• htm+JS实现绘制数学函数图像

    htm+JS实现绘制数学函数图像

    其中常用的函数可参见，JS中常用的Math方法 https://blog.51cto.com/u_10725738/5253407

    https://www.jb51.net/article/9151.htm

    JS(JavaScript)常用Math函数与用法说明

    方法描述示例
    abs(x)返回数的绝对值。Math.abs(-10)//返回10
    acos(x)返回数的反余弦值。Math.acos(1)//返回0
    asin(x)返回数的反正弦值。Math.asin(1)//返回1.5707963267948965
    atan(x)以介于 -PI/2 与 PI/2 弧度之间的数值来返回 x 的反正切值。Math.atan(0.50)//返回0.4636476090008061
    atan2(y,x)返回从 x 轴到点 (x,y) 的角度（介于 -PI/2 与 PI/2 弧度之间）。Math.atan2(5,5)//输出0.7853981633974483
    ceil(x)对数进行上舍入。

    Math.ceil(0.60)
    Math.ceil(-5.1) 

    		//返回1
    //返回-5
    cos(x)返回数的余弦。Math.cos(0)//返回1
    exp(x)返回 e 的指数。Math.exp(5)//返回148.4131591025766
    floor(x)对数进行下舍入。Math.floor(0.60)
    Math.floor(-5.1)    		//返回0
    //返回-6
    log(x)返回数的自然对数（底为e）。Math.log(1)//返回0
    max(x,y)返回 x 和 y 中的最高值。Math.max(5,7)//返回7
    min(x,y)返回 x 和 y 中的最低值。Math.min(5,7)//返回5
    pow(x,y)返回 x 的 y 次幂。Math.pow(2,4)//返回16
    random()返回 0 ~ 1 之间的随机数。Math.random()//返回类似0.6654807284142312的随机数
    round(x)把数四舍五入为最接近的整数。Math.round(0.60)
    Math.round(-4.40)    		//返回1
    //返回-4
    sin(x)返回数的正弦。Math.sin(0)//返回0
    sqrt(x)返回数的平方根。Math.sqrt(0.64)//返回0.8
    tan(x)返回角的正切。Math.tan(10)//返回0.6483608274590866

