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<!DOCTYPE html>
<html lang="zh-CN">
<head>
<meta charset="UTF-8">
<meta name="viewport" content="width=device-width, initial-scale=1.0">
<title>函数图像绘制器</title>
<style>
* {
box-sizing: border-box;
margin: 0;
padding: 0;
}
body {
font-family: -apple-system, BlinkMacSystemFont, "Segoe UI", "PingFang SC", "Microsoft YaHei", sans-serif;
background: #f5f7fa;
color: #333;
padding: 20px;
}
.container {
max-width: 1000px;
margin: 0 auto;
}
h1 {
text-align: center;
margin-bottom: 24px;
color: #2c3e50;
}
.panel {
background: white;
border-radius: 12px;
padding: 20px;
box-shadow: 0 2px 12px rgba(0,0,0,0.08);
margin-bottom: 20px;
}
.controls {
display: flex;
flex-wrap: wrap;
gap: 16px;
align-items: flex-end;
}
.control-group {
display: flex;
flex-direction: column;
gap: 6px;
}
label {
font-size: 14px;
color: #666;
font-weight: 500;
}
input[type="text"], input[type="number"] {
padding: 10px 14px;
border: 1px solid #ddd;
border-radius: 8px;
font-size: 15px;
outline: none;
transition: border-color 0.2s;
}
input[type="text"]:focus, input[type="number"]:focus {
border-color: #3498db;
}
#functionInput {
width: 260px;
}
.range-input {
width: 90px;
}
button {
padding: 10px 24px;
background: #3498db;
color: white;
border: none;
border-radius: 8px;
font-size: 15px;
cursor: pointer;
transition: background 0.2s;
}
button:hover {
background: #2980b9;
}
.zoom-btn {
padding: 10px 14px;
font-size: 18px;
font-weight: bold;
line-height: 1;
}
#canvas {
width: 100%;
height: 500px;
border-radius: 8px;
background: #fafbfc;
cursor: grab;
user-select: none;
-webkit-user-select: none;
}
#canvas:active {
cursor: grabbing;
}
.hint {
font-size: 13px;
color: #888;
margin-top: 12px;
line-height: 1.6;
}
.hint code {
background: #f0f4f8;
padding: 2px 6px;
border-radius: 4px;
color: #e74c3c;
}
.info {
display: flex;
gap: 24px;
margin-top: 16px;
flex-wrap: wrap;
font-size: 15px;
}
.info-item {
background: #f0f4f8;
padding: 10px 16px;
border-radius: 8px;
}
.info-item span {
color: #666;
}
.info-item strong {
color: #2c3e50;
margin-left: 6px;
}
#errorMsg {
color: #e74c3c;
margin-top: 10px;
font-size: 14px;
min-height: 20px;
}
.example-btn {
padding: 6px 12px;
background: #ecf0f1;
color: #555;
border-radius: 16px;
font-size: 13px;
cursor: pointer;
transition: background 0.2s;
}
.example-btn:hover {
background: #d5dbdb;
}
.examples-row {
display: flex;
align-items: center;
gap: 10px;
flex-wrap: wrap;
margin-top: 10px;
}
.example-label {
font-size: 13px;
color: #888;
min-width: 60px;
}
.point-result {
margin-top: 14px;
padding: 12px 16px;
background: #f0f4f8;
border-radius: 8px;
font-size: 14px;
line-height: 1.8;
min-height: 44px;
}
.point-result strong {
color: #2c3e50;
}
.checkbox-group {
display: flex;
align-items: center;
gap: 8px;
margin-bottom: 10px;
}
.checkbox-group input[type="checkbox"] {
width: 18px;
height: 18px;
cursor: pointer;
}
.checkbox-group label {
cursor: pointer;
margin: 0;
}
.legend {
display: flex;
gap: 20px;
margin-top: 12px;
font-size: 14px;
}
.legend-item {
display: flex;
align-items: center;
gap: 6px;
}
.legend-color {
width: 24px;
height: 3px;
border-radius: 2px;
}
</style>
</head>
<body>
<div class="container">
<h1>📈 函数图像绘制器</h1>
<div class="panel">
<div class="controls">
<div class="control-group">
<label for="functionInput">函数 f(x) =</label>
