部分 const gaussExp = -0.5 * ((xPrime * xPrime) / (sigma_x * sigma_x) + (yPrime * yPrime) / (sigma_y * sigma_y)); const gaussian = Math.exp(gaussExp); // 归一化因子 const norm = 1 / (2 * Math.PI * sigma_x * sigma_y); // 正弦部分 const frequency = (2 * Math.PI) / lambda; const phase = frequency * xPrime + psi; // 实部和虚部 const real = norm * gaussian * Math.cos(phase); const imag = norm * gaussian * Math.sin(phase); return { real, imag, magnitude: Math.sqrt(real * real + imag * imag), phase: Math.atan2(imag, real) }; }32:T7cd, class KDTree { constructor(points, indices = null) { if (!indices) { indices = points.map((_, i) => i); } this.root = this.buildTree(points, indices, 0); this.points = points; } buildTree(points, indices, depth) { if (indices.length === 0) return null; const axis = depth % 2; // 2D: 0 for x, 1 for y const sorted = [...indices].sort((a, b) => points[a][axis] - points[b][axis] ); const median = Math.floor(sorted.length / 2); const node = new KDNode( points[sorted[median]], sorted[median], depth ); node.left = this.buildTree(points, sorted.slice(0, median), depth + 1); node.right = this.buildTree(points, sorted.slice(median + 1), depth + 1); return node; } nearestNeighbor(target) { let best = { index: -1, distance: Infinity }; this.search(this.root, target, best); return best; } search(node, target, best) { if (!node) return; const dx = node.point.x - target.x; const dy = node.point.y - target.y; const distance = Math.sqrt(dx * dx + dy * dy); if (distance < best.distance) { best.index = node.index; best.distance = distance; best.point = node.point; } const axis = node.depth % 2; const diff = axis === 0 ? target.x - node.point.x : target.y - node.point.y; // 首先搜索更可能包含最近点的子树 const first = diff <= 0 ? node.left : node.right; const second = diff <= 0 ? node.right : node.left; this.search(first, target, best); // 如果另一边可能包含更近的点，也搜索一下 if (Math.abs(diff) < best.distance) { this.search(second, target, best); } } } 33:[] 2f:{"id":"e56773381f4b742b","slug":"leaf-auto-generation","title":"Leaf Auto Generation","thumbnail":"e68e3cd4740dd7ea5e3513d4c7db683a776386c651feab3474ce1b90fcba53aa","access_level":"public","create_time":"$D2026-01-16T01:39:09.138Z","update_time":"$D2026-01-16T10:56:20.645Z","view_time":null,"first_public_time":"$D2026-01-16T05:29:54.685Z","fork":false,"stars":1,"starred":false,"owner":{"type":"team","id":"bcd65cef1cb4d2ed","login":"listenzcc","name":"Chuncheng","avatar_url":"https://avatars-next.observableusercontent.com/bb3c68e77a708a587ffc2d663bb83421f20d67991dbe6c1623c6e5d2fb73d15e","tier":"starter_2024"},"version":446,"publish_version":null,"role":null,"authored":false,"authors":[{"type":"individual","id":"16328058352682a8","login":"listenzcc","name":"Chuncheng","avatar_url":"https://avatars-next.observableusercontent.com/bb3c68e77a708a587ffc2d663bb83421f20d67991dbe6c1623c6e5d2fb73d15e","tier":null}],"members":[{"type":"individual","id":"16328058352682a8","login":"listenzcc","name":"Chuncheng","avatar_url":"https://avatars-next.observableusercontent.com/bb3c68e77a708a587ffc2d663bb83421f20d67991dbe6c1623c6e5d2fb73d15e","tier":null,"role":"editor"},{"type":"team","id":"bcd65cef1cb4d2ed","login":"listenzcc","name":"Chuncheng","avatar_url":"https://avatars-next.observableusercontent.com/bb3c68e77a708a587ffc2d663bb83421f20d67991dbe6c1623c6e5d2fb73d15e","tier":"starter_2024","role":"editor"}],"comments":[],"custom_thumbnail":true,"trashed":false,"subscribed":null,"forks":0,"collection":null,"type":"notebook","body":{"title":"Leaf