build_helix Subroutine

pure subroutine build_helix(this, c, rh, p, n)

Map a straight pipe-like NURBS volume onto a cylindrical helix.

Each control point $\mathbf{X}_c=(x,y,z)$ is first expressed relative to the input center $\mathbf{c}=(c_x,c_y,c_z)$. For the axial (k) index, define a normalized parameter $$s(k) = \begin{cases} \dfrac{k-1}{n_c^{(z)}-1}, & n_c^{(z)} > 1,\\[4pt] 0, & \text{otherwise}, \end{cases}$$ which runs from 0 (start) to 1 (end) along the volume.

The helix angle as a function of $s$ is $$\theta(s) = 2\pi\,n\,s ,$$ where n is the number of turns. For a point at polar coordinates $\rho=\sqrt{(x-c_x)^2+(y-c_y)^2}$ and $\phi=\operatorname{atan2}(y-c_y,x-c_x)$, the mapping is: $$X = c_x + \bigl(r_h + \rho\cos\phi\bigr)\cos\theta(s),\quad Y = c_y + \bigl(r_h + \rho\cos\phi\bigr)\sin\theta(s),\quad Z = c_z + \rho\sin\phi + p\,s ,$$ where $r_h$ is the helix radius and $p$ is the pitch (axial rise per turn).

Knots are preserved; only the control points are updated.

Arguments