<input type="text" id="functionInput" value="x^2" placeholder="例如: sin(x) + x^2">
</div>
<div class="control-group checkbox-group">
<label for="showDerivative">显示导函数 f'(x)</label>
<input type="checkbox" id="showDerivative">
</div>
<button id="plotBtn">绘制图像</button>
<button id="clearBtn">清除</button>
<button id="zoomInBtn" class="zoom-btn" title="放大">+</button>
<button id="zoomOutBtn" class="zoom-btn" title="缩小">−</button>
</div>
<div class="examples-row">
<span class="example-label">幂函数</span>
<span class="example-btn" data-fn="x^2">x²</span>
<span class="example-btn" data-fn="x^3">x³</span>
<span class="example-btn" data-fn="x^4">x⁴</span>
<span class="example-btn" data-fn="sqrt(x)">√x</span>
<span class="example-btn" data-fn="1/x">1/x</span>
<span class="example-btn" data-fn="1/x^2">1/x²</span>
</div>
<div class="examples-row">
<span class="example-label">三角函数</span>
<span class="example-btn" data-fn="sin(x)">sin(x)</span>
<span class="example-btn" data-fn="cos(x)">cos(x)</span>
<span class="example-btn" data-fn="tan(x)">tan(x)</span>
<span class="example-btn" data-fn="sin(2*x)">sin(2x)</span>
<span class="example-btn" data-fn="cos(2*x)">cos(2x)</span>
<span class="example-btn" data-fn="1/tan(x)">cot(x)</span>
</div>
<div class="examples-row">
<span class="example-label">指数/对数</span>
<span class="example-btn" data-fn="e^x">eˣ</span>
<span class="example-btn" data-fn="exp(x)">exp(x)</span>
<span class="example-btn" data-fn="2^x">2ˣ</span>
<span class="example-btn" data-fn="ln(x)">ln(x)</span>
<span class="example-btn" data-fn="log(x)">log(x)</span>
</div>
<div class="examples-row">
<span class="example-label">复合/特殊</span>
<span class="example-btn" data-fn="abs(x)">|x|</span>
<span class="example-btn" data-fn="x*sin(x)">x·sin(x)</span>
<span class="example-btn" data-fn="x^2*sin(x)">x²·sin(x)</span>
<span class="example-btn" data-fn="e^(-x^2)">e^(-x²)</span>
<span class="example-btn" data-fn="sin(x)/x">sin(x)/x</span>
</div>
<div class="hint">
支持的运算符：<code>+</code> <code>-</code> <code>*</code> <code>/</code> <code>^</code>（乘方）<code>( )</code><br>
支持的函数：<code>sin</code> <code>cos</code> <code>tan</code> <code>exp</code> <code>ln</code> <code>log</code> <code>sqrt</code> <code>abs</code> <code>pi</code> <code>e</code><br>
<strong>提示：</strong>在图像上按住鼠标左右拖动可以平移视图，使用上方的 + / − 按钮缩放视图。
</div>
<div id="errorMsg"></div>
</div>
<div class="panel">
<canvas id="canvas" width="960" height="500"></canvas>
<div class="legend">
<div class="legend-item"><div class="legend-color" style="background: #3498db;"></div><span>f(x)</span></div>
<div class="legend-item"><div class="legend-color" style="background: #e67e22;"></div><span>f'(x)</span></div>
</div>
<div class="info">
<div class="info-item"><span>鼠标位置 x:</span><strong id="mouseX">-</strong></div>
<div class="info-item"><span>f(x):</span><strong id="mouseY">-</strong></div>
<div class="info-item"><span>f'(x) ≈</span><strong id="mouseDy">-</strong></div>
</div>
</div>
<div class="panel">
<h3 style="margin-bottom: 14px; color: #2c3e50;">点定位</h3>
<div class="controls">
<div class="control-group">
<label for="pointX">已知 x 求 f(x)</label>
<input type="number" id="pointX" class="range-input" placeholder="输入 x" step="any">
</div>
<button id="calcFromX">计算</button>
<div class="control-group" style="margin-left: 20px;">
<label for="pointY">已知 f(x) 求 x</label>
