Run results for: 双轴图刻度对齐算法性能对比

Run details:

User agent: Mozilla/5.0 (Macintosh; Intel Mac OS X 10_15_7) AppleWebKit/537.36 (KHTML, like Gecko) Chrome/135.0.0.0 Safari/537.36

Browser: Chrome 135

Operating system: Mac OS X 10.15.7

Device Platform: Desktop

Date tested: one year ago

Test name	Executions per second
双轴共同最优解	5890.4 Ops/sec
线性插值	446425.2 Ops/sec

HTML Preparation code:

<!--your preparation HTML code goes here-->

Script Preparation code:

"use strict";
const isArrayLike = function (value) {
    return value !== null && typeof value !== 'function' && isFinite(value.length);
};
function last(o) {
    if (isArrayLike(o)) {
        const arr = o;
        return arr[arr.length - 1];
    }
    return undefined;
}
// isFinite,
const isNil = function (value) {
    /**
     * isNil(null) => true
     * isNil() => true
     */
    return value === null || value === undefined;
};
function size(o) {
    if (isNil(o)) {
        return 0;
    }
    if (isArrayLike(o)) {
        return o.length;
    }
    return Object.keys(o).length;
}
function head(o) {
    if (isArrayLike(o)) {
        return o[0];
    }
    return undefined;
}
const indexOf = function (arr, obj) {
    if (!isArrayLike(arr)) {
        return -1;
    }
    const m = Array.prototype.indexOf;
    if (m) {
        return m.call(arr, obj);
    }
    let index = -1;
    for (let i = 0; i < arr.length; i++) {
        if (arr[i] === obj) {
            index = i;
            break;
        }
    }
    return index;
};
const DEFAULT_Q = [1, 5, 2, 2.5, 4, 3];
const ALL_Q = [1, 5, 2, 2.5, 4, 3, 1.5, 7, 6, 8, 9];
const eps = Number.EPSILON * 100;
function mod(n, m) {
    return ((n % m) + m) % m;
}
function round(n) {
    return Math.round(n * 1e12) / 1e12;
}
function simplicity(q, Q, j, lmin, lmax, lstep) {
    const n = size(Q);
    const i = indexOf(Q, q);
    let v = 0;
    const m = mod(lmin, lstep);
    if ((m < eps || lstep - m < eps) && lmin <= 0 && lmax >= 0) {
        v = 1;
    }
    return 1 - i / (n - 1) - j + v;
}
function simplicityMax(q, Q, j) {
    const n = size(Q);
    const i = indexOf(Q, q);
    const v = 1;
    return 1 - i / (n - 1) - j + v;
}
function density(k, m, dMin, dMax, lMin, lMax) {
    const r = (k - 1) / (lMax - lMin);
    const rt = (m - 1) / (Math.max(lMax, dMax) - Math.min(dMin, lMin));
    return 2 - Math.max(r / rt, rt / r);
}
function densityMax(k, m) {
    if (k >= m) {
        return 2 - (k - 1) / (m - 1);
    }
    return 1;
}
function coverage(dMin, dMax, lMin, lMax) {
    const range = dMax - dMin;
    return 1 - (0.5 * ((dMax - lMax) ** 2 + (dMin - lMin) ** 2)) / (0.1 * range) ** 2;
}
function coverageMax(dMin, dMax, span) {
    const range = dMax - dMin;
    if (span > range) {
        const half = (span - range) / 2;
        return 1 - half ** 2 / (0.1 * range) ** 2;
    }
    return 1;
}
function legibility() {
    return 1;
}
function extended(dMin, dMax, n = 5, onlyLoose = true, Q = DEFAULT_Q, w = [0.25, 0.2, 0.5, 0.05]) {
    // 处理小于 0 和小数的 tickCount
    const m = n < 0 ? 0 : Math.round(n);
    // nan 也会导致异常
    if (Number.isNaN(dMin) || Number.isNaN(dMax) || typeof dMin !== 'number' || typeof dMax !== 'number' || !m) {
        return {
            min: 0,
            max: 0,
            ticks: [],
        };
    }
    // js 极大值极小值问题，差值小于 1e-15 会导致计算出错
    if (dMax - dMin < 1e-15 || m === 1) {
        return {
