import { twoProduct, ddAddDd, ddDiffDd, ddMultByNeg2 } 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 tp  = twoProduct;
const qaq = ddAddDd;
const qmn2 = ddMultByNeg2;
const qdifq = ddDiffDd;


/**
 * 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 1 bezier curve given as an ordered array of its
 * control point coordinates, e.g. `[[0,0], [1,1]]`
 * @param p a point, e.g. `[1,2]`
 * 
 * @internal
 */
 function getFootpointPoly1Dd(ps: number[][], p: number[]): number[][] {
    const [[x0, y0], [x1, y1]] = ps;
    const [x, y] = p;

    const xx0 = x0 - x;
    const xx1 = x1 - x;
    const yy0 = y0 - y;
    const yy1 = y1 - y;

    const x00 = tp(xx0,xx0);
    const x01 = tp(xx0,xx1);
    const x11 = tp(xx1,xx1);

    const y00 = tp(yy0,yy0);
    const y01 = tp(yy0,yy1);
    const y11 = tp(yy1,yy1);

    const s1 = qaq(x01,y01);
    const s2 = qaq(y00,x00);

    //const t1 = (x11 + y11) + (s2 - 2*s1)
    const t1 = qaq(qaq(x11,y11),qaq(s2,qmn2(s1)));
    //const t0 = s1 - s2;
    const t0 = qdifq(s1,s2);

    return [t1,t0];
}


export { getFootpointPoly1Dd }