<input type="number" id="pointY" class="range-input" placeholder="输入 y" step="any">
</div>
<button id="calcFromY">计算</button>
</div>
<div id="pointResult" class="point-result"></div>
</div>
</div>
<script>
const canvas = document.getElementById('canvas');
const ctx = canvas.getContext('2d');
const functionInput = document.getElementById('functionInput');
const plotBtn = document.getElementById('plotBtn');
const clearBtn = document.getElementById('clearBtn');
const zoomInBtn = document.getElementById('zoomInBtn');
const zoomOutBtn = document.getElementById('zoomOutBtn');
const showDerivativeCheckbox = document.getElementById('showDerivative');
const errorMsg = document.getElementById('errorMsg');
const mouseXEl = document.getElementById('mouseX');
const mouseYEl = document.getElementById('mouseY');
const mouseDyEl = document.getElementById('mouseDy');
const pointXInput = document.getElementById('pointX');
const pointYInput = document.getElementById('pointY');
const calcFromXBtn = document.getElementById('calcFromX');
const calcFromYBtn = document.getElementById('calcFromY');
const pointResultEl = document.getElementById('pointResult');
// 词法分析：把输入字符串拆成 token
function tokenize(expr) {
const tokens = [];
let i = 0;
expr = expr.replace(/\s+/g, '');
while (i < expr.length) {
const ch = expr[i];
if (/[0-9]/.test(ch) || (ch === '.' && /[0-9]/.test(expr[i+1]))) {
let num = '';
while (i < expr.length && (/[0-9]/.test(expr[i]) || expr[i] === '.')) {
num += expr[i];
i++;
}
tokens.push({ type: 'number', value: parseFloat(num) });
} else if (/[a-zA-Z]/.test(ch)) {
let name = '';
while (i < expr.length && /[a-zA-Z]/.test(expr[i])) {
name += expr[i];
i++;
}
tokens.push({ type: 'name', value: name });
} else if ('+-*/^()'.includes(ch)) {
tokens.push({ type: 'op', value: ch });
i++;
} else {
throw new Error(`无法识别的字符: ${ch}`);
}
}
return tokens;
}
// 调度场算法：中缀表达式转后缀表达式（RPN）
function toRPN(tokens) {
const output = [];
const ops = [];
const precedence = { '+': 1, '-': 1, '*': 2, '/': 2, '^': 3 };
const rightAssoc = { '^': true };
const funcs = ['sin', 'cos', 'tan', 'exp', 'ln', 'log', 'sqrt', 'abs'];
const isFunction = (tok) => tok && tok.type === 'name' && funcs.includes(tok.value);
let prev = null;
for (let i = 0; i < tokens.length; i++) {
const tok = tokens[i];
if (tok.type === 'number') {
output.push(tok);
} else if (tok.type === 'name') {
if (tok.value === 'x' || tok.value === 'pi' || tok.value === 'e') {
output.push(tok);
} else if (isFunction(tok)) {
ops.push(tok);
} else {
throw new Error(`未知符号: ${tok.value}`);
}
} else if (tok.value === '(') {
ops.push(tok);
} else if (tok.value === ')') {
while (ops.length && ops[ops.length - 1].value !== '(') {
output.push(ops.pop());
}
if (!ops.length) throw new Error('括号不匹配');
ops.pop(); // 弹出 '('
if (ops.length && isFunction(ops[ops.length - 1])) {
output.push(ops.pop());
}
} else if (tok.type === 'op') {
// 处理一元负号
if (tok.value === '-' && (prev === null || prev.value === '(' || prev.type === 'op')) {
output.push({ type: 'number', value: 0 });
}
while (ops.length && ops[ops.length-1].value !== '(' && !isFunction(ops[ops.length-1]) &&
(precedence[ops[ops.length-1].value] > precedence[tok.value] ||
(precedence[ops[ops.length-1].value] === precedence[tok.value] && !rightAssoc[tok.value]))) {
output.push(ops.pop());
}
ops.push(tok);
}
prev = tok;
}
while (ops.length) {