    运行效果

     项目目录结构

     特别说明源码取自网络。

    数学函数绘图.html 源码：

    1. html>
    2. <html>
    3. 	<head>
    4. 		<meta charset="UTF-8">
    5. 		<title>函数图像绘制工具title>
    6. 		<script type="text/javascript" src="js/funcImg.js">script>
    7. 		<style>
    8. 			#div-img {
    9. 				/* 此决定画布的宽高 */
    10. 				width: 500px;
    11. 				height: 500px;
    12. 			}
    13. 			#input-controller {
    14. 				padding: 10px;
    15. 				background-color: azure;
    16. 			}
    17. 		style>
    18. 	head>
    19. 	<body>
    20. 		<div id="input-controller">
    21. 			<div id="function">
    22. 				<button onclick="Add()">添加函数button>
    23. 				<span id="mod" style="display:none" name="0">
    24. 					<input type="color"/>y=
    25. 					<input type="text" value="x^3" name="Fun"/>
    26. 					<button onclick="Delete(this.parentNode)">Deletebutton>
    27. 	                <input type="checkbox" onclick="reDraw()" checked="checked"/>Draw Line
    28. 				span>
    29. 			div>
    30. 			<div id="option">
    31. 				X：<input id="xLeftValue" /> ~
    32. 				<input id="xRightValue" />
    33. 				<br> Y：
    34. 				<input id="yLeftValue" /> ~
    35. 				<input id="yRightValue" />
    36. 				<br>
    37. 				<span id="show-size">Size:span>
    38. 			div>
    39. 			<button onclick="change()">画图button>
    40. 		div>
    41. 		<div id="main">
    42. 			<h1>函数图像绘制工具h1>
    43. 			<div id="div-img">
    44. 				<canvas id="graph">canvas>
    45. 			div>
    46. 		div>
    47. 	body>
    48. 	<script>
    49. 		const FONT_STYLE = "10px 黑体";
    50. 		const MIN = 1e-4;
    51. 		const MAX = 1e8;
    52. 		const EPS = 1e-12;
    53. 		const CANVAS = $("graph");
    54. 		const CONTEXT_2D = CANVAS.getContext("2d");
    55. 		const FUN_IMG_WIDTH = CANVAS.parentNode.clientWidth;
    56. 		const FUN_IMG_HEIGHT = CANVAS.parentNode.clientHeight;
    57. 		var xLeftValue = -FUN_IMG_WIDTH / 100; // x最左的值
    58. 		var xRightValue = FUN_IMG_WIDTH / 100;
    59. 		var yLeftValue = -FUN_IMG_HEIGHT / 100;
    60. 		var yRightValue = FUN_IMG_HEIGHT / 100;
    61. 		var tableX, tableY, countX, countY;
    62. 		var funStage = 0,
    63. 			mouseX, mouseY;
    64. 		var tmp;
    65. 	script>
    66. 	<script>
    67. 		CANVAS.width = FUN_IMG_WIDTH;
    68. 		CANVAS.height = FUN_IMG_HEIGHT;
    69. 		$("show-size").innerHTML = "Size：" + FUN_IMG_WIDTH + "*" + FUN_IMG_HEIGHT;
    70. 		CANVAS.onmousedown = function(ob) {
    71. 			mouseX = ob.layerX;
    72. 			mouseY = ob.layerY;
    73. 			funStage = 1;
    74. 		}
    75. 		CANVAS.onmousemove = function(ob) {
    76. 			if(funStage != 1) {
    77. 				return;
    78. 			}
    79. 			var NoX, NoY, det;
    80. 			NoX = ob.layerX;
    81. 			NoY = ob.layerY;
    82. 			det = (mouseX - NoX) / FUN_IMG_WIDTH * (xRightValue - xLeftValue);
    83. 			xLeftValue += det;
    84. 			xRightValue += det;
    85. 			det = (NoY - mouseY) / FUN_IMG_HEIGHT * (yRightValue - yLeftValue);
    86. 			yLeftValue += det;
    87. 			yRightValue += det;
    88. 			mouseX = NoX;
    89. 			mouseY = NoY;
    90. 			reDraw();
    91. 			update();
    92. 		}
    93. 		CANVAS.onmouseup = function(ob) {
    94. 			if(funStage == 1) {
    95. 				funStage = 0;
    96. 				reDraw();
    97. 			}
    98. 		}
    99. 		CANVAS.onmouseleave = function(ob) {
    100. 			if(funStage == 1) {
    101. 				funStage = 0;
    102. 				reDraw();
    103. 			}
    104. 		}
    105. 		CANVAS.onmousewheel = function(ob) {
    106. 			// 取消事件的默认动作
    107. 			ob.preventDefault();
    108. 			// 放大的比例
    109. 			var ScaleRate = 0.9;
    110. 			var detail;
    111. 			if(ob.wheelDelta) {
    112. 				detail = ob.wheelDelta;
    113. 			} else if(ob.detail) {
    114. 				detail = ob.detail;
    115. 			}
    116. 			if(detail > 0) {
    117. 				scale(ob.layerX, FUN_IMG_HEIGHT - 1 - ob.layerY, ScaleRate);
    118. 			} else {
    119. 				scale(ob.layerX, FUN_IMG_HEIGHT - 1 - ob.layerY, 1 / ScaleRate);
    120. 			}
    121. 			reDraw();
    122. 			update();
    123. 		}
    124. 		// 初始化
    125. 		reDraw();
    126. 		update();
    127. 		Add();
    128. 	script>
    129. html>

