B-splineRepresentationJavascript

B-spline Representation Javascript”翻译为“B样条曲线表示的Javascript”，即使用Javascript实现B样条曲线表示。B样条曲线是一种基于多项式的平滑曲线，它可以通过给定的控制点和次数来生成。在Javascript中，我们可以使用Canvas API来绘制B样条曲线，并根据需要对其进行编辑和变换。以下是一个简单的Javascript代码示例，用于绘制一条二次B样条曲线：

// 获取Canvas元素
var canvas = document.getElementById("myCanvas");
var context = canvas.getContext("2d");

// 定义控制点
var controlPoints = [
    {x: 50, y: 50},
    {x: 100, y: 150},
    {x: 200, y: 100}
];

// 定义次数
var degree = 2;

// 绘制曲线
context.beginPath();
context.moveTo(controlPoints[0].x, controlPoints[0].y);
for(var i=degree; i<controlPoints.length; i++) {
    var p = controlPoints.slice(i-degree, i+1);
    drawCurve(p);
}
context.stroke();

// 绘制曲线段
function drawCurve(points) {
    var curve = new BSpline(points, degree);
    for(var t=0; t<=1; t+=0.01) {
        var p = curve.calcAt(t);
        context.lineTo(p.x, p.y);
    }
}

// B样条曲线类
function BSpline(points, degree) {
    this.points = points;
    this.degree = degree;
    this.knots = [];
    this.calcKnots();
}

// 计算节点矢量
BSpline.prototype.calcKnots = function() {
    var n = this.points.length;
    var p = this.degree;
    for(var i=0; i<=n+p; i++) {
        if(i<p) {
            this.knots[i] = 0;
        }
        else if(i<=n) {
            this.knots[i] = i-p+1;
        }
        else {
            this.knots[i] = n-p+2;
        }
    }
}

// 计算曲线上某一点的坐标
BSpline.prototype.calcAt = function(t) {
    var n = this.points.length;
    var p = this.degree;
    var i = Math.floor(t*(n-p+1)) + p - 1;
    var u = t*(n-p+1) - i;
    var d = new Array(p+1);
    for(var j=0; j<=p; j++) {
        d[j] = this.points[i-p+j];
    }
    for(var r=1; r<=p; r++) {
        for(var j=p; j>=r; j--) {
            var alpha = (u-this.knots[i-p+j]) / (this.knots[i+1-j+r]-this.knots[i-p+j]);
            d[j] = {
                x: (1-alpha) * d[j-1].x + alpha * d[j].x,
                y: (1-alpha) * d[j-1].y + alpha * d[j].y
            };
        }
    }
    return d[p];
}

以上代码通过将控制点和次数传