const op = ops.pop();
if (op.value === '(' || op.value === ')') throw new Error('括号不匹配');
output.push(op);
}
return output;
}
// 计算后缀表达式在给定 x 下的值
function evalRPN(rpn, x) {
const stack = [];
const funcs = {
sin: Math.sin, cos: Math.cos, tan: Math.tan,
exp: Math.exp, ln: Math.log, log: Math.log10,
sqrt: Math.sqrt, abs: Math.abs
};
const consts = { pi: Math.PI, e: Math.E };
for (const tok of rpn) {
if (tok.type === 'number') {
stack.push(tok.value);
} else if (tok.type === 'name') {
if (tok.value === 'x') {
stack.push(x);
} else if (consts.hasOwnProperty(tok.value)) {
stack.push(consts[tok.value]);
} else if (funcs.hasOwnProperty(tok.value)) {
if (!stack.length) throw new Error(`函数 ${tok.value} 缺少参数`);
const arg = stack.pop();
stack.push(funcs[tok.value](arg));
} else {
throw new Error(`未知符号: ${tok.value}`);
}
} else if (tok.type === 'op') {
if (stack.length < 2) throw new Error('表达式格式错误');
const b = stack.pop();
const a = stack.pop();
switch (tok.value) {
case '+': stack.push(a + b); break;
case '-': stack.push(a - b); break;
case '*': stack.push(a * b); break;
case '/': stack.push(a / b); break;
case '^': stack.push(Math.pow(a, b)); break;
}
}
}
if (stack.length !== 1) throw new Error('表达式格式错误');
return stack[0];
}
function createFunction(expr) {
const tokens = tokenize(expr);
const rpn = toRPN(tokens);
return function(x) {
return evalRPN(rpn, x);
};
}
// 安全求值
function safeEval(f, x) {
try {
const y = f(x);
return isFinite(y) ? y : NaN;
} catch (e) {
return NaN;
}
}
// 数值求导（优先中心差分，边界处退化为单边差分）
function derivative(f, x) {
const h = 1e-6;
let y1 = safeEval(f, x + h);
let y2 = safeEval(f, x - h);
if (isFinite(y1) && isFinite(y2)) {
return (y1 - y2) / (2 * h);
}
// 尝试前向差分
y1 = safeEval(f, x + h);
y2 = safeEval(f, x);
if (isFinite(y1) && isFinite(y2)) {
return (y1 - y2) / h;
}
// 尝试后向差分
y1 = safeEval(f, x);
y2 = safeEval(f, x - h);
if (isFinite(y1) && isFinite(y2)) {
return (y1 - y2) / h;
}
return NaN;
}
const DEFAULT_X_MIN = -5;
const DEFAULT_X_MAX = 5;
let currentFn = null;
let currentXMin = DEFAULT_X_MIN;
let currentXMax = DEFAULT_X_MAX;
function resetView() {
currentXMin = DEFAULT_X_MIN;
currentXMax = DEFAULT_X_MAX;
}
function zoomView(factor) {
const center = (currentXMin + currentXMax) / 2;
let newRange = (currentXMax - currentXMin) * factor;
const MIN_RANGE = 1e-10;
const MAX_RANGE = 1e10;
if (newRange < MIN_RANGE) newRange = MIN_RANGE;
if (newRange > MAX_RANGE) newRange = MAX_RANGE;
currentXMin = center - newRange / 2;
currentXMax = center + newRange / 2;
draw();
}
function draw() {
errorMsg.textContent = '';
const expr = functionInput.value;
if (currentXMin >= currentXMax) {
currentXMin = DEFAULT_X_MIN;
currentXMax = DEFAULT_X_MAX;
}
try {
currentFn = createFunction(expr);
} catch (e) {
errorMsg.textContent = '表达式错误：' + e.message;
currentFn = null;
return;
}
const width = canvas.width;
const height = canvas.height;
const padding = 40;
const plotWidth = width - 2 * padding;
const plotHeight = height - 2 * padding;
// 清空画布
ctx.clearRect(0, 0, width, height);
// 计算 y 范围
const xStep = (currentXMax - currentXMin) / plotWidth;
const showDerivative = showDerivativeCheckbox.checked;
let yMin = Infinity, yMax = -Infinity;
for (let px = 0; px <= plotWidth; px++) {
const x = currentXMin + px * xStep;
const y = safeEval(currentFn, x);
if (isFinite(y)) {
if (y < yMin) yMin = y;
