About the Moving Frame

This section provides information on the moving frame types used in the Net Surface command.

See Also
Creating a Net Surface

The moving frame determines a local coordinate system that moves along the dominant guiding curve thus defining the profile's position on the curve.

The coordinate axes appear as:

  • N (x-axis) = Binormal vector of the moving frame

    It is the vector being normal to N and T.

  • B (y-axis) = Normal of an automatic plane

    A plane is computed reflecting the position of the guiding curve as good as possible, that is with a minimum distance from the guiding curve. The y-axis of the local coordinate system then aligns normal to this automatic plane.

  • T (z-axis) = Tangent of the dominant guiding curve

Depending on the selected guide and profile curves, the following moving frame types are available:

Selected curves Available moving frame types
2 profiles No moving frame options

1 guide and 1 profile

OR

1 guide and 2 or more profiles

3 moving frame options:

  • Parallel to plane
  • Perpendicular to the dominant guiding curve
  • Pseudo-perpendicular to the dominant guiding curve

2 guides

OR

2 or more guides and 2 or more profiles

5 moving frame options. Additionally:

  • Two guiding curves and perpendicular to the dominant guiding curve
  • Two guiding curves and pseudo-perpendicular to the dominant guiding curve

Using one guiding curve and parallel planes


  • Parallel to Plane

    The local coordinate system moves parallel to the Robot’s xz-plane. It is always defined independent from the guiding curve’s tangent.

Using one guiding curve and radial planes


  • Perpendicular to the dominant guiding curve

    The tangent of the guiding curve determines the z-axis (T). The y-axis (B) points in the normal direction of the automatic plane.

    The xy-plane is always perpendicular to the tangent of the guiding curve.

  • Pseudo-Perpendicular to the dominant guiding curve

    The normal of the automatic plane determines the y-axis (B). The z-axis (T) points in the tangent direction of the guiding curve.

    The xy-plane is not implicitly perpendicular to the guiding curve. It only appears perpendicular when looking in the direction of the normal.

Using two guiding curves


The connection to the second guiding curve determines the x-axis (N).
  • Two guiding curves and perpendicular to the dominant guiding curve

    The tangent of the guiding curve (z-axis, T) aligns the coordinate system.

  • Two guiding curves and pseudo-perpendicular to the dominant guiding curve

    The normal of the automatic plane (y-axis, B) aligns the coordinate system.