            min: dMin,
            max: dMax,
            ticks: [dMin],
        };
    }
    // js 超大值问题
    if (dMax - dMin > 1e148) {
        const count = n || 5;
        const step = (dMax - dMin) / count;
        return {
            min: dMin,
            max: dMax,
            ticks: Array(count)
                .fill(null)
                .map((_, idx) => {
                return prettyNumber(dMin + step * idx);
            }),
        };
    }
    const best = {
        score: -2,
        lmin: 0,
        lmax: 0,
        lstep: 0,
    };
    let j = 1;
    while (j < Infinity) {
        for (let i = 0; i < Q.length; i += 1) {
            const q = Q[i];
            const sm = simplicityMax(q, Q, j);
            if (w[0] * sm + w[1] + w[2] + w[3] < best.score) {
                j = Infinity;
                break;
            }
            let k = 2;
            while (k < Infinity) {
                const dm = densityMax(k, m);
                if (w[0] * sm + w[1] + w[2] * dm + w[3] < best.score) {
                    break;
                }
                const delta = (dMax - dMin) / (k + 1) / j / q;
                let z = Math.ceil(Math.log10(delta));
                while (z < Infinity) {
                    const step = j * q * 10 ** z;
                    const cm = coverageMax(dMin, dMax, step * (k - 1));
                    if (w[0] * sm + w[1] * cm + w[2] * dm + w[3] < best.score) {
                        break;
                    }
                    const minStart = Math.floor(dMax / step) * j - (k - 1) * j;
                    const maxStart = Math.ceil(dMin / step) * j;
                    if (minStart <= maxStart) {
                        const count = maxStart - minStart;
                        for (let i = 0; i <= count; i += 1) {
                            const start = minStart + i;
                            const lMin = start * (step / j);
                            const lMax = lMin + step * (k - 1);
                            const lStep = step;
                            const s = simplicity(q, Q, j, lMin, lMax, lStep);
                            const c = coverage(dMin, dMax, lMin, lMax);
                            const g = density(k, m, dMin, dMax, lMin, lMax);
                            const l = legibility();
                            const score = w[0] * s + w[1] * c + w[2] * g + w[3] * l;
                            if (score > best.score && (!onlyLoose || (lMin <= dMin && lMax >= dMax))) {
                                best.lmin = lMin;
                                best.lmax = lMax;
                                best.lstep = lStep;
                                best.score = score;
                            }
                        }
                    }
                    z += 1;
                }
                k += 1;
            }
        }
        j += 1;
    }
    // 处理精度问题，保证这三个数没有精度问题
    const lmax = prettyNumber(best.lmax);
    const lmin = prettyNumber(best.lmin);
    const lstep = prettyNumber(best.lstep);
    // 加 round 是为处理 extended(0.94, 1, 5)
    // 保证生成的 tickCount 没有精度问题
    const tickCount = Math.floor(round((lmax - lmin) / lstep)) + 1;
    const ticks = new Array(tickCount);
    // 少用乘法：防止出现 -1.2 + 1.2 * 3 = 2.3999999999999995 的情况
    ticks[0] = prettyNumber(lmin);
    for (let i = 1; i < tickCount; i++) {
        ticks[i] = prettyNumber(ticks[i - 1] + lstep);
