bend_pipe Subroutine

pure subroutine bend_pipe(this, center, radius1, radius2, length, rbend, angle_deg)

Bend a straight pipe-like NURBS volume into a circular arc. Each control point $\mathbf{X}_c=(x,y,z)$ is transformed relative to the center $\mathbf{c}=(c_x,c_y,c_z)$. Let the total bend angle in degrees be $\alpha^\circ$ (input), and define the total bend angle in radians $$\alpha_{\max} = \frac{\pi}{180}\,\alpha^\circ .$$ For each control point: $$\rho = \sqrt{(x-c_x)^2+(y-c_y)^2},\quad \phi = \operatorname{atan2}(y-c_y,\,x-c_x),\quad Z = z - c_z ,$$ $$\theta(Z) = \alpha_{\max}\,\min\!\bigl(1,\max\!\bigl(0,\tfrac{Z}{L}\bigr)\bigr) .$$ Mapping: $$x' = c_x + (\rho\cos\phi + R_b)\cos\theta,\quad y' = c_y + (\rho\cos\phi + R_b)\sin\theta,\quad z' = c_z + \rho\sin\phi .$$ Knots and weights are preserved; only the control lattice is updated.

Arguments