if (y > yMax) yMax = y;
}
if (showDerivative) {
const dy = derivative(currentFn, x);
if (isFinite(dy)) {
if (dy < yMin) yMin = dy;
if (dy > yMax) yMax = dy;
}
}
}
if (!isFinite(yMin) || !isFinite(yMax) || yMin === yMax) {
yMin = -5;
yMax = 5;
}
const yPadding = (yMax - yMin) * 0.1 || 1;
yMin -= yPadding;
yMax += yPadding;
currentYMin = yMin;
currentYMax = yMax;
// 坐标转换
function toCanvasX(x) {
return padding + (x - currentXMin) / (currentXMax - currentXMin) * plotWidth;
}
function toCanvasY(y) {
return height - padding - (y - yMin) / (yMax - yMin) * plotHeight;
}
// 绘制网格
ctx.strokeStyle = '#e0e4e8';
ctx.lineWidth = 1;
const xGridCount = 10;
const yGridCount = 8;
ctx.beginPath();
for (let i = 0; i <= xGridCount; i++) {
const x = currentXMin + (currentXMax - currentXMin) * i / xGridCount;
const cx = toCanvasX(x);
ctx.moveTo(cx, padding);
ctx.lineTo(cx, height - padding);
}
for (let i = 0; i <= yGridCount; i++) {
const y = yMin + (yMax - yMin) * i / yGridCount;
const cy = toCanvasY(y);
ctx.moveTo(padding, cy);
ctx.lineTo(width - padding, cy);
}
ctx.stroke();
// 绘制坐标轴
ctx.strokeStyle = '#7f8c8d';
ctx.lineWidth = 2;
ctx.beginPath();
const originX = toCanvasX(0);
const originY = toCanvasY(0);
if (originY >= padding && originY <= height - padding) {
ctx.moveTo(padding, originY);
ctx.lineTo(width - padding, originY);
}
if (originX >= padding && originX <= width - padding) {
ctx.moveTo(originX, padding);
ctx.lineTo(originX, height - padding);
}
ctx.stroke();
// 绘制刻度标签
ctx.fillStyle = '#666';
ctx.font = '12px sans-serif';
ctx.textAlign = 'center';
ctx.textBaseline = 'top';
for (let i = 0; i <= xGridCount; i++) {
const x = currentXMin + (currentXMax - currentXMin) * i / xGridCount;
const cx = toCanvasX(x);
if (cx >= padding && cx <= width - padding) {
ctx.fillText(parseFloat(x.toFixed(2)), cx, height - padding + 6);
}
}
ctx.textAlign = 'right';
ctx.textBaseline = 'middle';
for (let i = 0; i <= yGridCount; i++) {
const y = yMin + (yMax - yMin) * i / yGridCount;
const cy = toCanvasY(y);
if (cy >= padding && cy <= height - padding) {
ctx.fillText(parseFloat(y.toFixed(2)), padding - 8, cy);
}
}
// 通用曲线绘制辅助函数
function plotCurve(evaluator, color, lineWidth) {
ctx.strokeStyle = color;
ctx.lineWidth = lineWidth;
ctx.beginPath();
let first = true;
for (let px = 0; px <= plotWidth; px++) {
const x = currentXMin + px * xStep;
const y = evaluator(x);
if (!isFinite(y)) {
first = true;
continue;
}
const cx = toCanvasX(x);
const cy = toCanvasY(y);
if (first) {
ctx.moveTo(cx, cy);
first = false;
} else {
ctx.lineTo(cx, cy);
}
}
ctx.stroke();
}
// 绘制原函数 f(x)
plotCurve(x => safeEval(currentFn, x), '#3498db', 2.5);
// 绘制导函数 f'(x)
if (showDerivative) {
plotCurve(x => derivative(currentFn, x), '#e67e22', 2.5);
}
// 绘制定位点标记
function drawPointMarkers() {
if (!activePoints.length) return;
for (const pt of activePoints) {
const y = safeEval(currentFn, pt.x);
if (!isFinite(y)) continue;
const cx = toCanvasX(pt.x);
const cy = toCanvasY(y);
if (cx < padding || cx > width - padding || cy < padding || cy > height - padding) continue;
ctx.strokeStyle = pt.type === 'fromX' ? '#27ae60' : '#9b59b6';
ctx.fillStyle = pt.type === 'fromX' ? '#27ae60' : '#9b59b6';
ctx.lineWidth = 1.5;
// 十字准星
ctx.setLineDash([4, 4]);
ctx.beginPath();
ctx.moveTo(cx, padding);
ctx.lineTo(cx, height - padding);
ctx.moveTo(padding, cy);
ctx.lineTo(width - padding, cy);