    }
    return {
        min: Math.min(dMin, head(ticks)),
        max: Math.max(dMax, last(ticks)),
        ticks,
    };
}
function prettyNumber(n) {
    if (Math.abs(n) < 1e-15)
        return 0;
    // 处理接近整数的值
    const rounded = Math.round(n);
    if (Math.abs(n - rounded) < 1e-10)
        return rounded;
    // 基于数值大小动态调整精度
    const magnitude = Math.abs(n);
    if (magnitude >= 1000) {
        return Number(n.toFixed(2));
    }
    return parseFloat(n.toFixed(15));
}
function dualAxisNice(primaryRange, secondaryRange, minTickCount = 4, maxTickCount = 7) {
    // 生成刻度时的权重 - 提高density权重以确保刻度数量更接近目标值
    const generationWeights = [0.1, 0.1, 0.75, 0.05];
    // 为每个轴生成多种候选方案
    const primaryCandidates = [];
    const secondaryCandidates = [];
    // 生成不同刻度数量的候选方案
    for (let tickCount = minTickCount; tickCount <= maxTickCount; tickCount++) {
        // 为每个刻度数量使用不同的Q值集合
        const primaryQs = [
            DEFAULT_Q, // 默认优雅数字集合[1,5,2,2.5,4,3]
            ALL_Q, // 扩展集合包含更多倍数（如0.1,10等）
            generateSmartQ(primaryRange[0], primaryRange[1], tickCount), // 根据数据范围和目标刻度数量生成智能Q值
        ];
        const secondaryQs = [
            DEFAULT_Q, // 默认优雅数字集合[1,5,2,2.5,4,3]
            ALL_Q, // 扩展集合包含更多倍数（如0.1,10等）
            generateSmartQ(secondaryRange[0], secondaryRange[1], tickCount), // 根据数据范围和目标刻度数量生成智能Q值
        ];
        // 为主轴生成候选方案 - 使用增强density权重的参数
        for (const Q of primaryQs) {
            primaryCandidates.push({
                result: extended(primaryRange[0], primaryRange[1], tickCount, true, Q, generationWeights),
                targetCount: tickCount
            });
        }
        // 为次轴生成候选方案 - 使用增强density权重的参数
        for (const Q of secondaryQs) {
            secondaryCandidates.push({
                result: extended(secondaryRange[0], secondaryRange[1], tickCount, true, Q, generationWeights),
                targetCount: tickCount
            });
        }
    }
    // 按刻度数量分组
    const groupedByCount = new Map();
    // 收集所有出现的刻度数量
    const allTickCounts = new Set();
    // 对主轴候选方案按刻度数量分组
    primaryCandidates.forEach(candidate => {
        const tickCount = candidate.result.ticks.length;
        allTickCounts.add(tickCount);
        if (!groupedByCount.has(tickCount)) {
            groupedByCount.set(tickCount, { primary: [], secondary: [] });
        }
        groupedByCount.get(tickCount).primary.push(candidate);
    });
    // 对次轴候选方案按刻度数量分组
    secondaryCandidates.forEach(candidate => {
        const tickCount = candidate.result.ticks.length;
        allTickCounts.add(tickCount);
        if (!groupedByCount.has(tickCount)) {
            groupedByCount.set(tickCount, { primary: [], secondary: [] });
        }
        groupedByCount.get(tickCount).secondary.push(candidate);
    });
    // 找到最佳匹配的刻度组合
    let bestScore = -Infinity;
    let bestResult = null;
    // 对每个刻度数量分别评估
    allTickCounts.forEach(tickCount => {
        const group = groupedByCount.get(tickCount);
        // 确保这个刻度数量对于两个轴都有候选方案
        if (group.primary.length > 0 && group.secondary.length > 0) {
            for (const primary of group.primary) {
                for (const secondary of group.secondary) {
                    // 使用评估函数评估当前组合
                    const score = evaluateDualAxisMatch(primary.result, secondary.result, primaryRange, secondaryRange, primary.targetCount, secondary.targetCount);