    funcImg.js 源码：

    1. function $(id) {
    2. 	return document.getElementById(id);
    3. }
    4. function getRandomColor() {
    5. 	var color = '#' + ('00000' + (Math.random() * 0x1000000 << 0).toString(16)).substr(-6);
    6. 	return color;
    7. }
    8. function FunWork(f, x) {
    9. 	switch(f) {
    10. 		case "":
    11. 			{
    12. 				return x;
    13. 				break;
    14. 			}
    15. 		case "sin":
    16. 			{
    17. 				return Math.sin(x);
    18. 				break;
    19. 			}
    20. 		case "cos":
    21. 			{
    22. 				return Math.cos(x);
    23. 				break;
    24. 			}
    25. 		case "tan":
    26. 			{
    27. 				return Math.tan(x);
    28. 				break;
    29. 			}
    30. 		case "abs":
    31. 			{
    32. 				return Math.abs(x);
    33. 				break;
    34. 			}
    35. 		case "sqrt":
    36. 			{
    37. 				return Math.sqrt(x);
    38. 				break;
    39. 			}
    40. 		case "ln":
    41. 			{
    42. 				return Math.log(x);
    43. 				break;
    44. 			}
    45. 		case "log":
    46. 			{
    47. 				return Math.log(x) / Math.LN2;
    48. 				break;
    49. 			} //2为底
    50. 		case "lg":
    51. 			{
    52. 				return Math.log(x) / Math.LN10;
    53. 				break;
    54. 			} //10为底
    55. 		case "floor":
    56. 			{
    57. 				return Math.floor(x);
    58. 				break;
    59. 			}
    60. 		case "ceil":
    61. 			{
    62. 				return Math.ceil(x);
    63. 				break;
    64. 			}
    65. 		case "int":
    66. 			{
    67. 				return parseInt(x);
    68. 				break;
    69. 			}
    70. 		default:
    71. 			{
    72. 				return NaN;
    73. 				break;
    74. 			}
    75. 	}
    76. }
    77. function ChangeToPointY(y) {
    78. 	return FUN_IMG_HEIGHT - 1 - parseInt((y - yLeftValue) / (yRightValue - yLeftValue) * FUN_IMG_HEIGHT);
    79. }
    80. function isChar(c) {
    81. 	return(c >= 'a' && c <= 'z') || (c >= 'A' && c <= 'Z');
    82. }
    83. function isDigit(c) {
    84. 	return c >= '0' && c <= '9';
    85. }
    86. function priority(c) {
    87. 	switch(c) {
    88. 		case '(':
    89. 			return 0;
    90. 			break;
    91. 		case '+':
    92. 			return 1;
    93. 			break;
    94. 		case '-':
    95. 			return 1;
    96. 			break;
    97. 		case '*':
    98. 			return 2;
    99. 			break;
    100. 		case '/':
    101. 			return 2;
    102. 			break;
    103. 		case '^':
    104. 			return 3;
    105. 			break;
    106. 		default:
    107. 			return -1;
    108. 			break;
    109. 	}
    110. }
    111. // 是运算符
    112. function isOpt(c) {
    113. 	return priority(c) != -1;
    114. }
    115. function singleCalc(c, a, b) {
    116. 	if(c == '+') {
    117. 		return a + b;
    118. 	} else
    119. 	if(c == '-') {
    120. 		return a - b;
    121. 	} else
    122. 	if(c == '*') {
    123. 		return a * b;
    124. 	} else
    125. 	if(c == '/') {
    126. 		return a / b;
    127. 	} else
    128. 	if(c == '^') {
    129. 		return Math.pow(a, b);
    130. 	} else {
    131. 		return NaN;
