Pipe Surface Along Curve

Functionality

This node generates cylindrical “pipe” Surface along a given Curve; the result is the same as if you extruded circular profile curve along your curve.

If you want more complex (not cylindrical) profile, or you want more control over extrusion, you probably want to use [Surfaces-> Extrude Curve Along Curve] node.

The Profile curve (circle) may optionally be rotated while extruding, to make result look more naturally; though since the profile is always a circle, the choice of algorithm is not so important for this node, usually.

Several algorithms to calculate rotation of profile curve are available. In simplest cases, all of them will give very similar results. In more complex cases, results will be very different. Different algorithms give best results in different cases:

• “Frenet” or “Zero-Twist” algorithms give very good results in case when extrusion curve has non-zero curvature in all points. If the extrusion curve has zero curvature points, or, even worse, it has straight segments, these algorithms will either make “flipping” surface, or give an error.

• “Householder”, “Tracking” and “Rotation difference” algorithms are “curve-agnostic”, they work independently of curve by itself, depending only on tangent direction. They give “good enough” result (at least, without errors or sudden flips) for all extrusion curves, but may make twisted surfaces in some special cases.

• “Track normal” algorithm is supposed to give good results without twisting for all extrusion curves. It will give better results with higher values of “resolution” parameter, but that may be slow.

Surface domain: Along U direction - from 0 to 2*pi; along V direction - the same as of “extrusion” curve.

Inputs

This node has the following inputs:

• Curve. The curve to build pipe around (the extrusion curve). This input is mandatory.

• Radius. Pipe radius. The default value is 0.1.

  

• Resolution. Number of samples for Zero-Twist or Track normal rotation algorithm calculation. The more the number is, the more precise the calculation is, but the slower. The default value is 50. This input is only available when Algorithm parameter is set to Zero-Twist or Track normal.

  

Parameters

This node has the following parameters:

• Algorithm. Profile curve rotation calculation algorithm. The available options are:

  • Frenet. Rotate the profile curve according to Frenet frame of the extrusion curve.

    

  • Zero-Twist. Rotate the profile curve according to “zero-twist” frame of the extrusion curve.

    

  • Householder: calculate rotation by using Householder’s reflection matrix (see Wikipedia article).

    

  • Tracking: use the same algorithm as in Blender’s “TrackTo” kinematic constraint. This node currently always uses X as the Up axis.

    

  • Rotation difference: calculate rotation as rotation difference between two vectors.

    

  • Track normal: try to maintain constant normal direction by tracking it along the curve.

    

  The default option is Householder.

Outputs

This node has the following output:

• Surface. The generated pipe surface.

Example of usage

Build a pipe from cubic curve:

• Curves-> Cubic Spline

• Surfaces-> Evaluate Surface

• Vector-> Vector sort

• Viz-> Viewer Draw

• Scene-> Objects In Lite

• Generator->Generatots Extended-> Hilbert 3D

• Curves->Curve Primitives-> Fillet Polyline

• Curves-> Cubic Spline

• Surfaces-> Evaluate Surface

• Transform-> Randomize

• Viz-> Viewer Draw

• Viz-> Viewer Draw Curve