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GlobalTrend

ferreus_rbf.GlobalTrend

Defines an anisotropy transform for an RBF problem by specifying principal directions and scaling ratios.

The variant to use depends on the dimensionality of the RBF problem:

  • GlobalTrend.one - for 1D problems, with a single principal axis.
  • GlobalTrend.two - for 2D problems, with two axes lying in a plane, oriented by a rotation angle.
  • GlobalTrend.three - for 3D problems, with a full orientation defined by sequential rotations.

Each variant encodes the relative scaling (ratios) along its principal axes, providing a compact way to represent anisotropy and directional stretching appropriate for the problem dimension.

This is particularly useful when the input data shows a clear directional continuity or trend: by increasing the relative weighting along that direction, interpolation can better reflect the structure present in the data.

Note: All angles are specified in degrees.

one(major_ratio) classmethod

A 1D global trend.

Represents anisotropy with a single scaling ratio along one principal axis.

Parameters:

Name Type Description Default
major_ratio float

Scaling ratio along the principal axis.

 required

Returns:

Type Description
GlobalTrend

two(rotation_angle, major_ratio, minor_ratio) classmethod

A 2D global trend.

Defined within the XY plane, oriented by a rotation angle. Two scaling ratios describe the major and minor axes lying in the rotated space.

Parameters:

Name Type Description Default
rotation_angle float

Rotation angle in degrees (positive = clockwise).

 required
major_ratio float

Scaling ratio along the major axis, aligned with the rotation direction.

 required
minor_ratio float

Scaling ratio along the minor axis, perpendicular to the rotation direction within the plane.

 required

Returns:

Type Description
GlobalTrend

three(dip, dip_direction, pitch, major_ratio, semi_major_ratio, minor_ratio) classmethod

A 3D global trend.

Rotation conventions:

  • Left-hand rule for rotations (positive = clockwise).
  • Rotation sequence is Z-X-Z'.
     +Z     +Y
     ^      ^
     |     /
     |    /
     |   /
     |  /
     | /
     |/
     o- - - - - - - -> +X

Terminology:

  • dip_direction: azimuth angle in the XY plane.
  • dip: tilt angle from horizontal toward the dip direction.
  • strike: dip_direction - 90 (perpendicular to dip direction).
  • pitch: rotation within the tilted plane, measured from strike.

After the Z and X rotations, the plane is tilted; pitch rotates within that plane about the new Z' axis.

          +Z'
          ^
           \
            \       strike
             o - - - - - - - - - > -X'
            /                   /
           /                   /
          / - - - - - - - - - /
      dipdir        \ pitch /
        /            \     /
       v              \   /
      +Y' - - - - - - - - -

Parameters:

Name Type Description Default
dip float

Tilt angle in degrees from horizontal toward dip_direction.

 required
dip_direction float

Azimuth angle in degrees in the XY plane, defining tilt direction.

 required
pitch float

Rotation in degrees within the tilted plane, measured from strike.

 required
major_ratio float

Scaling ratio along the major axis (aligned with pitch).

 required
semi_major_ratio float

Scaling ratio along the semi-major axis (perpendicular to pitch within the plane).

 required
minor_ratio float

Scaling ratio along the minor axis (aligned with the plane normal).

 required

Returns:

Type Description
GlobalTrend