    132. 	}
    133. }
    134. function getTable() {
    135. 	tmp = (xRightValue - xLeftValue + EPS) / 20;
    136. 	tableX = 1;
    137. 	countX = 0;
    138. 	countY = 0;
    139. 	while(tableX < tmp) {
    140. 		tableX *= 10;
    141. 	}
    142. 	while(tableX / 10 > tmp) {
    143. 		tableX /= 10;
    144. 		countX++;
    145. 	}
    146. 	if(tableX >= 1) {
    147. 		countX = 0;
    148. 	}
    149. 	if(tableX / 5 > tmp) {
    150. 		tableX /= 5;
    151. 		countX++;
    152. 	} else if(tableX / 2 > tmp) {
    153. 		tableX /= 2;
    154. 		countX++;
    155. 	}
    156. 	var i = parseInt(xLeftValue / tableX) + (xLeftValue > 0)
    157. 	for(; i * tableX < xRightValue; i++) {
    158. 		if(i == 0) {
    159. 			// y轴
    160. 			CONTEXT_2D.fillStyle = "black";
    161. 		} else {
    162. 			// 普通竖线
    163. 			CONTEXT_2D.fillStyle = "#CDB7B5";
    164. 		}
    165. 		tmp = (i * tableX - xLeftValue) / (xRightValue - xLeftValue) * FUN_IMG_WIDTH;
    166. 		var _width = 1;
    167. 		var _height = FUN_IMG_HEIGHT;
    168. 		CONTEXT_2D.fillRect(tmp, 0, _width, _height);
    169. 		// 竖线上的数字
    170. 		CONTEXT_2D.fillStyle = "red";
    171. 		CONTEXT_2D.font = FONT_STYLE;
    172. 		var _text = (i * tableX).toFixed(countX);
    173. 		var _x = tmp + 2;
    174. 		var _y = 10;
    175. 		CONTEXT_2D.fillText(_text, _x, _y);
    176. 	}
    177. 	tmp = (yRightValue - yLeftValue + EPS) / 20;
    178. 	tableY = 1;
    179. 	while(tableY < tmp) {
    180. 		tableY *= 10;
    181. 	}
    182. 	while(tableY / 10 > tmp) {
    183. 		tableY /= 10, countY++;
    184. 	}
    185. 	if(tableY / 5 > tmp) {
    186. 		tableY /= 5, countY++;
    187. 	} else if(tableY / 2 > tmp) {
    188. 		tableY /= 2, countY++;
    189. 	}
    190. 	if(tableY >= 1) {
    191. 		countY = 0;
    192. 	}
    193. 	var i = parseInt(yLeftValue / tableY) + (yLeftValue > 0);
    194. 	for(; i * tableY < yRightValue; i++) {
    195. 		// 横线
    196. 		if(i == 0) {
    197. 			// x轴
    198. 			CONTEXT_2D.fillStyle = "black";
    199. 		} else {
    200. 			// 普通横线
    201. 			CONTEXT_2D.fillStyle = "#CDB7B5";
    202. 		}
    203. 		tmp = (i * tableY - yLeftValue) / (yRightValue - yLeftValue) * FUN_IMG_HEIGHT;
    204. 		CONTEXT_2D.fillRect(0, FUN_IMG_HEIGHT - 1 - tmp, FUN_IMG_WIDTH, 1);
    205. 		// 横线上的数字
    206. 		CONTEXT_2D.fillStyle = "blue";
    207. 		CONTEXT_2D.font = FONT_STYLE;
    208. 		CONTEXT_2D.fillText((i * tableY).toFixed(countY), 0, FUN_IMG_HEIGHT - 1 - tmp);
    209. 	}
    210. }
    211. function drawArc(x, y) {
    212. 	CONTEXT_2D.beginPath();
    213. 	// arc(弧形),画圆
    214. 	CONTEXT_2D.arc(x, y, 1, 0, Math.PI * 2);
    215. 	CONTEXT_2D.closePath();
    216. 	CONTEXT_2D.fill();
    217. }
    218. function drawLine(lx, ly, px, py) {
    219. 	CONTEXT_2D.beginPath();
    220. 	CONTEXT_2D.moveTo(lx, ly);
    221. 	CONTEXT_2D.lineTo(px, py);
    222. 	CONTEXT_2D.closePath();
    223. 	CONTEXT_2D.stroke(); // 绘制
    224. }
