import { eHorner } from 'flo-poly';
import { toPowerBasis_1stDerivativeExact } from '../../../to-power-basis/to-power-basis-1st-derivative/exact/to-power-basis-1st-derivative-exact.js';


/**
 * Returns the *exact* tangent vector (not necessarily of unit length) of an 
 * order 0,1,2 or 3 bezier curve at a specific parameter `t`, i.e.
 * returns the `[x,y]` value of the once differentiated (with respect to `t`) 
 * bezier curve's power basis when evaluated at `t`.
 * 
 * @param ps a linear, quadratic or cubic bezier, e.g. `[[0,0],[1,1],[2,1],[2,0]]`
 * @param t the t parameter
 * 
 * @doc
 */
 function tangentExact(
        ps: number[][], t: number): number[][] {

     const [dX, dY] = toPowerBasis_1stDerivativeExact(ps);

     return [eHorner(dX, t), eHorner(dY, t)];
 }


 export { tangentExact }