public override Vector2d GetSecondDerivative(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, 2); * * result: [-(m^2*(m*t+n)*sin((m*t+n)^2 / (2*a^2))) / a^2, * (m^2*(m*t+n)*cos((m*t+n)^2 / (2*a^2))) / a^2, * 0] * * m^2*[-((m*t+n)*sin((m*t+n)^2 / (2*a^2))) / a^2, * ((m*t+n)*cos((m*t+n)^2 / (2*a^2))) / a^2, * 0] * * m^2*[-(s*sin(s^2 / (2*a^2))) / a^2, * (s*cos(s^2 / (2*a^2))) / a^2, * 0] */ double m = this.ttransform.A; double m2 = m * m; double dl = this.GetL(t); Vector2d v = ClothoUtils.DClotho2(dl, this.InvertY, this.A); v = v.Mul(m2); return(this.transform.DoTransform(v)); }