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{ bisect, conjugateGradient, nelderMead, norm2, scale, zeros, zerosM } from 'fmin';\nimport { circleCircleIntersection, circleOverlap, distance, intersectionArea } from './circleintersection';\n\n/** given a list of set objects, and their corresponding overlaps.\nupdates the (x, y, radius) attribute on each set such that their positions\nroughly correspond to the desired overlaps */\nexport function venn(areas, parameters?: any) {\n parameters = parameters || {};\n parameters.maxIterations = parameters.maxIterations || 500;\n const initialLayout = parameters.initialLayout || bestInitialLayout;\n const loss = parameters.lossFunction || lossFunction;\n\n // add in missing pairwise areas as having 0 size\n areas = addMissingAreas(areas);\n\n // initial layout is done greedily\n const circles = initialLayout(areas, parameters);\n\n // transform x/y coordinates to a vector to optimize\n const initial = [],\n setids = [];\n let setid;\n for (setid in circles) {\n // eslint-disable-next-line\n if (circles.hasOwnProperty(setid)) {\n initial.push(circles[setid].x);\n initial.push(circles[setid].y);\n setids.push(setid);\n }\n }\n\n // optimize initial layout from our loss function\n const solution = nelderMead(\n function (values) {\n const current = {};\n for (let i = 0; i < setids.length; ++i) {\n const setid = setids[i];\n current[setid] = {\n x: values[2 * i],\n y: values[2 * i + 1],\n radius: circles[setid].radius,\n // size : circles[setid].size\n };\n }\n return loss(current, areas);\n },\n initial,\n parameters\n );\n\n // transform solution vector back to x/y points\n const positions = solution.x;\n for (let i = 0; i < setids.length; ++i) {\n setid = setids[i];\n circles[setid].x = positions[2 * i];\n circles[setid].y = positions[2 * i + 1];\n }\n\n return circles;\n}\n\nconst SMALL = 1e-10;\n\n/** Returns the distance necessary for two circles of radius r1 + r2 to\nhave the overlap area 'overlap' */\nexport function distanceFromIntersectArea(r1, r2, overlap) {\n // handle complete overlapped circles\n if (Math.min(r1, r2) * Math.min(r1, r2) * Math.PI <= overlap + SMALL) {\n return Math.abs(r1 - r2);\n }\n\n return bisect(\n function (distance) {\n return circleOverlap(r1, r2, distance) - overlap;\n },\n 0,\n r1 + r2\n );\n}\n\n/** Missing pair-wise intersection area data can cause problems:\n treating as an unknown means that sets will be laid out overlapping,\n which isn't what people expect. To reflect that we want disjoint sets\n here, set the overlap to 0 for all missing pairwise set intersections */\nfunction addMissingAreas(areas) {\n areas = areas.slice();\n\n // two circle intersections that aren't defined\n const ids: number[] = [],\n pairs: any = {};\n let i, j, a, b;\n for (i = 0; i < areas.length; ++i) {\n const area = areas[i];\n if (area.sets.length == 1) {\n ids.push(area.sets[0]);\n } else if (area.sets.length == 2) {\n a = area.sets[0];\n b = area.sets[1];\n // @ts-ignore\n pairs[[a, b]] = true;\n // @ts-ignore\n pairs[[b, a]] = true;\n }\n }\n ids.sort((a, b) => {\n return a > b ? 1 : -1;\n });\n\n for (i = 0; i < ids.length; ++i) {\n a = ids[i];\n for (j = i + 1; j < ids.length; ++j) {\n b = ids[j];\n // @ts-ignore\n if (!