import { toPowerBasis_1stDerivative } from '../../to-power-basis/to-power-basis-1st-derivative/double/to-power-basis-1st-derivative.js';
import { Horner } from 'flo-poly';


/**
 * Returns a normal vector (not necessarily of unit length) of a bezier curve 
 * at a specific given parameter value `t` by simply taking the `tangent` at
 * that point and rotating it by 90 degrees.
 * 
 * * uses double precision calculations internally
 * 
 * @param ps a linear, quadratic or cubic bezier curve given by its ordered
 * control points, e.g. `[[0,0],[1,1],[2,1],[2,0]]`
 * @param t the parameter value where the normal should be evaluated
 * 
 * @doc mdx
 */
function normal(ps: number[][], t: number): number[] {
	const [dX, dY] = toPowerBasis_1stDerivative(ps);

	return [
		-Horner(dY,t),
		Horner(dX,t)
	];
}


export { normal }