    225. function reDraw() {
    226. 	CONTEXT_2D.clearRect(0, 0, FUN_IMG_WIDTH, FUN_IMG_HEIGHT);
    227. 	getTable();
    228. 	getFunction();
    229. }
    230. function change() {
    231. 	xLeftValue = parseFloat($("xLeftValue").value);
    232. 	xRightValue = parseFloat($("xRightValue").value);
    233. 	yLeftValue = parseFloat($("yLeftValue").value);
    234. 	yRightValue = parseFloat($("yRightValue").value);
    235. 	reDraw();
    236. }
    237. function update() {
    238. 	$("xLeftValue").value = xLeftValue;
    239. 	$("xRightValue").value = xRightValue;
    240. 	$("yLeftValue").value = yLeftValue;
    241. 	$("yRightValue").value = yRightValue;
    242. }
    243. function scale(x, y, times) {
    244. 	if(x < 0 || x >= FUN_IMG_WIDTH || y < 0 || y >= FUN_IMG_HEIGHT) return;
    245. 	if(times < 1 && (xRightValue - xLeftValue < MIN || yRightValue - yLeftValue < MIN)) {
    246. 		return;
    247. 	}
    248. 	if(times > 1 && (xRightValue - xLeftValue > MAX || yRightValue - yLeftValue > MAX)) {
    249. 		return;
    250. 	}
    251. 	x = xLeftValue + (xRightValue - xLeftValue) / FUN_IMG_WIDTH * x;
    252. 	y = yLeftValue + (yRightValue - yLeftValue) / FUN_IMG_HEIGHT * y;
    253. 	xLeftValue = x - (x - xLeftValue) * times;
    254. 	xRightValue = x + (xRightValue - x) * times;
    255. 	yLeftValue = y - (y - yLeftValue) * times;
    256. 	yRightValue = y + (yRightValue - y) * times;
    257. }
    258. function Calc(fun, X, Value) {
    259. 	var number = new Array(),
    260. 		opt = new Array(),
    261. 		F = new Array(),
    262. 		now = 0,
    263. 		f = "",
    264. 		tmp, a, b, sign = 1,
    265. 		base = 0,
    266. 		j;
    267. 	for(var i = 0; i < fun.length; i++) {
    268. 		for(j = 0; j < X.length; j++)
    269. 			if(X[j] == fun[i]) {
    270. 				if(i == 0 || isOpt(fun[i - 1])) now = Value[j];
    271. 				else now *= Value[j];
    272. 				break;
    273. 			}
    274. 		if(j == X.length)
    275. 			if(fun[i] == '(') F.push(f), f = "", opt.push('(');
    276. 			else
    277. 		if(fun[i] == ')') {
    278. 			number.push(now * sign);
    279. 			now = 0;
    280. 			sign = 1;
    281. 			base = 0;
    282. 			while((tmp = opt.pop()) != '(') {
    283. 				b = number.pop();
    284. 				a = number.pop();
    285. 				tmp = singleCalc(tmp, a, b);
    286. 				number.push(tmp);
    287. 			}
    288. 			now = FunWork(F.pop(), number.pop());
    289. 		} else
    290. 		if(fun[i] == '.') base = 1;
    291. 		else
    292. 		if(fun[i] == '+' && (i == 0 || priority(fun[i - 1]) != -1));
    293. 		else
    294. 		if(fun[i] == '-' && (i == 0 || priority(fun[i - 1]) != -1)) sign = -1;
    295. 		else
    296. 		if(fun[i] == 'e')
    297. 			if(i == 0 || isOpt(fun[i - 1])) now = Math.E;
    298. 			else now *= Math.E;
    299. 		else
    300. 		if(fun[i] == 'p' && fun[i + 1] == 'i') {
    301. 			if(i == 0 || isOpt(fun[i - 1])) now = Math.PI;
    302. 			else now *= Math.PI;
    303. 			i += 1;
    304. 		} else