([a, b] in pairs)) {\n areas.push({ sets: [a, b], size: 0 });\n }\n }\n }\n return areas;\n}\n\n/// Returns two matrices, one of the euclidean distances between the sets\n/// and the other indicating if there are subset or disjoint set relationships\nexport function getDistanceMatrices(areas, sets, setids) {\n // initialize an empty distance matrix between all the points\n const distances = zerosM(sets.length, sets.length),\n constraints = zerosM(sets.length, sets.length);\n\n // compute required distances between all the sets such that\n // the areas match\n areas\n .filter(function (x) {\n return x.sets.length == 2;\n })\n .map(function (current) {\n const left = setids[current.sets[0]],\n right = setids[current.sets[1]],\n r1 = Math.sqrt(sets[left].size / Math.PI),\n r2 = Math.sqrt(sets[right].size / Math.PI),\n distance = distanceFromIntersectArea(r1, r2, current.size);\n\n distances[left][right] = distances[right][left] = distance;\n\n // also update constraints to indicate if its a subset or disjoint\n // relationship\n let c = 0;\n if (current.size + 1e-10 >= Math.min(sets[left].size, sets[right].size)) {\n c = 1;\n } else if (current.size <= 1e-10) {\n c = -1;\n }\n constraints[left][right] = constraints[right][left] = c;\n });\n\n return { distances: distances, constraints: constraints };\n}\n\n/// computes the gradient and loss simulatenously for our constrained MDS optimizer\nfunction constrainedMDSGradient(x, fxprime, distances, constraints) {\n let loss = 0,\n i;\n for (i = 0; i < fxprime.length; ++i) {\n fxprime[i] = 0;\n }\n\n for (i = 0; i < distances.length; ++i) {\n const xi = x[2 * i],\n yi = x[2 * i + 1];\n for (let j = i + 1; j < distances.length; ++j) {\n const xj = x[2 * j],\n yj = x[2 * j + 1],\n dij = distances[i][j],\n constraint = constraints[i][j];\n\n const squaredDistance = (xj - xi) * (xj - xi) + (yj - yi) * (yj - yi),\n distance = Math.sqrt(squaredDistance),\n delta = squaredDistance - dij * dij;\n\n if ((constraint > 0 && distance <= dij) || (constraint < 0 && distance >= dij)) {\n continue;\n }\n\n loss += 2 * delta * delta;\n\n fxprime[2 * i] += 4 * delta * (xi - xj);\n fxprime[2 * i + 1] += 4 * delta * (yi - yj);\n\n fxprime[2 * j] += 4 * delta * (xj - xi);\n fxprime[2 * j + 1] += 4 * delta * (yj - yi);\n }\n }\n return loss;\n}\n\n/// takes the best working variant of either constrained MDS or greedy\nexport function bestInitialLayout(areas, params) {\n let initial = greedyLayout(areas, params);\n const loss = params.lossFunction || lossFunction;\n\n // greedylayout is sufficient for all 2/3 circle cases. try out\n // constrained MDS for higher order problems, take its output\n // if it outperforms. (greedy is aesthetically better on 2/3 circles\n // since it axis aligns)\n if (areas.length >= 8) {\n const constrained = constrainedMDSLayout(areas, params),\n constrainedLoss = loss(constrained, areas),\n greedyLoss = loss(initial, areas);\n\n if (constrainedLoss + 1e-8 < greedyLoss) {\n initial = constrained;\n }\n }\n return initial;\n}\n\n/// use the constrained MDS variant to generate an initial layout\nexport function constrainedMDSLayout(areas, params) {\n params = params || {};\n const restarts = params.restarts || 10;\n\n // bidirectionally map sets to a rowid (so we can create a matrix)\n const sets = [],\n setids = {};\n let i;\n for (i = 0; i < areas.length; ++i) {\n const area = areas[i];\n if (area.sets.length == 1) {\n setids[area.sets[0]] = sets.length;\n sets.push(area);\n }\n }\n\n const matrices = getDistanceMatrices(areas, sets, setids);\n let distances = matrices.distances;\n const constraints = matrices.constraints;\n\n // keep distances bounded, things get messed up otherwise.\n // TODO: proper preconditioner?