Use canvas to draw a curve animation example-JS Tutorial-php.cn

Table of Contents

Bezier curve

Quadratic Bezier curve

四次贝塞尔曲线

五次贝塞尔曲线

绘制贝塞尔曲线

绘制贝塞尔曲线动画

方法一

方法二

绘制动画

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Use canvas to draw a curve animation example

小云云

Jan 03, 2018 pm 03:38 PM

canvas animation

In front-end development, Bezier curves are everywhere. This article mainly shares with you an example of using canvas to draw a curve animation. I hope it can help everyone.

It can be used to draw curves. In svg and canvas, the curves provided natively use Bezier curves
It can also be used to describe an easing algorithm, set the transition-timing-function attribute of css, and use the Bezier curve to describe the easing calculation of the transition
Almost all front-end 2D or 3D graphics charts libraries (echarts, d3, three.js) will use Bezier curves

I am going to start this article from Let’s start by implementing a very simple curve animation effect to help everyone thoroughly understand what a Bezier curve is and what its characteristics are. There are a few mathematical formulas in the article, but they are very simple :).

Use canvas to draw a curve animation example To achieve such a curve animation

You can click here to view an online demonstration

Before writing code, first understand what Besser is Let’s take a curve.

Bezier curve

The Bezier curve is a very important parametric curve in computer graphics. It describes a curve through an equation. According to the highest order of the equation , and are divided into linear Bezier curves, quadratic Bezier curves, cubic Bezier curves and higher-order Bezier curves.

The following is a detailed introduction to the more commonly used quadratic Bezier curve and cubic Bezier curve

Quadratic Bezier curve

Quadratic Bezier curve The curve is determined by three points P0, P1, P2. These points are also called control points. The equation of the curve is:

Use canvas to draw a curve animation example

This equation actually has its geometric meaning. It means that a curve can be drawn through such steps:

Select a t value of 0-1
through P0 Calculate point Q0 with P1, Q0 is on the straight line connected by P0 P1, and length( P0, Q0 ) = length( P0, P1 ) * t
Similarly, calculated by P1 and P2 Out Q1, so that length( P1, Q1 ) = length( P1, P2 ) * t
Repeat this step again, and pass Q1 and Q2 calculate B such that length( Q0, Q1 ) = length( Q0, B ) * t. B is the point on the current curve

Note: The above length represents the length between the two points

Use canvas to draw a curve animation example
Figure: Quadratic Bezier Curve Structure

With the curve equation, we can calculate the point## by directly substituting the specific t value #B.

If you transition the value of

t from 0 to 1 and continuously calculate the point B, you can get a two Quadratic Bezier curve:

Use canvas to draw a curve animation example Figure: Quadratic Bezier line drawing process

In canvas, draw quadratic Bezier line The method of the curve is

ctx.quadraticCurveTo( p1x, p1y, p2x, p2y )

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where

p1x, p1y, p2x, p2y is the horizontal direction of the last two control points (P1 and P2) Vertical coordinate, it defaults to the starting point of the current path as a control point (P0).

cubic Bezier curve

cubic Bezier curve requires four points

P0,P1,P2, P3 to determine, the curve equation is

Use canvas to draw a curve animation example

Its calculation process is similar to the quadratic Bezier curve, which will not be repeated here. To go into details, you can look at the picture below:

Use canvas to draw a curve animation example Picture: cubic Bezier curve structure

Similarly, change

t When the value transitions from 0 to 1, a cubic Bezier curve can be drawn:

Use canvas to draw a curve animation example Figure: Cubic Bezier curve drawing process

In canvas, the method of drawing cubic Bezier curve is

ctx.bezierCurveTo( p1x, p1y, p2x, p2y, p3x, p3y )

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where

p1x, p1y, p2x, p2y, p3x, p3y is the horizontal and vertical coordinates of the last three control points (P1, P2 and P3). By default, it takes the starting point of the current path as a control point (P0).

Characteristics of Bezier curves

Behind the cubic Bezier curve, there are higher-order Bezier curves, and the process of drawing them is also more complicated

四次贝塞尔曲线

Use canvas to draw a curve animation example
图：四次贝塞尔曲线

五次贝塞尔曲线

Use canvas to draw a curve animation example 图：五次贝塞尔曲线

我们可以归纳出贝塞尔曲线有几个重要的特征：

n阶贝塞尔曲线需要n+1个点来确定
贝塞尔曲线是平滑的
贝塞尔曲线的起点和终点与对应控制点的连线相切

绘制贝塞尔曲线

复习完基础概念，接下来就要讲如果绘制贝塞尔曲线啦

为简单起见，我们选择使用二次贝塞尔曲线。

我们先不考虑动画的事，我们先将问题简化成：给定一个起点和一个终点，需要实现一个函数，它能够绘制出一条曲线。

也就是说我们需要实现一个函数drawCurvePath，除渲染上下文ctx外（不清楚ctx是什么的同学可以先熟悉下canvas的基本概念），它接受三个参数，分别为二次贝塞尔曲线的三个控制点。我们将样式控制移到函数外，drawCurvePath只用来绘制路径。

