Bend Along Curve Field¶

https://github.com/nortikin/sverchok/assets/14288520/24e3fe93-4eb7-4cea-9d80-1b97e32802ab

Functionality¶

This node generates a Vector Field, which bends some part of 3D space along the provided Curve object.

https://github.com/nortikin/sverchok/assets/14288520/9b3e1f64-c352-487a-a9ef-86677644059f

It is in general not a trivial task to rotate a 3D object along a vector, because there are always 2 other axes of object and it is not clear where should they be directed to. So, this node supports 3 different algorithms of object rotation calculation. In many simple cases, all these algorithms will give exactly the same result. But in more complex setups, or in some corner cases, results can be very different. So, just try all algorithms and see which one fits you better.

“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.

Inputs¶

This node has the following inputs:

Curve. The curve to bend the space along. This input is mandatory.
Src T Min. The minimum value of the orientation coordinate, where the bending should begin. For example, if Orientation axis parameter is set to Z, this is the minimum value of Z coordinate. The default value is -1.0.
Src T Max. The maximum value of the orientation coordinate, where the bending should end. For example, if Orientation axis parameter is set to Z, this is the maximum value of Z coordinate. The default value is 1.0.
Cylinder Z start do not equal Src T min

Cylinder Z start equal “Src T min” and Cylinder Z top equal “Src T max” and Cylinder Height equal curve’s T Range
- Generator-> Cylinder
- Matrix-> Matrix In
- Matrix-> Matrix Apply to Mesh
Resolution. The number of samples along the curve, used to calculate curve length parameter. This input is only available when Scale along curve parameter is set to Curve length. The higher the value is, the more precise is the calculation, but more time it is going to take. The default value is 50.

The field bends the part of space which is between Src T Min and Src T Max, along the curve. For example, with default settings, the source part of space is the space between Z = -1 and Z = 1. The behaviour of the field outside of these bounds is not guaranteed.

Changing Cylinder height and position and Changing of T min/max (see example 2)

https://github.com/nortikin/sverchok/assets/14288520/6bebd03a-e0af-4f52-b6f7-b0c84a4d0782

Parameters¶

This node has the following parameters:

Orientation. Which axis of the source space should be elongated along the curve. The available values are X, Y and Z. The default value is Z. When the Algorithm parameter is set to Zero-Twist or Frenet, the only available option is Z.
Scale all axis. If checked, all three axis of the source space will be scaled by the same amount as is required to fit the space between Src T Min and Src T Max to the curve length. Otherwise, only orientation axis will be scaled. Checked by default.
- T Min, T Max: Number-> A Number
- CEIL X: Number-> Scalar Math
Algorithm. Rotation calculation algorithm. Available values are:
- 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 algorithm gives you a bit more flexibility comparing to other, by allowing to select the Up axis.
- Rotation difference: calculate rotation as rotation difference between two vectors.
- Frenet: rotate the space according to curve’s Frenet frame.
- Zero-Twist: rotate the space according to curve’s “zero-twist” frame.
- Track normal: try to maintain constant normal direction by tracking it along the curve.
Default value is Householder.
Up axis. Axis of donor object that should point up in result. This parameter is available only when Tracking algorithm is selected. Value of this parameter must differ from Orientation parameter, otherwise you will get an error. Default value is X.
Scale along curve. This defines how the scaling of the space along the curve is to be calculated. The available options are:
- Curve parameter. Scale the space proportional to curve’s T parameter.
- Curve length. Scale the space proportional to curve’s length. This usually gives more natural results, but takes more time to compute.
The default option is Curve parameter.