\(\renewcommand\AA{\unicode{x212B}}\)

BinMD Coordinate Transformations

Introduction

The algorithms BinMD v1 and SliceMD v1 allow an MD Workspace to be binned into a new coordinate system. This guide describes the coordinate transformations and relations between binned workspaces.

Binning an MDWorkspace

  • Begin with an initial MD Workspace called original_ws with two dimensions, Qx and Qy.

  • The BinMD v1 algorithm can transform these coordinates into a new coordinate space with, for example, a rotation and a translation:

Coordinate transform line example

  • The output MD Histogram Workspace, called binned_ws still has two dimensions, now called H and K.

  • The binned_ws workspace holds a reference to the original workspace.

    • This can be seen in the details of the workspace in the Workspaces widget (Binned from 'original_ws').

    • In C++, calling binned_ws->getOriginalWorkspace(0) will return a pointer to original_ws.

  • It also holds the coordinate transformations between workspaces:

    • (H, K) -> (Qx, Qy) : Binned coordinates back to original coordinates.

      • In C++, this can be accessed via binned_ws->getTransformToOriginal(0)

    • (Qx, Qy) -> (H, K) : original coordinates to the binned coordinates.

      • In C++, this is accessible via binned_ws->getTransformFromOriginal(0)

  • When moving the mouse in the Sliceviewer, for example, the coordinates in BOTH spaces will be displayed.

Binning a Line From an MDHistoWorkspace

It is possible to call BinMD v1 on an MD Histogram Workspace that has already been binned. For example, if you are viewing binned_ws in the Sliceviewer, you can use the Non-axis aligned cutting tool to bin a line from that.

Coordinate transform example

  • Say you bin binned_ws to a line with a width: line_ws.

    • The line_ws workspace has 2 dimensions (since it has a width).

    • The dimensions of line_ws have the generic names: (X,Y).

    • Only the X dimension has more than one bin, but the Y dimension still exists.

    • Each point in (X,Y) space has an equivalent in (H,K) and in (Qx,Qy) space.

  • The integration will actually be performed on the event data in the original_ws.

  • There are then two ‘original’ workspaces recorded in ‘line_ws’:

    • line_ws->getOriginalWorkspace(0) returns the original_ws (the event data).

      • line_ws->getTransformToOriginal(0) returns the (X,Y) -> (Qx,Qy) transform.

      • line_ws->getTransformFromOriginal(0) returns the (Qx,Qy) -> (X,Y) transform.

    • line_ws->getOriginalWorkspace(1) returns the intermediate workspace binned_ws (the 2D histogram data).

      • line_ws->getTransformToOriginal(1) returns the (X,Y) -> (H,K) transform.

      • line_ws->getTransformFromOriginal(1) returns the (H,K) -> (X,Y) transform.

  • When using the Plot MD menu on the line_ws, you can display the plot as the coordinates of the intermediate workspace.

    • In this example, this would be the (H,K) coordinates.

Category: Techniques