/**
 * 绘制二次贝赛尔曲线路径
 * @param  {Object} ctx
 * @param  {Array<number>} p0
 * @param  {Array<number>} p1
 * @param  {Array<number>} p2
 */
function drawCurvePath( ctx, p0, p1, p2 ) {
    // ...
}

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前文提到过，在canvas中，绘制二次贝赛尔曲线的方法是quadraticCurveTo，所以只要短短两行就能完成这个方法。

/**
 * 绘制二次贝赛尔曲线路径
 * @param  {CanvasRenderingContext2D} ctx
 * @param  {Array<number>} p0
 * @param  {Array<number>} p1
 * @param  {Array<number>} p2
 */
function drawCurvePath( ctx, p0, p1, p2 ) {
    ctx.moveTo( p0[ 0 ], p0[ 1 ] );
    ctx.quadraticCurveTo( 
        p1[ 0 ], p1[ 1 ],
        p2[ 0 ], p2[ 1 ]
    );
}

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这样就完成了基本的绘制二次贝塞尔曲线的方法了。

但是函数这样设计有点小问题

如果我们是在做一个图形库，我们想给使用者提供一个绘制曲线的方法。

对于使用者来说，他只想在给定的起点和终点间间绘制一条曲线，他想要得到的曲线尽量美观，但是又不想关心具体的实现细节，如果还需要给第三个点，使用者会有一定的学习成本（至少需要弄明白什么是贝塞尔曲线）。

看到这里你可能会比较疑惑，即使是二次贝塞尔曲线也需要三个控制点，只有起点和终点怎么绘制曲线呢。

我们可以在起点和终点的垂直平分线上选一点作为第三个控制点，可以提供给使用者一个参数来控制曲线的弯曲程度，现在函数就变成了这样

/**
 * 绘制一条曲线路径
 * @param  {CanvasRenderingContext2D} ctx
 * @param  {Array<number>} start 起点
 * @param  {Array<number>} end 终点
 * @param  {number} curveness 曲度(0-1)
 */
function drawCurvePath( ctx, start, end, curveness ) {
    // ...
}

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我们用curveness来表示曲线的弯曲程度，也就是第三个控制点的偏离程度。这样很容易就能计算出中间点。
现在完整的函数变成了这样：

/**
 * 绘制一条曲线路径
 * @param  {Object} ctx canvas渲染上下文
 * @param  {Array<number>} start 起点
 * @param  {Array<number>} end 终点
 * @param  {number} curveness 曲度(0-1)
 */
function drawCurvePath( ctx, start, end, curveness ) {
    // 计算中间控制点
    var cp = [
         ( start[ 0 ] + end[ 0 ] ) / 2 - ( start[ 1 ] - end[ 1 ] ) * curveness,
         ( start[ 1 ] + end[ 1 ] ) / 2 - ( end[ 0 ] - start[ 0 ] ) * curveness
    ];
    ctx.moveTo( start[ 0 ], start[ 1 ] );
    ctx.quadraticCurveTo( 
        cp[ 0 ], cp[ 1 ],
        end[ 0 ], end[ 1 ]
    );
}

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对，就这么短短几行，接下来我们就可以通过它来绘制一条曲线了，代码如下

<!DOCTYPE html>
<html lang="en">
    <head>
        <title>draw curve</title>
    </head>
    <body>
        <canvas id="canvas" width="800" height="800"></canvas>
        <script>
            var canvas = document.getElementById( 'canvas' );
            var ctx = canvas.getContext( '2d' );
            
            ctx.lineWidth = 2;
            ctx.strokeStyle = '#000';
            ctx.beginPath();
    
            drawCurvePath( 
                ctx,
                [ 100, 100 ],
                [ 200, 300 ],
                0.4
            );
            
            ctx.stroke();
            
            function drawCurvePath( ctx, start, end, curveness ) {
                // ...
            }
        </script>
    </body>
</html>