Auto Generation","cells":[{"id":0,"value":"# Leaf Auto Generation","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":64,"value":"---\n\n## Grids","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":9,"value":"viewof option = Inputs.form({\n grids: Inputs.range([100, 200], { label: \"Grids\", step: 1, value: 150 }),\n size: Inputs.range([10, 50], { label: \"Size\", step: 0.1 })\n})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":403,"value":"viewof useFixedToggle = Inputs.toggle({\n label: \"Use fixed toggle\",\n value: false\n})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":199,"value":"{\n let selectedGrids, nearestPair;\n for (let i = 0; i < 1000; ++i) {\n selectedGrids = selectGrids(50);\n nearestPair = findNearestPair(selectedGrids);\n\n if (nearestPair === undefined) break;\n\n addNode(nearestPair);\n yield draw(selectedGrids, nearestPair);\n }\n\n yield draw(selectedGrids, nearestPair);\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":320,"value":"viewof restartButton = Inputs.button(\"Restart\")","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":195,"value":"{\n stepButton;\n let selectedGrids = selectGrids(),\n nearestPair = findNearestPair(selectedGrids);\n\n addNode(nearestPair);\n return draw(selectedGrids, nearestPair);\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":161,"value":"viewof stepButton = Inputs.button(\"Step\")","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":410,"value":"colormap(0.5)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":408,"value":"colormap = d3\n .scaleSequential()\n .domain([0, 1])\n .interpolator(\n d3.interpolateRgbBasis([\n \"#ffe5d5\",\n \"#ffbdad\",\n \"#d99688\",\n \"#b17164\",\n \"#8a4e41\",\n \"#773d31\"\n // \"#5d251a\"\n ])\n )","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":70,"value":"function draw(selectedGrids, nearestPair) {\n let n = nodes.length;\n\n return Plot.plot({\n color: { legend: true, scheme: \"RdYlGn\" },\n r: { range: [1, 5] },\n aspectRatio: 1.0,\n width: 800,\n marks: [\n Plot.raster(grids, { x: \"x\", y: \"y\", fill: \"value\", pixelSize: 10 }),\n Plot.dot(nodes, {\n x: \"x\",\n y: \"y\",\n fill: \"white\",\n r: (d, i) => n - i\n // fill: (d, i) => colormap(1 - i / n)\n }),\n Plot.dot(selectedGrids[0] ? selectedGrids : [], {\n x: \"x\",\n y: \"y\",\n fill: \"red\"\n }),\n Plot.arrow(nearestPair ? [nearestPair] : [], {\n x1: (d) => d.n.x,\n x2: (d) => d.s.x,\n y1: (d) => d.n.y,\n y2: (d) => d.s.y\n })\n ]\n });\n}","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":60,"value":"---\n\n## Gabor kernel","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":40,"value":"viewof gaborParams = Inputs.form({\n sigma: Inputs.range([1, 10], {\n label: \"Sigma (σ)\",\n step: 0.1,\n value: 2.5,\n description: \"高斯包络标准差，控制滤波器大小\"\n }),\n\n theta: Inputs.range([0, Math.PI], {\n label: \"Theta (θ) - 方向角\",\n step: 0.01,\n value: 0,\n description: \"滤波器方向（弧度），0=水平，π/2=垂直\"\n }),\n\n lambda: Inputs.range([1, 20], {\n label: \"Lambda (λ) - 波长\",\n step: 0.1,\n value: 11.3,\n description: \"正弦波波长，λ=1/f，控制条纹密度\"\n }),\n\n psi: Inputs.range([-Math.PI, Math.PI], {\n label: \"Psi (ψ) - 相位\",\n step: 0.01,\n value: 0,\n description: \"相位偏移，ψ=0:偶对称，ψ=-π/2:奇对称\"\n }),\n\n gamma: Inputs.range([0.1, 2], {\n label: \"Gamma (γ) - 纵横比\",\n step: 0.1,\n value: 1.0,\n description: \"空间纵横比，γ=1:圆形，γ<1:y向扁，γ>1:x向扁\"\n }),\n\n // 可选：滤波器尺寸\n kernelSize: Inputs.range([3, 51], {\n label: \"核尺寸\",\n step: 2,\n value: 15,\n description: \"滤波器核大小（奇数）\"\n })\n})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":27,"value":"{\n const size = 5,\n array = [];\n\n let g;\n\n for (let x = -size; x < size; x += 0.1) {\n for (let y = -size; y < size; y += 0.1) {\n g = gabor2D(x, y, true).real;\n array.push({ x, y, g });\n }\n }\n\n return Plot.plot({\n x: { nice: true, ticks: [-size, size] },\n y: { nice: true, ticks: [-size, size] },\n width: 400,\n color: { legend: true, scheme: \"RdBu\" },\n aspectRatio: 1,\n marks: [Plot.raster(array, { x: \"x\", y: \"y\", fill: \"g\", pixelSize: 4 })]\n });\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":23,"value":"$31","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":343,"value":"---\n\n## Function and Variables","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":275,"value":"data = selectGrids()","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":150,"value":"nearestPair = {\n let nearestPair = findNearestPair(selectedGrids);\n\n // nearestPair = findNearestPairKDTree(nodes, selectedGrids);\n\n addNode(nearestPair);\n\n return nearestPair;\n}","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":157,"value":"function addNode(nearestPair) {\n if (nearestPair === undefined) return;\n\n const { size, grids: gridsNum } = option,\n r = size / gridsNum,\n { n, s } = nearestPair,\n x = n.x + (s.x - n.x) * 0.1,\n y = n.y + (s.y - n.y) * 0.1,\n g = d3.filter(\n grids,\n (g) => (Math.abs(x - g.x) < r) & (Math.abs(y - g.y) < r)\n )[0],\n node = { x, y, gi: g.i, gj: g.j };\n\n g.nodes.push(node);\n g.n += 1;\n\n nodes.push(node);\n}","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":147,"value":"/**\n * Find the nearest pair of nodes and selectedGrids by x-, y- coordinates.\n **/\nfunction findNearestPair(selectedGrids) {\n let minL2 = 100000000,\n l2,\n pair = {};\n\n if (selectedGrids[0] === undefined) return undefined;\n\n // nodes.map((n) => {\n // selectedGrids.map((s) => {\n // l2 = Math.pow(n.x - s.x, 2) + Math.pow(n.y - s.y, 2);\n // if (l2 < minL2) {\n // minL2 = l2;\n // Object.assign(pair, { n, s, l2 });\n // }\n // });\n // });\n\n grids\n .filter((g) => g.n > 0)\n .map((g) => {\n selectedGrids.map((s) => {\n l2 = Math.pow(g.x - s.x, 2) + Math.pow(g.y - s.y, 2);\n if (l2 < minL2) {\n minL2 = l2;\n Object.assign(pair, { g, s, l2 });\n }\n });\n });\n\n let node = pair.g.nodes[d3.randomInt(pair.g.nodes.length)()];\n Object.assign(pair, { n: node });\n\n return pair;\n}","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":132,"value":"selectedGrids = selectGrids();","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":121,"value":"function selectGrids(n = 30) {\n updateGrids();\n const negativeGrids = grids.filter((d) => d.value <= 0),\n selectedGrids = [],\n weights = negativeGrids.map((d) => -d.value),\n totalWeight = weights.reduce((sum, w) => sum + w, 0);\n\n for (let i = 0; i < n; ++i) {\n selectedGrids.push(\n weightedRandomLinear(negativeGrids, weights, totalWeight)\n );\n }\n\n return selectedGrids;\n}","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":119,"value":"/**\n * 按权重随机采样 - 线性搜索法\n * @param {Array} items - 待采样元素数组\n * @param {Array} weights - 权重数组，长度需与items相同\n * @returns {*} 采样到的元素\n */\nfunction weightedRandomLinear(items, weights, totalWeight) {\n // 计算总权重\n\n // 