javascript Spline代码

代码是通过网上一个winform代码中提取修改而来的。后转为javascript 版本。

/*
points = new Array();
points.push({x:1,y:2});
*/
function Spline(points) {
    var NewArrayFloat = function(n) {
        var arr = new Array(n);
        for (var i = 0; i < n; i++) {
            arr[i] = 0.0;
        }
        return arr;
    }
    /*
    C# (float[] sub, float[] diag, float[] sup, ref float[] b, int n)
    Js return float[] b;
    */
    var solveTridiag = function(sub, diag, sup, b, n) {
        /*
        solve linear system with tridiagonal n by n matrix a
        using Gaussian elimination *without* pivoting
        where   a(i,i-1) = sub[i]  for 2<=i<=n
        a(i,i)   = diag[i] for 1<=i<=n
        a(i,i+1) = sup[i]  for 1<=i<=n-1
        (the values sub[1], sup[n] are ignored)
        right hand side vector b[1:n] is overwritten with solution
        NOTE: 1...n is used in all arrays, 0 is unused */
        var i;
        /*factorization and forward substitution */
        for (i = 2; i <= n; i++) {
            sub[i] = sub[i] / diag[i - 1];
            diag[i] = diag[i] - sub[i] * sup[i - 1];
            b[i] = b[i] - sub[i] * b[i - 1];
        }
        b[n] = b[n] / diag[n];
        for (i = n - 1; i >= 1; i--) {
            b[i] = (b[i] - sup[i] * b[i + 1]) / diag[i];
        }
        return b;
    }
 
    var resultPoint = new Array();
    var precision = 10;
 
    var np = points.length;
    var yCoords = NewArrayFloat(np);
    var xCoords = NewArrayFloat(np);
    var x;
    var y;
    var oldy = 0;
    var oldx = 0;
 
    var npp = np * precision;
 
    // draw a border around the canvas
    if (np > 0) {
        // draw the control points
        for (var i = 0; i < np; i++) {
            var p = { x: points[i].x, y: points[i].y };
            xCoords[i] = p.x;
            yCoords[i] = p.y;
        }
 
        if (np > 1) {
            var a = new NewArrayFloat(np);
            var x1;
            var x2;
            var h = new NewArrayFloat(np);
            for (var i = 1; i <= np - 1; i++) {
                h[i] = xCoords[i] - xCoords[i - 1];
            }
            if (np > 2) {
                var sub = NewArrayFloat(np - 1);
                var diag = NewArrayFloat(np - 1);
                var sup = NewArrayFloat(np - 1);
 
                for (var i = 1; i <= np - 2; i++) {
                    diag[i] = (h[i] + h[i + 1]) / 3;
                    sup[i] = h[i + 1] / 6;
                    sub[i] = h[i] / 6;
                    a[i] = (yCoords[i + 1] - yCoords[i]) / h[i + 1] - (yCoords[i] - yCoords[i - 1]) / h[i];
                }
 
                //C# CODE param [a] = [ref a];
                a = solveTridiag(sub, diag, sup, a, np - 2);
            }
            // note that a[0]=a[np-1]=0
 
            oldx = xCoords[0];
            oldy = yCoords[0];
 
            resultPoint.push({ x: oldx, y: oldy });
 
            for (var i = 1; i <= np - 1; i++) {
                // loop over intervals between nodes
                for (var j = 1; j <= precision; j++) {
                    x1 = (h[i] * j) / precision;
                    x2 = h[i] - x1;
                    y = ((-a[i - 1] / 6 * (x2 + h[i]) * x1 + yCoords[i - 1]) * x2 +
                        (-a[i] / 6 * (x1 + h[i]) * x2 + yCoords[i]) * x1) / h[i];
                    x = xCoords[i - 1] + x1;
 
                    resultPoint.push({ x: x, y: y });
 
                    oldx = x;
                    oldy = y;
                }
            }
        }
    }
    return resultPoint;
}