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绘制结果：

Use canvas to draw a curve animation example
绘制一条曲线

绘制贝塞尔曲线动画

终于来到文章的本体啦，我们的目的不是绘制一条静态的曲线，我们想绘制一条有过渡效果的曲线。

简化一下问题，那就是我们希望绘制曲线的函数还接受另一个参数，表示绘制曲线的百分比。我们定时去调用这个函数，递增百分比这个参数，就能画出动画了。

我们新增一个参数percent来表示百分比，现在函数变成了这样：

/**
 * 绘制一条曲线路径
 * @param  {Object} ctx canvas渲染上下文
 * @param  {Array<number>} start 起点
 * @param  {Array<number>} end 终点
 * @param  {number} curveness 曲度(0-1)
 * @param  {number} percent 绘制百分比(0-100)
 */
function drawCurvePath( ctx, start, end, curveness, percent ) {
    // ...
}

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但是canvas提供的quadraticCurveTo方法只能绘制一条完整的二次贝赛尔曲线，没有办法去控制它只画一部分。

画完后用clearRect擦除掉一部分？这不太可行，因为很难确定要擦除的范围。如果曲线的线宽比较宽，就还需要保证擦除的边界和曲线末端垂直，问题就变得很复杂了。

现在再重新看看这张图

Use canvas to draw a curve animation example

我们是不是可以将percent这个参数理解成t值，然后通过贝赛尔曲线方程去计算出中间所有的点，用直线连接起来，以此模拟绘制贝赛尔曲线的一部分呢？

方法一

我们不再用canvas提供的quadraticCurveTo来绘制曲线，而是通过贝赛尔曲线的方程计算出一系列点，用多端直线来模拟曲线。

这样做的好处时，我们可以很容易的控制绘制的范围。

那么函数实现就变成了这样：

/**
 * 绘制一条曲线路径
 * @param  {Object} ctx canvas渲染上下文
 * @param  {Array<number>} start 起点
 * @param  {Array<number>} end 终点
 * @param  {number} curveness 曲度(0-1)
 * @param  {number} percent 绘制百分比(0-100)
 */
function drawCurvePath( ctx, start, end, curveness, percent ) {

    var cp = [
         ( start[ 0 ] + end[ 0 ] ) / 2 - ( start[ 1 ] - end[ 1 ] ) * curveness,
         ( start[ 1 ] + end[ 1 ] ) / 2 - ( end[ 0 ] - start[ 0 ] ) * curveness
    ];
    
    ctx.moveTo( start[ 0 ], start[ 1 ] );
    
    for ( var t = 0; t <= percent / 100; t += 0.01 ) {

        var x = quadraticBezier( start[ 0 ], cp[ 0 ], end[ 0 ], t );
        var y = quadraticBezier( start[ 1 ], cp[ 1 ], end[ 1 ], t );
        
        ctx.lineTo( x, y );
    }
    
}

function quadraticBezier( p0, p1, p2, t ) {
    var k = 1 - t;
    return k * k * p0 + 2 * ( 1 - t ) * t * p1 + t * t * p2;    // 这个方程就是二次贝赛尔曲线方程
}

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接下来就可以通过设置定时器，每隔一段时间调用一次这个方法，并且递增percent

为了动画更加平滑，我们使用requestAnimationFrame来代替定时器

<!DOCTYPE html>
<html lang="en">
    <head>
        <title>draw curve</title>
    </head>
    <body>
        <canvas id="canvas" width="800" height="800"></canvas>
        <script>
            var canvas = document.getElementById( 'canvas' );
            var ctx = canvas.getContext( '2d' );
            
            ctx.lineWidth = 2;
            ctx.strokeStyle = '#000';
            
            var percent = 0;
            
            function animate() {
                
                ctx.clearRect( 0, 0, 800, 800 );
                ctx.beginPath();

                drawCurvePath( 
                    ctx,
                    [ 100, 100 ],
                    [ 200, 300 ],
                    0.2,
                    percent
                );
    
                ctx.stroke();
    
                percent = ( percent + 1 ) % 100;
                
                requestAnimationFrame( animate );
                
            }
            
            animate();
            
            function drawCurvePath( ctx, start, end, curveness, percent ) {
                // ...
            }
        </script>
    </body>
</html>

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得到的结果：

Use canvas to draw a curve animation example

这样基本实现了我们的需求，但它有一个问题：

测试发现，进行一次lineTo的时间和一次quadraticCurveTo的时间差不多，但是quadraticCurveTo只需要一次就能画出曲线，而使用lineTo则需要数十次。

换言之，用这样的方式绘制曲线，和我们前面的实现方式相比性能下降了数十倍之多。在绘制一条曲线时可能感觉不到区别，但是如果需要同时绘制上千条曲线，性能就会受到很大的影响。

