import {
    ddAddDd, ddDiffDd, ddMultDd, ddMultDouble2, ddNegativeOf, twoDiff
} 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 qmd = ddMultDouble2;
const qmq = ddMultDd;
const qaq = ddAddDd;
const qdq = ddDiffDd


/**
 * Returns the polynomial whose zero is the t value of maximum absolute 
 * curvature for the given *quadratic* bezier curve.
 * 
 * * **precondition:** the given parabola is not degenerate to a line
 * * **non-exact:** there is floating point roundof during calculation
 * * see e.g. [math.stackexchange](https://math.stackexchange.com/a/2971112)'s
 * answer by [KeithWM](https://math.stackexchange.com/a/2971112/130809)
 * 
 * @param ps an order 2 bezier curve given as an array of control points, 
 * e.g. `[[0,0],[1,1],[2,1]]`
 * 
 * @internal
 */
function getCurvatureExtremaQuadraticPolyDd(
        ps: number[][]): number[][] {

    // Find the point of max curvature (of the parabola)

    // calculate t*
    const [[x0,y0],[x1,y1],[x2,y2]] = ps;

    const x10 = td(x1,x0);
    const x21 = td(x2,x1);
    const wx = qdq(x21,x10);

    const y10 = td(y1,y0);
    const y21 = td(y2,y1);
    const wy = qdq(y21,y10);

    const n = qaq(
        qdq(
            qmd(x0,(qdq(wx,[0,x1]))),
            qmd(x1,(qdq(x21,[0,x1])))
        ),
        qdq(
            qmd(y0,(qdq(wy,[0,y1]))),
            qmd(y1,(qdq(y21,[0,y1])))
        )
    );

    const d = qaq(qmq(wx,wx),qmq(wy,wy));

    return [d, ddNegativeOf(n)];
}


export { getCurvatureExtremaQuadraticPolyDd }