\n const norm = norm2(distances.map(norm2)) / distances.length;\n distances = distances.map(function (row) {\n return row.map(function (value) {\n return value / norm;\n });\n });\n\n const obj = function (x, fxprime) {\n return constrainedMDSGradient(x, fxprime, distances, constraints);\n };\n\n let best, current;\n for (i = 0; i < restarts; ++i) {\n const initial = zeros(distances.length * 2).map(Math.random);\n\n current = conjugateGradient(obj, initial, params);\n if (!best || current.fx < best.fx) {\n best = current;\n }\n }\n const positions = best.x;\n\n // translate rows back to (x,y,radius) coordinates\n const circles = {};\n for (i = 0; i < sets.length; ++i) {\n const set = sets[i];\n circles[set.sets[0]] = {\n x: positions[2 * i] * norm,\n y: positions[2 * i + 1] * norm,\n radius: Math.sqrt(set.size / Math.PI),\n };\n }\n\n if (params.history) {\n for (i = 0; i < params.history.length; ++i) {\n scale(params.history[i].x, norm);\n }\n }\n return circles;\n}\n\n/** Lays out a Venn diagram greedily, going from most overlapped sets to\nleast overlapped, attempting to position each new set such that the\noverlapping areas to already positioned sets are basically right */\nexport function greedyLayout(areas, params) {\n const loss = params && params.lossFunction ? params.lossFunction : lossFunction;\n // define a circle for each set\n const circles = {},\n setOverlaps = {};\n let set;\n for (let i = 0; i < areas.length; ++i) {\n const area = areas[i];\n if (area.sets.length == 1) {\n set = area.sets[0];\n circles[set] = {\n x: 1e10,\n y: 1e10,\n // rowid: circles.length, // fix to ->\n rowid: Object.keys(circles).length,\n size: area.size,\n radius: Math.sqrt(area.size / Math.PI),\n };\n setOverlaps[set] = [];\n }\n }\n areas = areas.filter(function (a) {\n return a.sets.length == 2;\n });\n\n // map each set to a list of all the other sets that overlap it\n for (let i = 0; i < areas.length; ++i) {\n const current = areas[i];\n // eslint-disable-next-line\n let weight = current.hasOwnProperty('weight') ? current.weight : 1.0;\n const left = current.sets[0],\n right = current.sets[1];\n\n // completely overlapped circles shouldn't be positioned early here\n if (current.size + SMALL >= Math.min(circles[left].size, circles[right].size)) {\n weight = 0;\n }\n\n setOverlaps[left].push({ set: right, size: current.size, weight: weight });\n setOverlaps[right].push({ set: left, size: current.size, weight: weight });\n }\n\n // get list of most overlapped sets\n const mostOverlapped = [];\n for (set in setOverlaps) {\n // eslint-disable-next-line\n if (setOverlaps.hasOwnProperty(set)) {\n let size = 0;\n for (let i = 0; i < setOverlaps[set].length; ++i) {\n size += setOverlaps[set][i].size * setOverlaps[set][i].weight;\n }\n\n mostOverlapped.push({ set: set, size: size });\n }\n }\n\n // sort by size desc\n function sortOrder(a, b) {\n return b.size - a.size;\n }\n mostOverlapped.sort(sortOrder);\n\n // keep track of what sets have been laid out\n const positioned = {};\n function isPositioned(element) {\n return element.set in positioned;\n }\n\n // adds a point to the output\n function positionSet(point, index) {\n circles[index].x = point.x;\n circles[index].y = point.y;\n positioned[index] = true;\n }\n\n // add most overlapped set at (0,0)\n positionSet({ x: 0, y: 0 }, mostOverlapped[0].set);\n\n // get distances between all points. TODO, necessary?