生成0到总权重之间的随机数\n let random = Math.random() * totalWeight;\n\n // 线性搜索：找到随机数落在哪个区间\n for (let i = 0; i < items.length; i++) {\n random -= weights[i];\n if (random <= 0) {\n return items[i];\n }\n }\n\n // 理论上不会执行到这里\n return items[items.length - 1];\n}","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":66,"value":"function updateGrids() {\n let dx,\n dy,\n n = nodes.length;\n\n if (n < 100) grids.map((g) => (g.value = 0));\n\n (n < 100 ? nodes : nodes.slice(n - 1)).map((node) => {\n grids.map((grid) => {\n dx = grid.x - node.x;\n dy = grid.y - node.y;\n if ((Math.abs(dx) < 3) & (Math.abs(dy) < 3))\n grid.value += gabor2D(dx, dy).real;\n });\n });\n return grids;\n}","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":13,"value":"nodes = {\n restartButton;\n const { size, grids: gridsNum } = option,\n r = size / gridsNum,\n scale = d3.scaleLinear().domain([0, 1]).range([0, size]),\n initNodes = 5,\n rnd = d3.randomUniform(scale(0.25), scale(0.75)),\n array = [];\n\n let x, y, g, node;\n for (let i = 0; i < initNodes; ++i) {\n x = rnd();\n y = rnd();\n if (useFixedToggle) {\n x = size * 0.9 + i * 0.5;\n y = size * 0.9 + i * 0.5;\n }\n\n g = d3.filter(\n grids,\n (g) => (Math.abs(x - g.x) < r) & (Math.abs(y - g.y) < r)\n )[0];\n node = { x, y, gi: g.i, gj: g.j };\n array.push(node);\n g.nodes.push(node);\n g.n += 1;\n }\n\n return array;\n}","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":22,"value":"nodes","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":7,"value":"grids = {\n restartButton;\n const { grids, size } = option,\n scale = d3.scaleLinear().domain([0, grids]).range([0, size]),\n array = [];\n\n let x, y;\n for (let i = 0; i < grids; ++i) {\n for (let j = 0; j < grids; ++j) {\n x = scale(i);\n y = scale(j);\n array.push({ i, j, x, y, value: 0, nodes: [], n: 0 });\n }\n }\n\n return array;\n}","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":12,"value":"grids","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":5,"value":"d3 = require(\"d3\")","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":206,"value":"class KDNode {\n constructor(point, index, depth, left = null, right = null) {\n this.point = point;\n this.index = index;\n this.depth = depth;\n this.left = left;\n this.right = right;\n }\n}","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":203,"value":"$32","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":209,"value":"/**\n * 使用K-D树加速最近对搜索\n */\nfunction findNearestPairKDTree(nodes, selectedGrids) {\n if (nodes.length === 0 || selectedGrids.length === 0) {\n return { distance: Infinity, nodeIndex: -1, gridIndex: -1 };\n }\n\n // 构建节点的K-D树\n const nodeTree = new KDTree(nodes);\n\n let minDistance = Infinity;\n let nearestNodeIndex = -1;\n let nearestGridIndex = -1;\n\n // 对每个网格点找最近的节点\n for (let i = 0; i < selectedGrids.length; i++) {\n const grid = selectedGrids[i];\n const nearest = nodeTree.nearestNeighbor(grid);\n\n if (nearest.distance < minDistance) {\n minDistance = nearest.distance;\n nearestNodeIndex = nearest.index;\n nearestGridIndex = i;\n }\n }\n\n return {\n distance: minDistance,\n nodeIndex: nearestNodeIndex,\n gridIndex: nearestGridIndex,\n n: nearestNodeIndex >= 0 ? nodes[nearestNodeIndex] : null,\n s: nearestGridIndex >= 0 ? selectedGrids[nearestGridIndex] : null\n };\n}","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"}],"files":"$W33","stdlib":"1","titling":"auto"}} 30:"$2f:body"