Physically, 3D tendons are steel bars used in post-tensioned concrete bridges.
Mathematically, 3D tendons are 3D curves.
You can get a vertial surface (VS) by cutting the bridge from its top vertially down along its longitudinal axis.
If the axis of the bridge is a straight line, the VS is a vertical plane (VP).
But if the axis of the bridge is a curve, then the VS is a cylindrical surface, the aligement of the cylinder is parallel to the axis of the bridge. The VS needs to be FLATTENED to get the VP.
In general, tendons are “projeced” on two planes: vertical plane (VP) and horizontal plane (HP).
The HP is always perpendicular to the VP.
The curve in these two planes are polycurves made of lines and circular arcs, red lines shown in the image
Now I know the curves on VP and HP in CAD, if the axis of the bridge is a curve, which means the VS is a cylindrical surface, then how can I combine the curves from VP and HP to get 3D curves?