Canvas implements high-order Bezier curve

This article mainly introduces the implementation of high-order Bezier curve (N-order Bezier curve generator) in canvas. The editor thinks it is quite good. Now I will share it with you and give you a reference. Let’s follow the editor to take a look, I hope it can help everyone.

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Since the native Canvas only supports up to third-order Bezier curves, what should I do if I want to add multiple control points? (Even most complex curves can be simulated with third-order Bezier) At the same time, it is difficult for us to clearly understand the position of the Bezier control points very intuitively and how much the control points should be set to form the curve we want. . In order to solve the above two pain points, there seems to be no N-level solution (js version) in the community, so this time the author is very serious about open source bezierMaker.js!

bezierMaker.js theoretically supports the generation of N-order Bezier curves, and also provides a testing ground for developers to add and drag control points to ultimately generate a set of drawing animations. It is very intuitive for developers to know the different generation curves corresponding to control points at different positions.

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Why is a testing site needed?

When drawing a complex high-order Bezier curve, you cannot know the precise location of the control points of the curve you need. By simulating in the test field, the coordinate values ​​of the control points can be obtained in real time. The obtained point coordinates can be converted into an object array and passed into the BezierMaker class to generate the target curve

Effect diagram

##Function

##[x] Any number of control points can be added to the test site
[x] The test site supports displaying the formation animation of curve drawing
[x] Control points can be freely dragged
[x] Supports display of tangent lines in the formation process of Bezier curves
[x] The drawing of Bezier curves of order 3 and below uses native API

<script src="./bezierMaker.js"></script>

The above rendering is For the use of the test site, after you obtain the accurate coordinates of the control points through the test site, you can call bezierMaker.js to draw the curve directly.

/**
 * canvas canvas的dom对象
 * bezierCtrlNodesArr 控制点数组，包含x，y坐标
 * color 曲线颜色
 */
var canvas = document.getElementById('canvas')
//3阶之前采用原生方法实现
var arr0 = [{x:70,y:25},{x:24,y:51}]
var arr1 = [{x:233,y:225},{x:170,y:279},{x:240,y:51}]
var arr2 = [{x:23,y:225},{x:70,y:79},{x:40,y:51},{x:300, y:44}]
var arr3 = [{x:333,y:15},{x:70,y:79},{x:40,y:551},{x:170,y:279},{x:17,y:239}]
var arr4 = [{x:53,y:85},{x:170,y:279},{x:240,y:551},{x:70,y:79},{x:40,y:551},{x:170,y:279}]
var bezier0 = new BezierMaker(canvas, arr0, 'black')
var bezier1 = new BezierMaker(canvas, arr1, 'red')
var bezier2 = new BezierMaker(canvas, arr2, 'blue')
var bezier3 = new BezierMaker(canvas, arr3, 'yellow')
var bezier4 = new BezierMaker(canvas, arr4, 'green')
bezier0.drawBezier()
bezier1.drawBezier()
bezier2.drawBezier()
bezier3.drawBezier()
bezier4.drawBezier()

When there are less than 3 control points, the native API interface will be used. . When there are more than 2 control points, the function we implement will be used to draw the points.

Drawing Bezier curve

The core point of drawing Bezier curve lies in the application of Bezier formula:

The P0-Pn in this formula represent various power operations from the starting point to each control point to the end point and the proportion t.

BezierMaker.prototype.bezier = function(t) { //贝塞尔公式调用
    var x = 0,
        y = 0,
        bezierCtrlNodesArr = this.bezierCtrlNodesArr,
        //控制点数组
        n = bezierCtrlNodesArr.length - 1,
        self = this
    bezierCtrlNodesArr.forEach(function(item, index) {
        if(!index) {
            x += item.x * Math.pow(( 1 - t ), n - index) * Math.pow(t, index) 
            y += item.y * Math.pow(( 1 - t ), n - index) * Math.pow(t, index) 
        } else {
        //factorial为阶乘函数
            x += self.factorial(n) / self.factorial(index) / self.factorial(n - index) * item.x * Math.pow(( 1 - t ), n - index) * Math.pow(t, index) 
            y += self.factorial(n) / self.factorial(index) / self.factorial(n - index) * item.y * Math.pow(( 1 - t ), n - index) * Math.pow(t, index) 
        }
    })
    return {
        x: x,
        y: y
    }
}

The author will specifically explain the derivation of the Bezier formula in a later article. Now you only need to know that we use the Bezier formula to calculate the points at which the actual Bezier curve is divided into 1000 equal parts. , a class curve can be simulated by connecting each point with a straight line.

For the implementation of Bezier curve generation animation in the simulation field

This part of the relevant code can be referred to here

The overall idea is to use recursion to control each layer The points are treated as first-order Bessel functions to calculate the next layer of control points and corresponding connections. The author will leave the specific logic until the in-depth explanation of the Bezier curve formula principle and sort out the animation generation principle of the test site~

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