贝塞尔曲线算法，js贝塞尔曲线路径点

时间 2019-11-07 标签曲线算法路径

 　　　　//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全部点的方法，javascript

方法引用了引用公式：css

下面是示例代码html

<!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>

运行结果图以下：java

一次、二次、三次贝塞尔曲线函数jquery

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;
}