这篇文章给大家介绍Javascript中怎么生成平滑曲线，内容非常详细，感兴趣的小伙伴们可以参考借鉴，希望对大家能有所帮助。
前言
平滑曲线生成是一个很实用的技术
很多时候，我们都需要通过绘制一些折线，然后让计算机平滑的连接起来，
先来看下最终效果(红色为我们输入的直线，蓝色为拟合过后的曲线) 首尾可以特殊处理让图形看起来更好：）
实现思路是利用贝塞尔曲线进行拟合
贝塞尔曲线简介
贝塞尔曲线（英语：Bézier curve）是计算机图形学中相当重要的参数曲线。
二次贝塞尔曲线
二次方贝塞尔曲线的路径由给定点P0、P1、P2的函数B（t）追踪：
三次贝塞尔曲线
对于三次曲线，可由线性贝塞尔曲线描述的中介点Q0、Q1、Q2，和由二次曲线描述的点R0、R1所建构
贝塞尔曲线计算函数
根据上面的公式我们可有得到计算函数
二阶
bezier2P(p0: number, p1: number, p2: number, t: number) { const P0 = p0 * Math.pow(1 - t, 2); const P1 = p1 * 2 * t * (1 - t); const P2 = p2 * t * t; return P0 + P1 + P2; } getBezierNowPoint2P( p0: Point, p1: Point, p2: Point, num: number, tick: number, ): Point { return { x: this.bezier2P(p0.x, p1.x, p2.x, num * tick), y: this.bezier2P(p0.y, p1.y, p2.y, num * tick), }; } create2PBezier( p0: Point, p1: Point, p2: Point, num: number = 100, tick: number = 1, ) { const t = tick / (num - 1); const points = []; for (let i = 0; i < num; i++) { const point = this.getBezierNowPoint2P(p0, p1, p2, i, t); points.push({x: point.x, y: point.y}); } return points; }三阶
bezier3P(p0: number, p1: number, p2: number, p3: number, t: number) { const P0 = p0 * Math.pow(1 - t, 3); const P1 = 3 * p1 * t * Math.pow(1 - t, 2); const P2 = 3 * p2 * Math.pow(t, 2) * (1 - t); const P3 = p3 * Math.pow(t, 3); return P0 + P1 + P2 + P3; } getBezierNowPoint3P( p0: Point, p1: Point, p2: Point, p3: Point, num: number, tick: number, ) { return { x: this.bezier3P(p0.x, p1.x, p2.x, p3.x, num * tick), y: this.bezier3P(p0.y, p1.y, p2.y, p3.y, num * tick), }; } create3PBezier( p0: Point, p1: Point, p2: Point, p3: Point, num: number = 100, tick: number = 1, ) { const pointMum = num; const _tick = tick; const t = _tick / (pointMum - 1); const points = []; for (let i = 0; i < pointMum; i++) { const point = this.getBezierNowPoint3P(p0, p1, p2, p3, i, t); points.push({x: point.x, y: point.y}); } return points; }拟合算法
问题在于如何得到控制点，我们以比较简单的方法
取 p1-pt-p2的角平分线 c1c2垂直于该条角平分线 c2为p2的投影点取短边作为c1-pt c2-pt的长度对该长度进行缩放 这个长度可以大概理解为曲线的弯曲程度
ab线段 这里简单处理 只使用了二阶的曲线生成 -> ? 这里可以按照个人想法处理
bc线段使用abc计算出来的控制点c2和bcd计算出来的控制点c3 以此类推
createSmoothLineControlPoint( p1: Vector2D, pt: Vector2D, p2: Vector2D, ratio: number = 0.3, ) { const vec1T: Vector2D = vector2dMinus(p1, pt); const vecT2: Vector2D = vector2dMinus(p1, pt); const len1: number = vec1T.length; const len2: number = vecT2.length; const v: number = len1 / len2; let delta; if (v > 1) { delta = vector2dMinus( p1, vector2dPlus(pt, vector2dMinus(p2, pt).scale(1 / v)), ); } else { delta = vector2dMinus( vector2dPlus(pt, vector2dMinus(p1, pt).scale(v)), p2, ); } delta = delta.scale(ratio); const control1: Point = { x: vector2dPlus(pt, delta).x, y: vector2dPlus(pt, delta).y, }; const control2: Point = { x: vector2dMinus(pt, delta).x, y: vector2dMinus(pt, delta).y, }; return {control1, control2}; } createSmoothLine(points: Point[], ratio: number = 0.3) { const len = points.length; let resultPoints = []; const controlPoints = []; if (len < 3) return; for (let i = 0; i < len - 2; i++) { const {control1, control2} = this.createSmoothLineControlPoint( new Vector2D(points[i].x, points[i].y), new Vector2D(points[i + 1].x, points[i + 1].y), new Vector2D(points[i + 2].x, points[i + 2].y), ratio, ); controlPoints.push(control1); controlPoints.push(control2); let points1; let points2; // 首端控制点只用一个 if (i === 0) { points1 = this.create2PBezier(points[i], control1, points[i + 1], 50); } else { console.log(controlPoints); points1 = this.create3PBezier( points[i], controlPoints[2 * i - 1], control1, points[i + 1], 50, ); } // 尾端部分 if (i + 2 === len - 1) { points2 = this.create2PBezier( points[i + 1], control2, points[i + 2], 50, ); } if (i + 2 === len - 1) { resultPoints = [...resultPoints, ...points1, ...points2]; } else { resultPoints = [...resultPoints, ...points1]; } } return resultPoints; }案例代码
const input = [ { x: 0, y: 0 }, { x: 150, y: 150 }, { x: 300, y: 0 }, { x: 400, y: 150 }, { x: 500, y: 0 }, { x: 650, y: 150 }, ] const s = path.createSmoothLine(input); let ctx = document.getElementById('cv').getContext('2d'); ctx.strokeStyle = 'blue'; ctx.beginPath(); ctx.moveTo(0, 0); for (let i = 0; i < s.length; i++) { ctx.lineTo(s[i].x, s[i].y); } ctx.stroke(); ctx.beginPath(); ctx.moveTo(0, 0); for (let i = 0; i < input.length; i++) { ctx.lineTo(input[i].x, input[i].y); } ctx.strokeStyle = 'red'; ctx.stroke(); document.getElementById('btn').addEventListener('click', () => { let app = document.getElementById('app'); let index = 0; let move = () => { if (index < s.length) { app.style.left = s[index].x - 10 + 'px'; app.style.top = s[index].y - 10 + 'px'; index++; requestAnimationFrame(move) } } move() })附录：Vector2D相关的代码
class Vector2D extends Array { constructor(x: number = 1, y: number = 0) { super(); this.x = x; this.y = y; } set x(v) { this[0] = v; } set y(v) { this[1] = v; } get x() { return this[0]; } get y() { return this[1]; } get length() { return Math.hypot(this.x, this.y); } get dir() { return Math.atan2(this.y, this.x); } copy() { return new Vector2D(this.x, this.y); } add(v) { this.x += v.x; this.y += v.y; return this; } sub(v) { this.x -= v.x; this.y -= v.y; return this; } scale(a) { this.x *= a; this.y *= a; return this; } rotate(rad) { const c = Math.cos(rad); const s = Math.sin(rad); const [x, y] = this; this.x = x * c + y * -s; this.y = x * s + y * c; return this; } cross(v) { return this.x * v.y - v.x * this.y; } dot(v) { return this.x * v.x + v.y * this.y; } normalize() { return this.scale(1 / this.length); }}function vector2dPlus(vec1, vec2) { return new Vector2D(vec1.x + vec2.x, vec1.y + vec2.y);}function vector2dMinus(vec1, vec2) { return new Vector2D(vec1.x - vec2.x, vec1.y - vec2.y);}export {Vector2D, vector2dPlus, vector2dMinus};关于Javascript中怎么生成平滑曲线就分享到这里了，希望以上内容可以对大家有一定的帮助，可以学到更多知识。如果觉得文章不错，可以把它分享出去让更多的人看到。