                    if (score > bestScore) {
                        bestScore = score;
                        bestResult = { primary: primary.result, secondary: secondary.result };
                    }
                }
            }
        }
    });
    return bestResult;
}
function generateSmartQ(min, max, n) {
    const span = max - min;
    if (span === 0)
        return [1];
    const power = 10 ** Math.floor(Math.log10(span));
    const baseQ = [1, 2, 5, 2.5, 4, 3];
    let Q = baseQ.map((q) => q * power);
    // 根据基准步长扩展候选
    const step = span / (n - 1);
    Q.push(step); // 加入基准步长
    Q.push(step * 2); // 加入倍数
    // 去重、排序、截断
    Q = Array.from(new Set(Q))
        .sort((a, b) => a - b)
        .slice(0, 10)
        // 修复小数精度问题: 根据数值大小智能限制小数位数
        .map((i) => {
        // 对大数值取整，对中等数值保留1位小数，对小数值保留2位小数
        if (i >= 100) {
            return Math.round(i);
        }
        else if (i >= 10) {
            return Number(i.toFixed(1));
        }
        else {
            return Number(i.toFixed(2));
        }
    });
    return Q;
}
// 评估双轴刻度匹配度 - 不考虑density，提高simplicity和coverage的权重
function evaluateDualAxisMatch(primary, secondary, primaryRange, secondaryRange, primaryTargetCount = 0, secondaryTargetCount = 0) {
    // 确保两个轴有相同数量的刻度
    if (primary.ticks.length !== secondary.ticks.length) {
        return -Infinity;
    }
    // 评估权重 - 提高simplicity和coverage权重，不考虑density
    const evaluationWeights = [0.45, 0.45, 0, 0.1];
    // 计算主轴和次轴的刻度美观度 - 使用调整后的评估权重
    const primaryScore = calculateAxisScore(primary.ticks, primaryRange, primaryTargetCount, evaluationWeights);
    const secondaryScore = calculateAxisScore(secondary.ticks, secondaryRange, secondaryTargetCount, evaluationWeights);
    // 计算映射一致性 - 理想情况下，相对位置应该均匀对应
    const mappingConsistency = calculateMappingConsistency(primary.ticks, primaryRange, secondary.ticks, secondaryRange);
    // 计算总分 - 权重可以根据需要调整
    return 0.3 * primaryScore + 0.3 * secondaryScore + 0.4 * mappingConsistency;
}
// 计算单个轴的评分
function calculateAxisScore(ticks, dataRange, targetCount = 0, weights = [0.45, 0.45, 0, 0.1]) {
    if (ticks.length < 2)
        return 0;
    // 从ticks中提取关键信息
    const lmin = ticks[0];
    const lmax = ticks[ticks.length - 1];
    const lstep = ticks[1] - ticks[0];
    // 确保步长一致性
    const isConsistentStep = ticks.every((t, i) => i === 0 || Math.abs((t - ticks[i - 1]) - lstep) < 1e-10);
    if (!isConsistentStep)
        return 0; // 如果步长不一致，评分为0
    // 提取数据范围
    const [dMin, dMax] = dataRange;
    const m = targetCount || ticks.length;
    // 计算q值（从step反推）
    const magnitude = Math.pow(10, Math.floor(Math.log10(lstep)));
    const q = lstep / magnitude;
    const j = 1; // 简化处理
    // 复用现有函数计算各项评分
    const s = simplicity(q, DEFAULT_Q, j, lmin, lmax, lstep);
    const c = coverage(dMin, dMax, lmin, lmax);
    const g = density(ticks.length, m, dMin, dMax, lmin, lmax);
    const l = legibility();
    // 使用提供的权重计算总分
    return weights[0] * s + weights[1] * c + weights[2] * g + weights[3] * l;
}
// 计算映射一致性 - 检查相对位置的线性关系
function calculateMappingConsistency(primaryTicks, primaryRange, secondaryTicks, secondaryRange) {
    // 针对不同长度的刻度数组处理映射一致性
    // 计算归一化位置
    const primaryNormalized = primaryTicks.map(t => (t - primaryRange[0]) / (primaryRange[1] - primaryRange[0]));
    const secondaryNormalized = secondaryTicks.map(t => (t - secondaryRange[0]) / (secondaryRange[1] - secondaryRange[0]));
