import type { ImplicitFormExact1 } from "../implicit-form-types.js";
import { toPowerBasis1Exact } from "../../to-power-basis/to-power-basis/exact/to-power-basis-exact.js";

// We *have* to do the below to improve performance with bundlers❗ The assignee is a getter❗ The assigned is a pure function❗
import { scaleExpansion2, eDiff, eNegativeOf } from "big-float-ts";
import { eSign as _eSign } from 'big-float-ts';


const sce = scaleExpansion2;
const edif = eDiff;
const eno = eNegativeOf;
const eSign = _eSign;


/**
 * Returns the *exact* implicit form of the given linear bezier curve (a line 
 * segment) or `undefined` if the line degenerates to a point.
 * 
 * * returned coefficients are subscripted to match their monomial's variables,
 * e.g. `vₓᵧ` is the coefficient of the monomial `vₓᵧxy`
 * * returned coefficients are given *exactly* as [Shewchuk](https://people.eecs.berkeley.edu/~jrs/papers/robustr.pdf) expansions
 * * the implicit form is given by: `vₓx + vᵧy + v = 0`
 * * adapted from [Indrek Mandre](http://www.mare.ee/indrek/misc/2d.pdf)
 * 
 * @param ps 
 * 
 * @doc mdx
 */
function getImplicitForm1Exact(
        ps: number[][]): { vₓ: number[]; vᵧ: number[]; v: number[]; } | undefined {

    return getImplicitForm1ExactPb(
        toPowerBasis1Exact(ps)
    );
}


/**
 * The power basis version of [[getImplicitForm1Exact]].
 * 
 * @param pspb the power basis representation of a linear bezier curve that 
 * can be found via [[toPowerBasis1Exact]]
 * 
 * @internal
 */
 function getImplicitForm1ExactPb(
    pspb: [
            [number[], number[]], 
            [number[], number[]]
        ]): ImplicitFormExact1 | undefined {

    const [[a1,[a0]], [b1,[b0]]] = pspb;

    if (eSign(a1) === 0 && eSign(b1) === 0) {
        // the input bezier curve is in fact not linear but has order < 1
        // it is a point and no implicit form is possible
        return undefined;
    }

    const vₓ = eno(b1);
    const vᵧ = a1;

    //const v = a1*b0 - a0*b1;
    const v = edif(
        sce(a0,b1),
        sce(b0,a1)
    );

    return { vₓ, vᵧ, v };
}


export { getImplicitForm1Exact, getImplicitForm1ExactPb }