cocos-enhance-kit/engine/cocos2d/animation/bezier.js

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//var bezier = (function () {
//    function B1 (t) { return (t * t * t); }
//    function B2 (t) { return (3 * t * t * (1 - t)); }
//    function B3 (t) { return (3 * t * (1 - t) * (1 - t)); }
//    function B4 (t) { return ((1 - t) * (1 - t) * (1 - t)); }
//    function bezier (C1, C2, C3, C4, t) {
//        return C1 * B1(t) + C2 * B2(t) + C3 * B3(t) + C4 * B4(t);
//    }
//
//    //function bezier (C1, C2, C3, C4, t, out) {
//    //    out.x = C1.x * B1(t) + C2.x * B2(t) + C3.x * B3(t) + C4.x * B4(t);
//    //    out.y = C1.y * B1(t) + C2.y * B2(t) + C3.y * B3(t) + C4.y * B4(t);
//    //}
//
//    return bezier;
//})();
function bezier (C1, C2, C3, C4, t) {
    var t1 = 1 - t;
    return t1 * (t1 * (C1 + (C2 * 3 - C1) * t) + C3 * 3 * t * t) + C4 * t * t * t;
}
//function bezier (c0, c1, c2, c3, t) {
//    var cy = 3.0 * (c1);
//    var by = 3.0 * (c3 - c1) - cy;
//    var ay = 1 - cy - by;
//    return (ay * t * t * t) + (by * t * t) + (cy * t);
//}

//var sin = Math.sin;
var cos = Math.cos,
    acos = Math.acos,
    max = Math.max,
    //atan2 = Math.atan2,
    pi = Math.PI,
    tau = 2 * pi,
    sqrt = Math.sqrt;

function crt (v) {
    if (v < 0) {
        return -Math.pow(-v, 1 / 3);
    }
    else {
        return Math.pow(v, 1 / 3);
    }
}

//function align (curve, line) {
//    var tx = line.p1.x,
//        ty = line.p1.y,
//        a = -atan2(line.p2.y-ty, line.p2.x-tx);
//    curve = [{x:0, y:1}, {x: curve[0], y: 1-curve[1]}, {x: curve[2], y: 1-curve[3]}, {x:1, y:0}];
//    return curve.map(function(v) {
//        return {
//            x: (v.x-tx)*cos(a) - (v.y-ty)*sin(a),
//            y: (v.x-tx)*sin(a) + (v.y-ty)*cos(a)
//        };
//    });
//}

// Modified from http://jsbin.com/yibipofeqi/1/edit, optimized for animations.
// The origin Cardano's algorithm is based on http://www.trans4mind.com/personal_development/mathematics/polynomials/cubicAlgebra.htm
function cardano (curve, x) {
    // align curve with the intersecting line:
        //var line = {p1: {x: x, y: 0}, p2: {x: x, y: 1}};
        //var aligned = align(curve, line);
        //// and rewrite from [a(1-t)^3 + 3bt(1-t)^2 + 3c(1-t)t^2 + dt^3] form
        //    pa = aligned[0].y,
        //    pb = aligned[1].y,
        //    pc = aligned[2].y,
        //    pd = aligned[3].y;
        ////// curve = [{x:0, y:1}, {x: curve[0], y: 1-curve[1]}, {x: curve[2], y: 1-curve[3]}, {x:1, y:0}];
    var pa = x - 0;
    var pb = x - curve[0];
    var pc = x - curve[2];
    var pd = x - 1;

    // to [t^3 + at^2 + bt + c] form:
    var pa3 = pa * 3;
    var pb3 = pb * 3;
    var pc3 = pc * 3;
    var d = (-pa + pb3 - pc3 + pd),
        rd = 1 / d,
        r3 = 1 / 3,
        a = (pa3 - 6 * pb + pc3) * rd,
        a3 = a * r3,
        b = (-pa3 + pb3) * rd,
        c = pa * rd,
    // then, determine p and q:
        p = (3 * b - a * a) * r3,
        p3 = p * r3,
        q = (2 * a * a * a - 9 * a * b + 27 * c) / 27,
        q2 = q / 2,
    // and determine the discriminant:
        discriminant = q2 * q2 + p3 * p3 * p3,
    // and some reserved variables
        u1, v1, x1, x2, x3;

    // If the discriminant is negative, use polar coordinates
    // to get around square roots of negative numbers
    if (discriminant < 0) {
        var mp3 = -p * r3,
            mp33 = mp3 * mp3 * mp3,
            r = sqrt(mp33),
        // compute cosphi corrected for IEEE float rounding:
            t = -q / (2 * r),
            cosphi = t < -1 ? -1 : t > 1 ? 1 : t,
            phi = acos(cosphi),
            crtr = crt(r),
            t1 = 2 * crtr;
        x1 = t1 * cos(phi * r3) - a3;
        x2 = t1 * cos((phi + tau) * r3) - a3;
        x3 = t1 * cos((phi + 2 * tau) * r3) - a3;

        // choose best percentage
        if (0 <= x1 && x1 <= 1) {
            if (0 <= x2 && x2 <= 1) {
                if (0 <= x3 && x3 <= 1) {
                    return max(x1, x2, x3);
                }
                else {
                    return max(x1, x2);
                }
            }
            else if (0 <= x3 && x3 <= 1) {
                return max(x1, x3);
            }
            else {
                return x1;
            }
        }
        else {
            if (0 <= x2 && x2 <= 1) {
                if (0 <= x3 && x3 <= 1) {
                    return max(x2, x3);
                }
                else {
                    return x2;
                }
            }
            else {
                return x3;
            }
        }
    }
    else if (discriminant === 0) {
        u1 = q2 < 0 ? crt(-q2) : -crt(q2);
        x1 = 2 * u1 - a3;
        x2 = -u1 - a3;

        // choose best percentage
        if (0 <= x1 && x1 <= 1) {
            if (0 <= x2 && x2 <= 1) {
                return max(x1, x2);
            }
            else {
                return x1;
            }
        }
        else {
            return x2;
        }
    }
    // one real root, and two imaginary roots
    else {
        var sd = sqrt(discriminant);
        u1 = crt(-q2 + sd);
        v1 = crt(q2 + sd);
        x1 = u1 - v1 - a3;
        return x1;
    }
}

function bezierByTime (controlPoints, x) {
    var percent = cardano(controlPoints, x);    // t
    var p1y = controlPoints[1]; // b
    var p2y = controlPoints[3]; // c
    // return bezier(0, p1y, p2y, 1, percent);
    return ((1 - percent) * (p1y + (p2y - p1y) * percent) * 3 + percent * percent) * percent;
}

if (CC_TEST) {
    cc._Test.bezier = bezier;
    cc._Test.bezierByTime = bezierByTime;
}

module.exports = {
    bezier: bezier,
    bezierByTime: bezierByTime
};