Offset Curve

Functionality

This node generates a Curve, calculated as offset of another Curve by some amount. It takes all points of original curve and moves them in direction perpendicular to curve’s tangent. In other words, this “offsetting” operation can be described as extruding one single point along the curve.

When we say “offset all points of curve in direction perpendicular to curve’s tangent”, there is a good question: where exactly? There are several algorithms how to define a reference frame associated with curve’s point and curve’s tangent direction. 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 (The curvature of a straight line is zero). 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.

• Specified plane algorithm selects offset direction vector so that it satisfies two conditions: 1) it is perpendicular to curve’s tangent vector, and 2) it lies in so-called “offset operation plane”, which is specified by user by providing the normal vector of such plane (in other words, offset direction vector is perpendicular to normal vector provided by user). This algorithm is supposed to give good results for planar or almost planar curves. The resulting curve may have twists in places where original curve’s tangent vector is parallel to offset operation plane’s normal (i.e. tangent is perpendicular to offset operation plane). Hint: you may use “Linear approximation” node to automatically calculate normal vector of offset operation plane.

https://gist.github.com/0f8f8c8d4b0dca3a403534fb1c423305

Animation for “specified plane” mode (press image to open):

For all algorithms, reference frame’s Z axis is always pointing along curve’s tangent direction. Two other axes are always perpendicular to tangent direction, but where exactly they are pointing - depends on the algorithm. For Frenet algorithm, X axis is pointing along curve’s normal and Y axis is pointing along curve’s binormal.

Curve domain and parametrization: the same as of original curve.

Inputs

This node has the following inputs:

• Curve. The curve to be offset. This input is mandatory.

• Offset. Offset amount. This input is available only if Algorithm parameter is set to Specified plane, or the Direction parameter is set to X (Normal) or Y (Binormal). The input is not available when Offset type parameter is set to Variable. The default value is 0.1.

• OffsetCurve. The curve defining the offset amount for each point of original curve. The curve is supposed to lie in XOY coordinate plane. The node uses this curve’s mapping of T parameter to Y coordinate. For parameter of this offset curve, the node will use either parameter of the original curve, or it’s length share, depending on Offset curve type parameter. This input is available and mandatory only if Offset type parameter is set to Variable.

• Vector. Offset direction vector. This input is available only if Algorithm parameter is set to Specified plane, or the Direction parameter is set to Custom (N/B/T).

  • For Specified plane algorithm, this input defines the normal vector of offset operation plane (offset direction vector will be always perpendicular to it).

    

  • For other algorithms, Components of the vector are used within curve frame, calculated according to Algorithm parameter. For Frenet algorithm, X component of the vector represents offset along curve’s normal, Y component of the vector represents offset along curve’s binormal, and Z component of the vector represents offset along curve’s tangent.

    

  The default value is (0.1, 0, 0).

• Resolution. Number of samples for Zero-Twist or Track normal rotation algorithm calculation. It is also used for curve length calculation, when Offset type parameter is set to Variable, and Offset curve use parameter is set to Curve length. 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, or when Offset type parameter is set to Variable and Offset curve use parameter is set to Curve length.

Parameters

This node has the following parameters:

• Algorithm. Curve frame calculation algorithm. The available options are:

https://gist.github.com/0ca7f735f7d85f5ed6ff456b89f088ff

• Frenet. Rotate the profile curve according to Frenet frame of the extrusion curve (press image to animate).

  

• 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.

  

• Specified plane. Offset direction vector will be always lying in a plane which is defined by normal vector provided in Vector input. (https://gist.github.com/c000254e670af7a3435e84ca301ded81)

  

The default option is Householder.

• Direction. This defines offset direction. This input is not available when Algorithm parameter is set to Specified plane. The available options are:

  • X (Normal). Offset along curve reference frame’s X axis (for Frenet frame - curve normal).

  • Y (Binormal). Offset along curve reference frame’s Y axis (for Frenet frame - curve binormal).

  • Custom (N/B/T). Offset along user-provided vector.

  The default option is X (Normal).

Outputs

This node has the following output:

• Curve. The offsetted curve.

Examples of usage

Offset one curve with several different offset amounts:

• Curves-> Cubic Spline

• Curves-> Evaluate Curve

• Number-> Number Range

• Vector-> Vector sort

• Viz-> Viewer Draw

• Scene-> Get Objects Data

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Example of Custom (N/B/T) mode usage:

• Curves-> Cubic Spline

• Curves-> Evaluate Curve

• Number-> Number Range

• Vector-> Vector sort

• Vector-> Vector Polar Input

• Scene-> Get Objects Data

• Viz-> Viewer Draw

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Example of Specified plane mode usage. Here Linear approximation node is used to automatically detect the plane where the curve is lying (mostly); it outputs a normal vector, which is nearly OY axis, so the offset operation plane will be nearly XOZ. Note that the offsetted curve has a twist in a place where the tangent of original curve is perpendicular to offset operation plane.

• Generator-> Line

• Generator-> Segment

• Generator-> Plane

• Curves-> Cubic Spline

• Curves-> Evaluate Curve

• Analyzers-> Linear Approximation

• Number-> A Number

• Vector-> Vector sort

• List->List Struct-> List Item

• Scene-> Get Objects Data

• Text-> Stethoscope

• Viz-> Viewer Draw

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Example of Variable offset mode usage:

• Generator-> Line

• Generator-> Segment

• Generator-> Plane

• Curves-> Cubic Spline

• Curves-> Evaluate Curve

• Surfaces-> Curve Formula

• Analyzers-> Linear Approximation

• Number-> A Number

• Vector-> Vector sort

• List->List Struct-> List Item

• Scene-> Get Objects Data

• Text-> Stethoscope

• Viz-> Viewer Draw