\n // answer: probably not\n // var distances = venn.getDistanceMatrices(circles, areas).distances;\n for (let i = 1; i < mostOverlapped.length; ++i) {\n const setIndex = mostOverlapped[i].set,\n overlap = setOverlaps[setIndex].filter(isPositioned);\n set = circles[setIndex];\n overlap.sort(sortOrder);\n\n if (overlap.length === 0) {\n // this shouldn't happen anymore with addMissingAreas\n throw 'ERROR: missing pairwise overlap information';\n }\n\n const points = [];\n for (let j = 0; j < overlap.length; ++j) {\n // get appropriate distance from most overlapped already added set\n const p1 = circles[overlap[j].set],\n d1 = distanceFromIntersectArea(set.radius, p1.radius, overlap[j].size);\n\n // sample positions at 90 degrees for maximum aesthetics\n points.push({ x: p1.x + d1, y: p1.y });\n points.push({ x: p1.x - d1, y: p1.y });\n points.push({ y: p1.y + d1, x: p1.x });\n points.push({ y: p1.y - d1, x: p1.x });\n\n // if we have at least 2 overlaps, then figure out where the\n // set should be positioned analytically and try those too\n for (let k = j + 1; k < overlap.length; ++k) {\n const p2 = circles[overlap[k].set],\n d2 = distanceFromIntersectArea(set.radius, p2.radius, overlap[k].size);\n\n const extraPoints = circleCircleIntersection(\n { x: p1.x, y: p1.y, radius: d1 },\n { x: p2.x, y: p2.y, radius: d2 }\n );\n\n for (let l = 0; l < extraPoints.length; ++l) {\n points.push(extraPoints[l]);\n }\n }\n }\n\n // we have some candidate positions for the set, examine loss\n // at each position to figure out where to put it at\n let bestLoss = 1e50,\n bestPoint = points[0];\n for (let j = 0; j < points.length; ++j) {\n circles[setIndex].x = points[j].x;\n circles[setIndex].y = points[j].y;\n const localLoss = loss(circles, areas);\n if (localLoss < bestLoss) {\n bestLoss = localLoss;\n bestPoint = points[j];\n }\n }\n\n positionSet(bestPoint, setIndex);\n }\n\n return circles;\n}\n\n/** Given a bunch of sets, and the desired overlaps between these sets - computes\nthe distance from the actual overlaps to the desired overlaps. Note that\nthis method ignores overlaps of more than 2 circles */\nexport function lossFunction(sets, overlaps) {\n let output = 0;\n\n function getCircles(indices) {\n return indices.map(function (i) {\n return sets[i];\n });\n }\n\n for (let i = 0; i < overlaps.length; ++i) {\n const area = overlaps[i];\n let overlap;\n if (area.sets.length == 1) {\n continue;\n } else if (area.sets.length == 2) {\n const left = sets[area.sets[0]],\n right = sets[area.sets[1]];\n overlap = circleOverlap(left.radius, right.radius, distance(left, right));\n } else {\n overlap = intersectionArea(getCircles(area.sets));\n }\n\n // eslint-disable-next-line\n const weight = area.hasOwnProperty('weight') ? area.weight : 1.0;\n output += weight * (overlap - area.size) * (overlap - area.size);\n }\n\n return output;\n}\n\n// orientates a bunch of circles to point in orientation\nfunction orientateCircles(circles, orientation, orientationOrder) {\n if (orientationOrder === null) {\n circles.sort(function (a, b) {\n return b.radius - a.radius;\n });\n } else {\n circles.sort(orientationOrder);\n }\n\n let i;\n // shift circles so largest circle is at (0, 0)\n if (circles.length > 0) {\n const largestX = circles[0].x,\n largestY = circles[0].y;\n\n for (i = 0; i < circles.length; ++i) {\n circles[i].x -= largestX;\n circles[i].y -= largestY;\n }\n }\n\n if (circles.length == 2) {\n // if the second circle is a subset of the first, arrange so that\n // it is off to one side. hack for https://github.com/benfred/venn.js/issues/120\n const dist = distance(circles[0], circles[1]);\n if (dist < Math.abs(circles[1].radius - circles[0].radius)) {\n circles[1].x = circles[0].x + circles[0].radius - circles[1].radius - 1e-10;\n circles[1].y = circles[0].y;\n }\n }\n\n // rotate circles so that second largest is at an angle of 'orientation'\n // from largest\n if (circles.length > 1) {\n const rotation = Math.atan2(circles[1].x, circles[1].y) - orientation;\n let x, y;\n const c = Math.cos(rotation),\n s = Math.sin(rotation);\n for (i = 0; i < circles.length; ++i) {\n x = circles[i].x;\n y = circles[i].y;\n circles[i].x = c * x - s * y;\n circles[i].y = s * x + c * y;\n }\n }\n\n // mirror solution if third solution is above plane specified by\n // first two circles\n if (circles.length > 2) {\n let angle = Math.atan2(circles[2].x, circles[2].y) - orientation;\n while (angle < 0) {\n angle += 2 * Math.PI;\n }\n while (angle > 2 * Math.PI) {\n angle -= 2 * Math.PI;\n }\n if (angle > Math.PI) {\n const slope = circles[1].y / (1e-10 + circles[1].x);\n for (i = 0; i < circles.length; ++i) {\n const d = (circles[i].x + slope * circles[i].y) / (1 + slope * slope);\n circles[i].x = 2 * d - circles[i].x;\n circles[i].y = 2 * d * slope - circles[i].y;\n }\n }\n }\n}\n\nexport function disjointCluster(circles) {\n // union-find clustering to get disjoint sets\n circles.map(function (circle) {\n circle.parent = circle;\n });\n\n // path compression step in union find\n function find(circle) {\n if (circle.parent !== circle) {\n circle.parent = find(circle.parent);\n }\n return circle.parent;\n }\n\n function union(x, y) {\n const xRoot = find(x),\n yRoot = find(y);\n xRoot.parent = yRoot;\n }\n\n // get the union of all overlapping sets\n for (let i = 0; i < circles.length; ++i) {\n for (let j = i + 1; j < circles.length; ++j) {\n const maxDistance = circles[i].radius + circles[j].radius;\n if (distance(circles[i], circles[j]) + 1e-10 < maxDistance) {\n union(circles[j], circles[i]);\n }\n }\n }\n\n // find all the disjoint clusters and group them together\n const disjointClusters = {};\n let setid;\n for (let i = 0; i < circles.length; ++i) {\n setid = find(circles[i]).parent.setid;\n if (!(setid in disjointClusters)) {\n disjointClusters[setid] = [];\n }\n disjointClusters[setid].push(circles[i]);\n }\n\n // cleanup bookkeeping\n circles.map(function (circle) {\n delete circle.parent;\n });\n\n // return in more usable form\n const ret = [];\n for (setid in disjointClusters) {\n // eslint-disable-next-line\n if (disjointClusters.hasOwnProperty(setid)) {\n ret.push(disjointClusters[setid]);\n }\n }\n return ret;\n}\n\nfunction getBoundingBox(circles) {\n const minMax = function (d) {\n const hi = Math.max.apply(\n null,\n circles.map(function (c) {\n return c[d] + c.radius;\n })\n ),\n lo = Math.min.apply(\n null,\n circles.map(function (c) {\n return c[d] - c.radius;\n })\n );\n return { max: hi, min: lo };\n };\n\n return { xRange: minMax('x'), yRange: minMax('y') };\n}\n\nexport function normalizeSolution(solution, orientation, orientationOrder) {\n if (orientation === null) {\n orientation = Math.PI / 2;\n }\n\n // work with a list instead of a dictionary, and take a copy so we\n // don't mutate input\n let circles = [],\n i,\n setid;\n for (setid in solution) {\n // eslint-disable-next-line\n if (solution.hasOwnProperty(setid)) {\n const previous = solution[setid];\n circles.push({ x: previous.x, y: previous.y, radius: previous.radius, setid: setid });\n }\n }\n\n // get all the disjoint clusters\n