Stereographic3D

Group (Subgroup)

OrientationAnalysis (Conversion Filters)

Description

This Filter takes a set of quaternions as input and projects them into a 3D unit-radius ball using an equal-angle projection, i.e., a stereographic projection. This is a convenient and intuitive way to represent in 3D the quaternion unit hemisphere, which lives embedded in a 4D space, in the same way that a standard 2D stereographic projection represents data lying on the surface of a 2D spherical surface embedded in a 3D space. The filter generates a set of 3D stereographic coordinates, all of which have a modules less than or equal to 1. Starting from the quaternion q, with scalar part w, the filter computes the stereographic vectors, s, according to the following relation:

Images/Stereographic3D_Equations.png

Note that if the value of w equals -1.0 then the filter will exit early and present an error. This is because with a value of -1 the output value would divide by zero. This should not happen if the angle falls inside the proper range.

Data Layout Notes

DREAM.3D orders a quaternion as ( < x, y, z >, w)>. If you are importing quaternions from another source, please ensure that the quaternions are in the correct order.

Parameters

None

Required Geometry

Not Applicable

Required Objects

Kind Default Name Type Component Dimensions Description
Element Attribute Array Quats float (4) Specifies the orientation of the Element in quaternion representation

Created Objects

Kind Default Name Type Component Dimensions Description
Attribute Array Coordinates float 3 Converted quaternion

Example Pipelines

Please see the description file distributed with this plugin.

DREAM3D Mailing Lists

If you need more help with a filter, please consider asking your question on the DREAM3D Users mailing list: https://groups.google.com/forum/?hl=en#!forum/dream3d-users