    // 如果两个轴的刻度数不同，我们需要通过插值来比较它们的映射一致性
    if (primaryNormalized.length !== secondaryNormalized.length) {
        // 获取较短的数组长度和较长的数组
        const minLength = Math.min(primaryNormalized.length, secondaryNormalized.length);
        const maxLength = Math.max(primaryNormalized.length, secondaryNormalized.length);
        const shorterArray = primaryNormalized.length < secondaryNormalized.length ? primaryNormalized : secondaryNormalized;
        const longerArray = primaryNormalized.length < secondaryNormalized.length ? secondaryNormalized : primaryNormalized;
        // 计算长度比例惩罚 - 长度差距越大，惩罚越大
        const lengthPenalty = 1 - Math.min(0.5, (maxLength - minLength) / maxLength);
        // 计算关键点的映射差异
        let sumSquaredDiff = 0;
        // 对较短数组中的每个点，在较长数组中找到对应位置的插值
        for (let i = 0; i < minLength; i++) {
            // 根据位置比例在较长数组中查找对应点
            const position = i / (minLength - 1);
            const interpolatedIndex = position * (maxLength - 1);
            const lowerIndex = Math.floor(interpolatedIndex);
            const upperIndex = Math.ceil(interpolatedIndex);
            // 如果索引相同，直接取值
            let interpolatedValue;
            if (lowerIndex === upperIndex) {
                interpolatedValue = longerArray[lowerIndex];
            }
            else {
                // 否则进行线性插值
                const weight = interpolatedIndex - lowerIndex;
                interpolatedValue = longerArray[lowerIndex] * (1 - weight) + longerArray[upperIndex] * weight;
            }
            // 计算差异
            const diff = shorterArray[i] - interpolatedValue;
            sumSquaredDiff += diff * diff;
        }
        const rmsDiff = Math.sqrt(sumSquaredDiff / minLength);
        // 返回考虑长度惩罚的评分
        return lengthPenalty * (1 - Math.min(1, rmsDiff * 10));
    }
    // 如果两个轴的刻度数相同，使用原来的逻辑
    let sumSquaredDiff = 0;
    for (let i = 0; i < primaryNormalized.length; i++) {
        const diff = primaryNormalized[i] - secondaryNormalized[i];
        sumSquaredDiff += diff * diff;
    }
    const rmsDiff = Math.sqrt(sumSquaredDiff / primaryNormalized.length);
    // 返回[0,1]范围的评分，0表示完全不匹配，1表示完美匹配
    return 1 - Math.min(1, rmsDiff * 10);
}
function linearInterpolation(range, proportions, decimals) {
    const { min, max } = range;
    const propMin = Math.min(...proportions);
    const propMax = Math.max(...proportions);
    const propGap = propMax - propMin;
    const rangeGap = max - min;
    const interpolate = (value) => {
        const result = min + ((value - propMin) * rangeGap) / propGap;
        return decimals == null ? result : Number(result.toFixed(decimals));
    };
    const ticks = proportions.map(interpolate);
    // 若有NaN则表示失败（比如除数为0），返回空
    return ticks.some(isNaN) ? undefined : ticks;
}
const testArray = [
  [10, 50], [200, 800],
  [0.06, 0.09], [400, 800],
  [0.273, 0.894], [-800, -200],
  [0.01, 0.05], [1000, 5000],
  [0.1, 0.8], [10000, 90000],
  [2.71, 3.14], [100, 900],
  [0.001, 0.009], [100, 900],
  [1, 2], [0, 1000],
  [0.1, 0.5], [1.5, 3.5],
  [0.999, 1.001], [9999, 10001],
]

Tests:

双轴共同最优解
testArray.forEach(item => { dualAxisNice(item[0], item[1]); })
线性插值
testArray.forEach(item => { linearInterpolation({ min: item[0][0], max: item[0][1] }, extended(item[1][0], item[1][1]).ticks); })

Run results for: 双轴图刻度对齐算法性能对比

双轴共同最优解

线性插值