import { ImplicitForm3Coeffs } from "../../implicit-form-types.js";


/**
 * Evaluates and returns the result of evaluating the given implicit function
 * (a degree 3 bivariate polynomial in `x` and `y`) at the point `[x,y]`.
 * 
 * * the implicit form is given by: `vₓₓₓx³ + vₓₓᵧx²y + vₓᵧᵧxy² + vᵧᵧᵧy³ + vₓₓx² +vₓᵧxy + vᵧᵧy² + vₓx + vᵧy + v`, 
 * where the `vₓ`, `vₓ`, `v`, etc are constants
 * 
 * @example
 * ```typescript
 * evaluateImplicit3({ vₓₓₓ: -1, vₓₓᵧ: -2, vₓᵧᵧ: -3, vᵧᵧᵧ: -4, vₓₓ: 4, vₓᵧ: 5, vᵧᵧ: 6, vₓ: 1, vᵧ: 2, v: 3 }, 7, -4);  //=> 123
 * ```
 * 
 * @param cs the polynomial to evaluate
 * @param x the `x` variable at which to evaluate
 * @param y the `y` variable at which to evaluate
 * 
 * @doc
 */
function evaluateImplicit3(
        cs: {
            vₓₓₓ: number; vₓₓᵧ: number; vₓᵧᵧ: number; vᵧᵧᵧ: number;
            vₓₓ: number; vₓᵧ: number; vᵧᵧ: number;
            vₓ: number; vᵧ: number; v: number;
        },
        x: number,
        y: number): number {

    const { vₓₓₓ, vₓₓᵧ, vₓᵧᵧ, vᵧᵧᵧ, vₓₓ, vₓᵧ, vᵧᵧ, vₓ, vᵧ, v } = cs;

    return (
        vₓₓₓ*x*x*x + 
        vₓₓᵧ*x*x*y +
        vₓᵧᵧ*x*y*y +
        vᵧᵧᵧ*y*y*y +
        vₓₓ*x*x + 
        vₓᵧ*x*y + 
        vᵧᵧ*y*y +
        vₓ*x + 
        vᵧ*y + 
        v
    );
}


export { evaluateImplicit3 }