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JS 绘制平滑曲线

本文介绍在 JS 中绘制平滑曲线的实现,调用下面的函数 drawSmoothCurve() 即可。默认曲线的 2 个顶点之间被分割为 16 个小线段来拟合曲线,下图展示了 tension 为 0.3,0.5,0.7 时的曲线效果,tension 并不是越大越好,默认的 0.5 大多数时候就不错。

算法来自于 How to draw smooth curve through N points using javascript HTML5 canvas?

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<!DOCTYPE html>
<html>

<head>
<meta charset="utf-8">
<title>绘制平滑曲线</title>
<script src="http://cdn.bootcss.com/jquery/3.2.1/jquery.min.js"></script>
<style media="screen">
canvas {
border: 1px solid #BBB;
border-radius: 4px;
}
</style>
</head>

<body>
<canvas id="canvas" width="500" height="600">Your browser does not support canvas.</canvas>

<script>
var canvas = $('#canvas').get(0);
var context = canvas.getContext('2d');
context.lineWidth = 2;

// 曲线顶点坐标数组,points[i] 是第 i 个点的 x 坐标,points[i+1] 是第 i 个点的 y 坐标
var points = [];
var showPoints = true;

for (var x = 10; x < canvas.width;) {
var dx = Math.random() * 30 + 10;
var y = Math.random() * 150 + 20;
points.push(x);
points.push(y);
x += dx;
}

// tension 不一样,对比效果
drawSmoothCurve(context, points, showPoints, 0.3);

context.strokeStyle = 'darkred';
context.translate(0, 200);
drawSmoothCurve(context, points, showPoints); // tension 默认为 0.5,效果不错

context.strokeStyle = 'darkblue';
context.translate(0, 200);
drawSmoothCurve(context, points, showPoints, 0.7);

/**
* 绘制平滑曲线。
*
* @param {Object} context Canvas 的 context
* @param {Array} points 曲线顶点坐标数组,
* points[i+0] 是第 i 个点的 x 坐标,
* points[i+1] 是第 i 个点的 y 坐标
* @param {Boolean} showPoints 是否绘制曲线的顶点
* @param {Float} tension 密集程度,默认为 0.5
* @param {Boolean} closed 是否创建闭合曲线,默认为 false
* @param {Int} numberOfSegments 平滑曲线 2 个顶点间的线段数,默认为 16
* @return 无返回值
*/
function drawSmoothCurve(context, points, showPoints, tension, closed, numberOfSegments) {
drawLines(context, createSmoothCurvePoints(points, tension, closed, numberOfSegments));
showPoints && drawPoints(context, points);
}

/**
* 使用传入的曲线的顶点坐标创建平滑曲线的顶点。
*
* @param {Array} points 曲线顶点坐标数组,
* points[i+0] 是第 i 个点的 x 坐标,
* points[i+1] 是第 i 个点的 y 坐标
* @param {Float} tension 密集程度,默认为 0.5
* @param {Boolean} closed 是否创建闭合曲线,默认为 false
* @param {Int} numberOfSegments 平滑曲线 2 个顶点间的线段数,默认为 16
* @return {Array} 平滑曲线的顶点坐标数组
*/
function createSmoothCurvePoints(points, tension, closed, numberOfSegments) {
if (points.length < 4) { return points; }

// use input value if provided, or use a default value
tension = tension ? tension : 0.5;
closed = closed ? true : false;
numberOfSegments = numberOfSegments ? numberOfSegments : 16;

var ps = points.slice(0), // clone array so we don't change the original
result = [], // result points
x, y, // our x,y coords
t1x, t2x, t1y, t2y, // tension vectors
c1, c2, c3, c4, // cardinal points
st, t, i; // steps based on number of segments

// The algorithm require a previous and next point to the actual point array.
// Check if we will draw closed or open curve.
// If closed, copy end points to beginning and first points to end
// If open, duplicate first points to befinning, end points to end
if (closed) {
ps.unshift(points[points.length - 1]);
ps.unshift(points[points.length - 2]);
ps.unshift(points[points.length - 1]);
ps.unshift(points[points.length - 2]);
ps.push(points[0]);
ps.push(points[1]);
} else {
ps.unshift(points[1]); // copy 1st point and insert at beginning
ps.unshift(points[0]);
ps.push(points[points.length - 2]); // copy last point and append
ps.push(points[points.length - 1]);
}

// 1. loop goes through point array
// 2. loop goes through each segment between the 2 points + 1e point before and after
for (i = 2; i < (ps.length - 4); i += 2) {
// calculate tension vectors
t1x = (ps[i + 2] - ps[i - 2]) * tension;
t2x = (ps[i + 4] - ps[i - 0]) * tension;
t1y = (ps[i + 3] - ps[i - 1]) * tension;
t2y = (ps[i + 5] - ps[i + 1]) * tension;

for (t = 0; t <= numberOfSegments; t++) {
// calculate step
st = t / numberOfSegments;

// calculate cardinals
c1 = 2 * Math.pow(st, 3) - 3 * Math.pow(st, 2) + 1;
c2 = -(2 * Math.pow(st, 3)) + 3 * Math.pow(st, 2);
c3 = Math.pow(st, 3) - 2 * Math.pow(st, 2) + st;
c4 = Math.pow(st, 3) - Math.pow(st, 2);

// calculate x and y cords with common control vectors
x = c1 * ps[i] + c2 * ps[i + 2] + c3 * t1x + c4 * t2x;
y = c1 * ps[i + 1] + c2 * ps[i + 3] + c3 * t1y + c4 * t2y;

//store points in array
result.push(x);
result.push(y);
}
}

return result;
}

function drawLines(context, points) {
context.beginPath();
context.moveTo(points[0], points[1]);
for (i = 2; i < points.length - 1; i += 2) {
context.lineTo(points[i], points[i + 1]);
}
context.stroke();
}

function drawPoints(context, points) {
for (var i = 0; i < points.length - 1; i += 2) {
context.beginPath();
context.arc(points[i], points[i + 1], 3, 0, Math.PI * 2);
context.fill();
}
}
</script>
</body>

</html>