ctx.stroke();
ctx.setLineDash([]);
// 中心点
ctx.beginPath();
ctx.arc(cx, cy, 5, 0, Math.PI * 2);
ctx.fill();
}
}
// 绘制函数公式标签
ctx.font = 'bold 13px sans-serif';
ctx.textAlign = 'left';
ctx.textBaseline = 'top';
const labelX = padding + 12;
const labelY = padding + 10;
ctx.fillStyle = '#3498db';
ctx.fillText('f(x) = ' + (expr || '未输入'), labelX, labelY);
if (showDerivative) {
ctx.fillStyle = '#e67e22';
ctx.fillText("f'(x) ≈ [f(x+h) - f(x-h)] / (2h)", labelX, labelY + 20);
}
// 标注由点定位计算出的位置
drawPointMarkers();
}
let currentYMin = -5;
let currentYMax = 5;
let activePoints = [];
// 二分法求根：在 [a,b] 上找 f(x) = target 的解（假设两端异号）
function bisect(f, a, b, target, tol) {
let fa = safeEval(f, a) - target;
let fb = safeEval(f, b) - target;
if (!isFinite(fa) || !isFinite(fb)) return NaN;
if (fa === 0) return a;
if (fb === 0) return b;
if (fa * fb > 0) return NaN;
for (let i = 0; i < 60; i++) {
const mid = (a + b) / 2;
const fm = safeEval(f, mid) - target;
if (!isFinite(fm)) return NaN;
if (Math.abs(fm) < tol || (b - a) < tol) return mid;
if (fa * fm <= 0) {
b = mid;
fb = fm;
} else {
a = mid;
fa = fm;
}
}
return (a + b) / 2;
}
// 扫描视图范围，寻找 f(x) = targetY 的所有解
function findRootsForY(targetY) {
if (!currentFn) return [];
const roots = [];
const samples = 400;
const step = (currentXMax - currentXMin) / samples;
let prevX = currentXMin;
let prevVal = safeEval(currentFn, prevX) - targetY;
for (let i = 1; i <= samples; i++) {
const x = currentXMin + i * step;
const val = safeEval(currentFn, x) - targetY;
if (!isFinite(val) || !isFinite(prevVal)) {
prevX = x;
prevVal = val;
continue;
}
if (val === 0) {
roots.push(x);
} else if (prevVal !== 0 && prevVal * val < 0) {
const root = bisect(currentFn, prevX, x, targetY, 1e-10);
if (isFinite(root)) roots.push(root);
}
prevX = x;
prevVal = val;
}
// 去重（容差内）
const unique = [];
for (const r of roots) {
if (!unique.some(u => Math.abs(u - r) < 1e-6)) {
unique.push(r);
}
}
return unique;
}
function formatNum(n) {
if (!isFinite(n)) return '无定义';
return parseFloat(n.toFixed(6)).toString();
}
canvas.addEventListener('mousemove', function(e) {
if (!currentFn) return;
const rect = canvas.getBoundingClientRect();
const px = e.clientX - rect.left;
const py = e.clientY - rect.top;
const padding = 40;
const plotWidth = canvas.width - 2 * padding;
const plotHeight = canvas.height - 2 * padding;
if (isDragging) {
const dx = px - dragStartX;
const xRange = dragStartXMax - dragStartXMin;
const shift = -dx * xRange / plotWidth;
currentXMin = dragStartXMin + shift;
currentXMax = dragStartXMax + shift;
draw();
return;
}
if (px < padding || px > canvas.width - padding || py < padding || py > canvas.height - padding) {
mouseXEl.textContent = '-';
mouseYEl.textContent = '-';
mouseDyEl.textContent = '-';
return;
}
const x = currentXMin + (px - padding) / plotWidth * (currentXMax - currentXMin);
let y;
try {
y = currentFn(x);
} catch (e) {
mouseYEl.textContent = '错误';
return;
}
if (!isFinite(y)) {
mouseXEl.textContent = x.toFixed(4);
mouseYEl.textContent = '无定义';
mouseDyEl.textContent = '-';
} else {
mouseXEl.textContent = x.toFixed(4);
mouseYEl.textContent = y.toFixed(4);
const dy = derivative(currentFn, x);
mouseDyEl.textContent = isFinite(dy) ? dy.toFixed(4) : '无定义';
}
// 重绘并显示指示线
draw();
const cx = padding + (x - currentXMin) / (currentXMax - currentXMin) * plotWidth;
