import { eAdd, eCompress, eDiff, eMult } from 'big-float-ts';
import { eHorner } from 'flo-poly';
import { toPowerBasis_1stDerivativeDd } from '../to-power-basis/to-power-basis-1st-derivative/double-double/to-power-basis-1st-derivative-dd.js';
import { toPowerBasis_1stDerivativeExact } from '../to-power-basis/to-power-basis-1st-derivative/exact/to-power-basis-1st-derivative-exact.js';
import { toPowerBasis_2ndDerivativeDd } from '../to-power-basis/to-power-basis-2nd-derivative/double-double/to-power-basis-2nd-derivative-dd.js';
import { toPowerBasis_2ndDerivativeExact } from '../to-power-basis/to-power-basis-2nd-derivative/exact/to-power-basis-2nd-derivative-exact.js';


/**
 * Returns the curvature `κ` of the given linear, quadratic or cubic bezier 
 * curve at a specific given parameter value `t`. 
 * 
 * * returns `Number.NaN` at a cusp - this can be tested for with `Number.isNaN`
 * 
 * @param ps an order 1,2 or 3 bezier curve, e.g. `[[[0],[0]],[[1],[1]],[[2],[1]],[[2],[0]]]`
 * @param t the parameter value where the curvature should be evaluated
 */
function eCurvature(ps: number[][], t: number): number {
    const [dX,dY] = toPowerBasis_1stDerivativeExact(ps);
    const [ddX,ddY] = toPowerBasis_2ndDerivativeExact(ps);

	const dx  = eHorner(dX, t);
	const dy  = eHorner(dY, t);
	const ddx = eHorner(ddX, t);
	const ddy = eHorner(ddY, t);
	
	const a = eCompress(eDiff(eMult(dx,ddy),eMult(dy,ddx)));
	const _b = eCompress(eAdd(eMult(dx,dx),eMult(dy,dy)));
	const __b = eMult(_b,eMult(_b,_b));
	const b = Math.sqrt(__b[__b.length-1]);
	const a_ = a[a.length-1];

	return a_/b;
}


export { eCurvature }