Parametric Aortic Arch

$D(\xi) = D_\mathrm{asc}\bigl[1 - (1-\tau)\,\xi^{\,p}\bigr]$,   $\xi = s / S_\mathrm{total}$

$D_i = D_\mathrm{asc} \times r_i$
$s_\mathrm{BCA} = s_\mathrm{crown} - 1.5\delta$,   $s_\mathrm{LCCA} = s_\mathrm{crown} - 0.5\delta$,   $s_\mathrm{LSA} = s_\mathrm{crown} + 0.5\delta$

$r_\mathrm{throat} = r\sqrt{1-\alpha}$,   $s_\mathrm{CoA} = s_\mathrm{LSA} + d_\mathrm{CoA}$
$f(\xi_c) = \begin{cases}(2\xi_c)^{a_p} & \xi_c \le 0.5 \\ (2(1-\xi_c))^{a_d} & \xi_c > 0.5\end{cases}$
$a_p = 1.5 + 0.5\sigma$,   $a_d = 4 - 2\sigma$

$r_\mathrm{hyp}(s) = r(s)\bigl[1 - \eta \cdot \tfrac{1}{2}(1 - \cos 2\pi\xi_h)\bigr]$
$\xi_h = \frac{s - s_\mathrm{BCA}}{s_\mathrm{LSA} - s_\mathrm{BCA}}$,   for $s \in [s_\mathrm{BCA},\, s_\mathrm{LSA}]$

$\hat{r}_i = 0.06\,r_{i-2} + 0.24\,r_{i-1} + 0.40\,r_i + 0.24\,r_{i+1} + 0.06\,r_{i+2}$
Throat $\pm 3$ pts pinned. Applied $N$ passes.