//anchorpoints：贝塞尔基点
//pointsAmount：生成的点数
//return 路径点的Array
function CreateBezierPoints(anchorpoints, pointsAmount) {
var points = [];
for (var i = 0; i < pointsAmount; i++) {
var point = MultiPointBezier(anchorpoints, i / pointsAmount);
points.push(point);
}
return points;
} function MultiPointBezier(points, t) {
var len = points.length;
var x = 0, y = 0;
var erxiangshi = function (start, end) {
var cs = 1, bcs = 1;
while (end > 0) {
cs *= start;
bcs *= end;
start--;
end--;
}
return (cs / bcs);
};
for (var i = 0; i < len; i++) {
var point = points[i];
x += point.x * Math.pow((1 - t), (len - 1 - i)) * Math.pow(t, i) * (erxiangshi(len - 1, i));
y += point.y * Math.pow((1 - t), (len - 1 - i)) * Math.pow(t, i) * (erxiangshi(len - 1, i));
}
return { x: x, y: y };
}
以上是计算高阶贝赛尔曲线所有点的方法，
方法引用了引用公式：
下面是示例代码
<!DOCTYPE html>
<html xmlns="http://www.w3.org/1999/xhtml">
<head>
<meta http-equiv="Content-Type" content="text/html; charset=utf-8" />
<title></title>
<script src="Scripts/jquery-1.7.1.min.js"></script>
<script type="text/javascript">
var guijipoints = [];
var index = 0;
$(document).ready(function () {
var ps = [{ x: 0, y: 0 }, { x: 100, y: 200 }, { x: 200, y: 10 }, { x: 300, y: 400 }, { x: 400, y: 20 }, { x: 200, y: 500 }, { x: 500, y: 30 }, { x: 700, y: 300 }, { x: 800, y: 800 }, { x: 800, y: 800 }];
guijipoints = CreateBezierPoints(ps, 1000);
var moveobj = $("#move_div");
setInterval(function () {
var p = guijipoints[index];
console.log(p.x);
moveobj.css({ left: p.x, top: p.y });
index++;
if (index >= guijipoints.length) {
index = 0;
}
}, 1000 / 100);
guijipoints.forEach(function (obj, i) {
createDiv(obj.x, obj.y);
});
}); function createDiv(x, y) {
$("body").append('<div style="position: absolute; width: 2px; height: 2px; left:' + x + 'px;top:' + y + 'px; overflow: hidden; background-color: #FF0000"></div>');
} //anchorpoints：贝塞尔基点
//pointsAmount：生成的点数
function CreateBezierPoints(anchorpoints, pointsAmount) {
var points = [];
for (var i = 0; i < pointsAmount; i++) {
var point = MultiPointBezier(anchorpoints, i / pointsAmount);
points.push(point);
}
return points;
} function MultiPointBezier(points, t) {
var len = points.length;
var x = 0, y = 0;
var erxiangshi = function (start, end) {
var cs = 1, bcs = 1;
while (end > 0) {
cs *= start;
bcs *= end;
start--;
end--;
}
return (cs / bcs);
};
for (var i = 0; i < len; i++) {
var point = points[i];
x += point.x * Math.pow((1 - t), (len - 1 - i)) * Math.pow(t, i) * (erxiangshi(len - 1, i));
y += point.y * Math.pow((1 - t), (len - 1 - i)) * Math.pow(t, i) * (erxiangshi(len - 1, i));
}
return { x: x, y: y };
} </script> </head> <body>
<div id="move_div" style=" position: absolute; left: 0px; top: 0px; height: 10px; width: 10px; background-color: red; "></div>
</body>
</html>
运行结果图如下：
一次、二次、三次贝塞尔曲线函数
function onebsr(t, a1, a2) {
return a1 + (a2 - a1) * t;
}
function twobsr(t, a1, a2, a3) {
return ((1 - t) * (1 - t)) * a1 + 2 * t * (1 - t) * a2 + t * t * a3;
}
function threebsr(t, a1, a2, a3, a4) {
return a1 * (1 - t) * (1 - t) * (1 - t) + 3 * a2 * t * (1 - t) * (1 - t) + 3 * a3 * t * t * (1 - t) + a4 * t * t * t;
}