    305. 		if(isDigit(fun[i]))
    306. 			if(base == 0) now = now * 10 + (fun[i] - '0');
    307. 			else base /= 10, now += base * (fun[i] - '0');
    308. 		else
    309. 		if(isChar(fun[i])) f += fun[i];
    310. 		else if(isOpt(fun[i])) {
    311. 			number.push(now * sign);
    312. 			now = 0;
    313. 			sign = 1;
    314. 			base = 0;
    315. 			var s = priority(fun[i]);
    316. 			if(s == -1) return 0;
    317. 			while(s <= priority(opt[opt.length - 1])) {
    318. 				b = number.pop();
    319. 				a = number.pop();
    320. 				tmp = singleCalc(opt.pop(), a, b);
    321. 				number.push(tmp);
    322. 			}
    323. 			opt.push(fun[i]);
    324. 		}
    325. 	}
    326. 	number.push(now * sign);
    327. 	while(opt.length > 0) {
    328. 		b = number.pop();
    329. 		a = number.pop();
    330. 		tmp = singleCalc(opt.pop(), a, b);
    331. 		number.push(tmp);
    332. 	}
    333. 	return number.pop();
    334. }
    335. function getFunction() {
    336. 	// group：函数（可能是复数）
    337. 	var group = document.getElementsByName("Fun");
    338. 	var x, y;
    339. 	var lax, lay;
    340. 	var px, py
    341. 	var color, outSide, type
    342. 	var ValueL, ValueR, ValueS, isDrawLine, tmp, TMP;
    343. 	for(var k = 1; k < group.length; k++) {
    344. 		var _funcItem = group[k].parentNode;
    345. 		outSide = 1;
    346. 		//type = _funcItem.children[0].value;
    347. 		// 颜色
    348. 		color = _funcItem.children[0].value;
    349. 		// 函数表达式
    350. 		funcExpression = group[k].value;
    351. 		// 是否画线（默认画点）
    352. 		isDrawLine = _funcItem.children[3].checked;
    353. 		CONTEXT_2D.fillStyle = CONTEXT_2D.strokeStyle = color;
    354. 		for(var i = 0; i < FUN_IMG_WIDTH; i++) {
    355. 			x = xLeftValue + (xRightValue - xLeftValue) / FUN_IMG_WIDTH * i;
    356. 			y = Calc(funcExpression, ['x'], [x]);
    357. 			if(isNaN(y)) {
    358. 				continue;
    359. 			}
    360. 			px = i;
    361. 			py = ChangeToPointY(y);
    362. 			if(y >= yLeftValue && y < yRightValue) {
    363. 				// 画圆
    364. 				drawArc(px, py);
    365. 				if(isDrawLine) {
    366. 					drawLine(lax, lay, px, py);
    367. 				}
    368. 				outSide = 0;
    369. 			} else {
    370. 				if(isDrawLine) {
    371. 					if(!outSide) {
    372. 						drawLine(lax, lay, px, py);
    373. 					}
    374. 				} else {}
    375. 				outSide = 1;
    376. 			}
    377. 			lax = px;
    378. 			lay = py;
    379. 		}
    380. 	}
    381. }
    382. function Add() {
    383. 	var newInput = $("mod").cloneNode(true);
    384. 	newInput.style.display = "block";
    385. 	newInput.children[0].value = getRandomColor();
    386. 	$("function").appendChild(newInput);
    387. }
    388. function Delete(node) {
    389. 	node.parentNode.removeChild(node);
    390. }

    附学习资料
    https://blog.csdn.net/Mingyueyixi/article/details/80964430

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  • 原文地址：https://blog.csdn.net/cnds123/article/details/127587986