const clusters = disjointCluster(circles);\n\n // orientate all disjoint sets, get sizes\n for (i = 0; i < clusters.length; ++i) {\n orientateCircles(clusters[i], orientation, orientationOrder);\n const bounds = getBoundingBox(clusters[i]);\n clusters[i].size = (bounds.xRange.max - bounds.xRange.min) * (bounds.yRange.max - bounds.yRange.min);\n clusters[i].bounds = bounds;\n }\n clusters.sort(function (a, b) {\n return b.size - a.size;\n });\n\n // orientate the largest at 0,0, and get the bounds\n circles = clusters[0];\n // @ts-ignore fixme 从逻辑上看似乎是不对的，后续看看\n let returnBounds = circles.bounds;\n\n const spacing = (returnBounds.xRange.max - returnBounds.xRange.min) / 50;\n\n function addCluster(cluster, right, bottom) {\n if (!cluster) return;\n\n const bounds = cluster.bounds;\n let xOffset, yOffset, centreing;\n\n if (right) {\n xOffset = returnBounds.xRange.max - bounds.xRange.min + spacing;\n } else {\n xOffset = returnBounds.xRange.max - bounds.xRange.max;\n centreing = (bounds.xRange.max - bounds.xRange.min) / 2 - (returnBounds.xRange.max - returnBounds.xRange.min) / 2;\n if (centreing < 0) xOffset += centreing;\n }\n\n if (bottom) {\n yOffset = returnBounds.yRange.max - bounds.yRange.min + spacing;\n } else {\n yOffset = returnBounds.yRange.max - bounds.yRange.max;\n centreing = (bounds.yRange.max - bounds.yRange.min) / 2 - (returnBounds.yRange.max - returnBounds.yRange.min) / 2;\n if (centreing < 0) yOffset += centreing;\n }\n\n for (let j = 0; j < cluster.length; ++j) {\n cluster[j].x += xOffset;\n cluster[j].y += yOffset;\n circles.push(cluster[j]);\n }\n }\n\n let index = 1;\n while (index < clusters.length) {\n addCluster(clusters[index], true, false);\n addCluster(clusters[index + 1], false, true);\n addCluster(clusters[index + 2], true, true);\n index += 3;\n\n // have one cluster (in top left). lay out next three relative\n // to it in a grid\n returnBounds = getBoundingBox(circles);\n }\n\n // convert back to solution form\n const ret = {};\n for (i = 0; i < circles.length; ++i) {\n ret[circles[i].setid] = circles[i];\n }\n return ret;\n}\n\n/** Scales a solution from venn.venn or venn.greedyLayout such that it fits in\na rectangle of width/height - with padding around the borders. also\ncenters the diagram in the available space at the same time */\nexport function scaleSolution(solution, width, height, padding) {\n const circles = [],\n setids = [];\n for (const setid in solution) {\n // eslint-disable-next-line\n if (solution.hasOwnProperty(setid)) {\n setids.push(setid);\n circles.push(solution[setid]);\n }\n }\n\n width -= 2 * padding;\n height -= 2 * padding;\n\n const bounds = getBoundingBox(circles),\n xRange = bounds.xRange,\n yRange = bounds.yRange;\n\n if (xRange.max == xRange.min || yRange.max == yRange.min) {\n console.log('not scaling solution: zero size detected');\n return solution;\n }\n\n const xScaling = width / (xRange.max - xRange.min),\n yScaling = height / (yRange.max - yRange.min),\n scaling = Math.min(yScaling, xScaling),\n // while we're at it, center the diagram too\n xOffset = (width - (xRange.max - xRange.min) * scaling) / 2,\n yOffset = (height - (yRange.max - yRange.min) * scaling) / 2;\n\n const scaled = {};\n for (let i = 0; i < circles.length; ++i) {\n const circle = circles[i];\n scaled[setids[i]] = {\n radius: scaling * circle.radius,\n x: padding + xOffset + (circle.x - xRange.min) * scaling,\n y: padding + yOffset + (circle.y - yRange.min) * scaling,\n };\n }\n\n return scaled;\n}\n"]}