function dot2D(vectorA, vectorB) { return vectorA[0] * vectorB[0] + vectorA[1] * vectorB[1]; }
function cross2D(vectorA, vectorB) { return vectorA[0] * vectorB[1] - vectorA[1] * vectorB[0]; }
function magnitude2D(vector) { return Math.sqrt(dot2D(vector, vector)); }
function perpendicular2D(v) { return [v[1], -v[0]]; }
function reverse2D(v) { return [-v[0], -v[1]]; }
function normalize2D(v) {
    let length = Math.sqrt(dot2D(v, v));
    if (length < 0.0001) { return [0.0, 0.0]; }
    return [v[0] / length, v[1] / length];
}
function signedAngle(lhs, rhs) {return Math.atan2(cross2D(lhs, rhs), dot2D(lhs, rhs));}
function angleBetween(lhs, rhs) {return Math.abs(signedAngle(lhs, rhs));}
function positiveAngle(lhs, rhs) {
    var a = signedAngle(lhs, rhs);
    return a < 0 ? a + Math.PI * 2 : a;
}

function getSide(A, B, C, D) {
    const BA = [A[0] - B[0], A[1] - B[1]];
    const BD = [D[0] - B[0], D[1] - B[1]];
    const BC = [C[0] - B[0], C[1] - B[1]];
    const theta0 = positiveAngle(BA, BD);
    const theta1 = positiveAngle(BA, BC);

    if (theta0 == 0 || theta0 == theta1) {
        return 0;
    } else if (theta0 < theta1) {
        return 1;
    } else {
        return -1
    }
}

function slerp2D(ca, cb, t) {
    const calen = magnitude2D(ca);
    const cblen = magnitude2D(cb);
    const lent = calen + (cblen - calen) * t;
    const cq = [ca[0] * lent / calen, ca[1] * lent / calen];

    const angle = signedAngle(ca, cb) * t;
    const xt = cq[0] * Math.cos(angle) - cq[1] * Math.sin(angle);
    const yt = cq[0] * Math.sin(angle) + cq[1] * Math.cos(angle);

    return [xt, yt];
}