De Casteljau Bezier

bezier.js

function DeCasteljauBezier(points, density, step){
    //if (points.length < 3) return null;
    console.time('bezier');
    var ps = points.map(function(p){
            return {
                x: p.x,
                y: p.y
            };
        }),
        results = [],
        len = ps.length,
        epsilon = 0.00001;
    density = density || 20; // 密度，决定了采样精度（曲线平滑程度）
    step = step || 0.00001; // bezier递推步长
    var dest = {
        x: points[points.length-1].x,
        y: points[points.length-1].y
    };
    var mindist = pow(density, 2);
    results.push({
        x: ps[0].x,
        y: ps[0].y
    });
    // 递推
    for (var t=0; t<=1; t+=step){
        for (var i=1; i<len; ++i){
            for (var j=0; j<len - i; ++j){
                ps[j].x = ps[j].x * (1 - t) + ps[j + 1].x * t;
                ps[j].y = ps[j].y * (1 - t) + ps[j + 1].y * t;
            }
        }
        var now = {
            x: ps[0].x,
            y: ps[0].y
        }
        if (pow(now.x-dest.x, 2) + pow(now.y-dest.y, 2) < epsilon){
            break;
        }
        results.push(now);
    }

    // 采样
    var last = results[0];
    var results2 = [last];
    for (var i=1; i<results.length; ++i){
        var now = results[i];
        var dist = pow(now.x-last.x, 2) + pow(now.y-last.y, 2);
        if (dist >= mindist){
            results2.push(now);
            last = now;
        }
    }
    results2.push(dest);
    //console.log(results.length, results2.length);
    console.timeEnd('bezier');
    return results2;
}