import { ddAddDd, ddDiffDd, ddMultBy2, ddMultDouble2, ddMultBy4, twoDiff, ddMultDd } from "double-double";

// We *have* to do the below to improve performance with bundlers❗ The assignee is a getter❗ The assigned is a pure function❗
const td  = twoDiff;
const qaq = ddAddDd;
const qmd = ddMultDouble2;
const qmq = ddMultDd;
const qm2 = ddMultBy2;
const qdifq = ddDiffDd;
const qm4 = ddMultBy4;


/**
 * Returns the polynomial whose roots are all the `t` values on the given bezier 
 * curve such that the line from the given point to the point on the bezier 
 * evaluated at `t` is tangent to the bezier curve at `t`.
 * 
 * * intermediate calculations are done (and the final result returned in)
 * double-double precision
 * 
 * @param ps an order 2 bezier curve given as an ordered array of its
 * control point coordinates, e.g. `[[0,0], [1,1], [2,1]]`
 * @param p a point, e.g. `[1,2]`
 * 
 * @internal
 */
function getFootpointPoly2Dd(
        ps: number[][], p: number[]): number[][] {

    const [[x0, y0], [x1, y1], [x2, y2]] = ps;
    const [x, y] = p;

    const xx0 = td(x0,x);
    const xx1 = td(x1,x);
    const xx2 = td(x2,x);
    const yy0 = td(y0,y);
    const yy1 = td(y1,y);
    const yy2 = td(y2,y);

    const x00 = qmq(xx0,xx0);
    const x01 = qmq(xx0,xx1);
    const x02 = qmq(xx0,xx2);
    const x11 = qmq(xx1,xx1);
    const x12 = qmq(xx1,xx2);
    const x22 = qmq(xx2,xx2);

    const y00 = qmq(yy0,yy0);
    const y01 = qmq(yy0,yy1);
    const y02 = qmq(yy0,yy2);
    const y11 = qmq(yy1,yy1);
    const y12 = qmq(yy1,yy2);
    const y22 = qmq(yy2,yy2);

    const q1 = qaq(y02,qm2(y11));
    const r1 = qaq(x02,qm2(x11));

    //const t3 = ((y22 + y00) + 2*q1 - 4*(y12 + y01)) + 
    //           ((x22 + x00) + 2*r1 - 4*(x12 + x01));
    const t3 = qaq(
        qdifq(qaq(qaq(y22,y00),qm2(q1)),qm4(qaq(y12,y01))),
        qdifq(qaq(qaq(x22,x00),qm2(r1)),qm4(qaq(x12,x01)))
    );

    //const t2 = 3*(((y12 - q1) + (3*y01 - y00)) + 
    //              ((x12 - r1) + (3*x01 - x00)));
    const t2 = qmd(
        3,
        qaq(
            qaq(qdifq(y12,q1),qdifq(qmd(3,y01),y00)),
            qaq(qdifq(x12,r1),qdifq(qmd(3,x01),x00))
        )
    );

    //const t1 = (q1 - 3*(2*y01 - y00)) + 
    //           (r1 - 3*(2*x01 - x00));
    const t1 = qaq(
        qdifq(q1,qmd(3,qdifq(qm2(y01),y00))),
        qdifq(r1,qmd(3,qdifq(qm2(x01),x00)))
    );

    //const t0 = (y01 - y00) + 
    //           (x01 - x00);
    const t0 = qaq(
        qdifq(y01,y00),
        qdifq(x01,x00)
    );

    return [t3,t2,t1,t0];
}


export { getFootpointPoly2Dd }