public override Vector2d GetFirstDerivative(double t)
{
/*
* Maxima:
* s: t * m + n;
* x: a*sqrt(%pi)*fresnel_c(s/(a*sqrt(%pi)));
* y: a*sqrt(%pi)*fresnel_s(s/(a*sqrt(%pi)));
* z: 1;
* result: diff([ x, y, z ], t, 1);
*
* result: [m*cos((m*t+n)^2 / (2*a^2)),
* m*sin((m*t+n)^2 / (2*a^2)),
* 0]
*
* m*[cos((m*t+n)^2 / (2*a^2)),
* sin((m*t+n)^2 / (2*a^2)),
* 0]
*
* m*[cos(s^2 / (2*a^2)),
* sin(s^2 / (2*a^2)),
* 0]
*/
double m = this.ttransform.A;
double dl = this.GetL(t);
Vector2d v = ClothoUtils.DClotho(dl, this.InvertY, this.A);
v = v.Mul(m);
return(this.transform.DoTransform(v));
}
public void Test1()
{
for (double a = 0.5; a < 10; a += 0.5)
{
foreach (bool invertY in new[] { false, true })
{
int ysign = invertY ? -1 : 1;
double[] angles =
{
ysign * 0,
ysign *SysMath.PI / 4,
ysign *SysMath.PI / 2,
ysign * 3 *SysMath.PI / 4
};
foreach (double angle in angles)
{
Vec2d v = vecMath.NewRotate(angle);
double l = ClothoUtils.FindTangent(invertY, a, v);
double l_v2 = ClothoUtils.FindTangent(invertY, a, angle);
// Se comprueba que las busquedas de tangente sean equivalentes.
Assert.IsTrue(l.EpsilonEquals(l_v2));
// Se comprueba que la solucion corresponde con el vector tangente.
Vec2d d_pos = ClothoUtils.DClotho(l, invertY, a);
Assert.IsTrue(d_pos.Cross(v).EpsilonEquals(0));
Vec2d d_neg = ClothoUtils.DClotho(-l, invertY, a);
Assert.IsTrue(d_neg.Cross(v).EpsilonEquals(0));
}
}
}
}