动画原理——曲线
书籍名称：HTML5-Animation-with-JavaScript
书籍源码：https://github.com/lamberta/html5-animation
1.使用quadraticCurveTo，
- 开始点：moveTo(20,20)
- 控制点：quadraticCurveTo(20,100,200,20)的前两个参数，
- 结束点：quadraticCurveTo(20,100,200,20)的后两个参数
图示如下：
2.曲线经过的点
如果你想让曲线经过一个点，可以利用下面这个公式来计算。其中xt，yt是我们希望曲线经过的目标点，而x0,y0,x2,y2分别为两个端点。通过这个公式可以计算出控制点x1，y1
x1 = xt * 2 - (x0 + x2) / 2;
y1 = yt * 2 - (y0 + y2) / 2;
03-curve-through-point.html代码：
<!doctype html>
<html>
<head>
<meta charset="utf-8">
<title>Curve Through Point</title>
<link rel="stylesheet" href="../include/style.css">
</head>
<body>
<header>
Example from <a href="http://amzn.com/1430236655?tag=html5anim-20"><em>Foundation HTML5 Animation with JavaScript</em></a>
</header>
<canvas id="canvas" width="400" height="400"></canvas>
<aside>Move mouse on canvas element.</aside>
<script src="../include/utils.js"></script>
<script>
window.onload = function () {
var canvas = document.getElementById('canvas'),
context = canvas.getContext('2d'),
mouse = utils.captureMouse(canvas),
x0 = 100,
y0 = 200,
x2 = 300,
y2 = 200;
canvas.addEventListener('mousemove', function () {
context.clearRect(0, 0, canvas.width, canvas.height);
var x1 = mouse.x * 2 - (x0 + x2) / 2,
y1 = mouse.y * 2 - (y0 + y2) / 2;
//curve through mouse
context.beginPath();
context.moveTo(x0, y0);
context.quadraticCurveTo(x1, y1, x2, y2);
context.stroke();
}, false);
};
</script>
</body>
</html>
3.多重平滑曲线
一，作为首次尝试，先讲一个容易写的一个错的方法，从每个点依次画曲线。
根据图示可以看出，红色圈出的地方是尖角，而并非平滑曲线。
<!doctype html>
<html>
<head>
<meta charset="utf-8">
<title>Multi Curve 1</title>
<link rel="stylesheet" href="../include/style.css">
</head>
<body>
<header>
Example from <a href="http://amzn.com/1430236655?tag=html5anim-20"><em>Foundation HTML5 Animation with JavaScript</em></a>
</header>
<canvas id="canvas" width="400" height="400"></canvas>
<aside>Refresh page for random curves.</aside>
<script>
window.onload = function () {
var canvas = document.getElementById('canvas'),
context = canvas.getContext('2d'),
points = [],
numPoints = 9;
//array of random point objects
for (var i = 0; i < numPoints; i++) {
points.push({
x: Math.random() * canvas.width,
y: Math.random() * canvas.height
});
}
//move to the first point
context.beginPath();
context.moveTo(points[0].x, points[0].y);
//and loop through each successive pair
for (i = 1; i < numPoints; i += 2) {
context.quadraticCurveTo(points[i].x, points[i].y,
points[i+1].x, points[i+1].y);
}
context.stroke();
};
</script>
</body>
</html>
二，平滑多重曲线
先来分析下图，白色的为控制点，黑色为中点，除首位两个中点不在曲线上，其余都在曲线上。鉴于此可以绘画平滑的曲线。
<!doctype html>
<html>
<head>
<meta charset="utf-8">
<title>Multi Curve 3</title>
<link rel="stylesheet" href="../include/style.css">
</head>
<body>
<header>
Example from <a href="http://amzn.com/1430236655?tag=html5anim-20"><em>Foundation HTML5 Animation with JavaScript</em></a>
</header>
<canvas id="canvas" width="400" height="400"></canvas>
<aside>Refresh page for random curves.</aside>
<script>
window.onload = function () {
var canvas = document.getElementById('canvas'),
context = canvas.getContext('2d'),
points = [],
numPoints = 9,
ctrlPoint = {},
ctrlPoint1 = {};
for (var i = 0; i < numPoints; i++) {
points.push({
x: Math.random() * canvas.width,
y: Math.random() * canvas.height
});
}
//find the first midpoint and move to it
ctrlPoint1.x = (points[0].x + points[numPoints-1].x) / 2;
ctrlPoint1.y = (points[0].y + points[numPoints-1].y) / 2;
context.beginPath();
context.moveTo(ctrlPoint1.x, ctrlPoint1.y);
//curve through the rest, stopping at each midpoint
for (i = 0; i < numPoints - 1; i++) {
ctrlPoint.x = (points[i].x + points[i+1].x) / 2;
ctrlPoint.y = (points[i].y + points[i+1].y) / 2;
context.quadraticCurveTo(points[i].x, points[i].y,
ctrlPoint.x, ctrlPoint.y);
}
//curve through the last point, back to the first midpoint
context.quadraticCurveTo(points[i].x, points[i].y,
ctrlPoint1.x, ctrlPoint1.y);
context.stroke();
};
</script>
</body>
</html>
三，首尾相连的平滑曲线
和之间的方法一样，只是连端点也要作为两个控制点的中点。
<!doctype html>
<html>
<head>
<meta charset="utf-8">
<title>Multi Curve 3</title>
<link rel="stylesheet" href="../include/style.css">
</head>
<body>
<header>
Example from <a href="http://amzn.com/1430236655?tag=html5anim-20"><em>Foundation HTML5 Animation with JavaScript</em></a>
</header>
<canvas id="canvas" width="400" height="400"></canvas>
<aside>Refresh page for random curves.</aside>
<script>
window.onload = function () {
var canvas = document.getElementById('canvas'),
context = canvas.getContext('2d'),
points = [],
numPoints = 9,
ctrlPoint = {},
ctrlPoint1 = {};
for (var i = 0; i < numPoints; i++) {
points.push({
x: Math.random() * canvas.width,
y: Math.random() * canvas.height
});
}
//find the first midpoint and move to it
ctrlPoint1.x = (points[0].x + points[numPoints-1].x) / 2;
ctrlPoint1.y = (points[0].y + points[numPoints-1].y) / 2;
context.beginPath();
context.moveTo(ctrlPoint1.x, ctrlPoint1.y);
//curve through the rest, stopping at each midpoint
for (i = 0; i < numPoints - 1; i++) {
ctrlPoint.x = (points[i].x + points[i+1].x) / 2;
ctrlPoint.y = (points[i].y + points[i+1].y) / 2;
context.quadraticCurveTo(points[i].x, points[i].y,
ctrlPoint.x, ctrlPoint.y);
}
//curve through the last point, back to the first midpoint
context.quadraticCurveTo(points[i].x, points[i].y,
ctrlPoint1.x, ctrlPoint1.y);
context.stroke();
};
</script>
</body>
</html>