const cy = canvas.height - padding - (y - currentYMin) / (currentYMax - currentYMin) * plotHeight;
if (isFinite(y)) {
ctx.strokeStyle = '#e74c3c';
ctx.lineWidth = 1;
ctx.setLineDash([5, 5]);
ctx.beginPath();
ctx.moveTo(cx, padding);
ctx.lineTo(cx, canvas.height - padding);
ctx.moveTo(padding, cy);
ctx.lineTo(canvas.width - padding, cy);
ctx.stroke();
ctx.setLineDash([]);
ctx.fillStyle = '#e74c3c';
ctx.beginPath();
ctx.arc(cx, cy, 5, 0, Math.PI * 2);
ctx.fill();
}
});
let isDragging = false;
let dragStartX = 0;
let dragStartXMin = 0;
let dragStartXMax = 0;
canvas.addEventListener('mousedown', function(e) {
if (e.button !== 0) return;
const rect = canvas.getBoundingClientRect();
const px = e.clientX - rect.left;
const py = e.clientY - rect.top;
const padding = 40;
if (px < padding || px > canvas.width - padding || py < padding || py > canvas.height - padding) return;
isDragging = true;
dragStartX = px;
dragStartXMin = currentXMin;
dragStartXMax = currentXMax;
canvas.style.cursor = 'grabbing';
});
canvas.addEventListener('mouseup', function() {
isDragging = false;
canvas.style.cursor = 'grab';
});
canvas.addEventListener('mouseleave', function() {
isDragging = false;
canvas.style.cursor = 'grab';
mouseXEl.textContent = '-';
mouseYEl.textContent = '-';
mouseDyEl.textContent = '-';
draw();
});
// 示例按钮：在光标位置插入函数
document.querySelectorAll('.example-btn').forEach(btn => {
btn.addEventListener('click', function() {
const text = this.dataset.fn;
const start = functionInput.selectionStart || 0;
const end = functionInput.selectionEnd || 0;
const current = functionInput.value;
functionInput.value = current.slice(0, start) + text + current.slice(end);
functionInput.focus();
const newPos = start + text.length;
functionInput.setSelectionRange(newPos, newPos);
draw();
});
});
plotBtn.addEventListener('click', draw);
showDerivativeCheckbox.addEventListener('change', draw);
functionInput.addEventListener('keydown', function(e) {
if (e.key === 'Enter') draw();
});
clearBtn.addEventListener('click', function() {
functionInput.value = '';
resetView();
activePoints = [];
pointResultEl.textContent = '';
draw();
});
zoomInBtn.addEventListener('click', function() {
zoomView(0.75);
});
zoomOutBtn.addEventListener('click', function() {
zoomView(1.3333333333333333);
});
calcFromXBtn.addEventListener('click', function() {
if (!currentFn) {
pointResultEl.textContent = '请先输入并绘制函数。';
return;
}
const x = parseFloat(pointXInput.value);
if (!isFinite(x)) {
pointResultEl.textContent = '请输入有效的 x 值。';
return;
}
const y = safeEval(currentFn, x);
const dy = derivative(currentFn, x);
if (!isFinite(y)) {
pointResultEl.textContent = `在 x = ${formatNum(x)} 处函数无定义。`;
activePoints = [];
} else {
pointResultEl.innerHTML = `x = <strong>${formatNum(x)}</strong> 时，f(x) = <strong>${formatNum(y)}</strong>，f'(x) ≈ <strong>${formatNum(dy)}</strong>`;
activePoints = [{ x, type: 'fromX' }];
}
draw();
});
calcFromYBtn.addEventListener('click', function() {
if (!currentFn) {
pointResultEl.textContent = '请先输入并绘制函数。';
return;
}
const y = parseFloat(pointYInput.value);
if (!isFinite(y)) {
pointResultEl.textContent = '请输入有效的 y 值。';
return;
}
const roots = findRootsForY(y);
if (roots.length === 0) {
pointResultEl.textContent = `在视图范围内未找到 f(x) = ${formatNum(y)} 的解。`;
activePoints = [];
} else {
const items = roots.map(r => {
const fy = safeEval(currentFn, r);