方法二

那有没有什么方法可以做到用quadraticCurveTo来实现绘制完整曲线的一部分呢？

我们再次回到这张图

Use canvas to draw a curve animation example

在中间的某一时刻，例如t=0.25时，它是这样的：

Use canvas to draw a curve animation example

我们注意到，曲线P0-B这一段似乎也是贝赛尔曲线，它的控制点变成了P0，Q0，B。

现在问题就迎刃而解了，我们只需要每次计算出Q0，B，就能得到其中一小段贝赛尔曲线的控制点，然后就可以通过quadraticCurveTo来绘制它了。

代码如下：

/**
 * 绘制一条曲线路径
 * @param  {Object} ctx canvas渲染上下文
 * @param  {Array<number>} start 起点
 * @param  {Array<number>} end 终点
 * @param  {number} curveness 曲度(0-1)
 * @param  {number} percent 绘制百分比(0-100)
 */
function drawCurvePath( ctx, start, end, curveness, percent ) {

    var cp = [
         ( start[ 0 ] + end[ 0 ] ) / 2 - ( start[ 1 ] - end[ 1 ] ) * curveness,
         ( start[ 1 ] + end[ 1 ] ) / 2 - ( end[ 0 ] - start[ 0 ] ) * curveness
    ];
    
    var t = percent / 100;
    
    var p0 = start;
    var p1 = cp;
    var p2 = end;
    
    var v01 = [ p1[ 0 ] - p0[ 0 ], p1[ 1 ] - p0[ 1 ] ];     // 向量<p0, p1>
    var v12 = [ p2[ 0 ] - p1[ 0 ], p2[ 1 ] - p1[ 1 ] ];     // 向量<p1, p2>

    var q0 = [ p0[ 0 ] + v01[ 0 ] * t, p0[ 1 ] + v01[ 1 ] * t ];
    var q1 = [ p1[ 0 ] + v12[ 0 ] * t, p1[ 1 ] + v12[ 1 ] * t ];
    
    var v = [ q1[ 0 ] - q0[ 0 ], q1[ 1 ] - q0[ 1 ] ];       // 向量<q0, q1>

    var b = [ q0[ 0 ] + v[ 0 ] * t, q0[ 1 ] + v[ 1 ] * t ];
    
    ctx.moveTo( p0[ 0 ], p0[ 1 ] );

    ctx.quadraticCurveTo( 
        q0[ 0 ], q0[ 1 ],
        b[ 0 ], b[ 1 ]
    );

}

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将前面写的页面替换成上面的代码，可以看到得到的结果是一样的：

Use canvas to draw a curve animation example

绘制动画

现在已经解决了最关键的问题，我们可以绘制动画啦。
不过这一部分并不重要，我就不贴代码了。

完整代码可以看这里

Use canvas to draw a curve animation example

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The final trailer for Netflix's claymation film "Chicken Run 2" has been released. The film is expected to be released on December 15. This site noticed that the trailer for "Chicken Run 2" shows Chicken Loki and King Kong. Jay launches an operation to find his daughter Molly. Molly is taken away by a truck at FunLand Farm, and Rocky and Ginger risk their lives to retrieve their daughter. The film is directed by Sam Fehr and stars Sandy Way Newton, Zachary Levi, Bella Ramsey, Imelda Staunton and David Bradley. It is understood that "Chicken Run 2" is the sequel to "Chicken Run" after more than 20 years. The first work was released in China on January 2, 2001. It tells the story of a group of chickens who face the fate of being turned into chicken pies in a chicken factory.

Netflix animated series 'Sonic: Homecoming' Season 3 clips released, to be released next year Nov 12, 2023 am 09:25 AM

Netflix Sorry, I can help you rewrite the content, but I need to know the original content you want to rewrite. Can you provide it to me? A clip from the third season of the animated series "Sonic: Homecoming Adventures" was announced at Geek Week, which is expected to be launched in 2024. Sorry, I can help you rewrite the content, but I need to know what you want to rewrite. Original content. Can you provide it to me? According to this site, "Sonic: Homecoming Adventure" is produced by Sega and WildBrain. Sorry, I can help you rewrite the content, but I need to know the original content you want to rewrite. Can you provide it to me? Studio Sorry, I can help you rewrite the content, but I need to know the original content you want to rewrite. Can you provide it to me? and sorry i can help you rewrite the content but i need

Best Free AI Animation Art Generator Feb 19, 2024 pm 10:50 PM

If you are eager to find the top free AI animation art generator, you can end your search. The world of anime art has been captivating audiences for decades with its unique character designs, captivating colors and captivating plots. However, creating anime art requires talent, skill, and a lot of time. However, with the continuous development of artificial intelligence (AI), you can now explore the world of animation art without having to delve into complex technologies with the help of the best free AI animation art generator. This will open up new possibilities for you to unleash your creativity. What is an AI anime art generator? The AI Animation Art Generator utilizes sophisticated algorithms and machine learning techniques to analyze an extensive database of animation works. Through these algorithms, the system learns and identifies different animation styles

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