Geometry 3D Rotation - Failure to Grok

[Gan Uesli Starling]

Wanting to rotate an arbitrary 3D point, cords X,Y,Z relative to XYZ location 0,0,0 in a 3D system.

But all I find is Math/Geometry/3D Rot (direct and euler) which both take ARRAYS for their input, and a 3X3 ARRAY for it's command. I do not grok this concept at all. What's going on? How can I use it instead to deal with a single point (anywhere) relative to the system origin?

Problem relates to a calculator I have built for the design of log-periodic antennas. The antenna consists of wires, paired as XYZ_from and XYZ_to with also a subunit 'segments' for each, thus a 4xN array of (X,Y,Z,Segs) of arbitrary length. First wire is always on the origin. So I'm wanting to perform pitch/roll/yaw on this antenna from point 0,0,0. But do it by running my coordinates X,Y,Z for each wire-end, one set at a time, through a transformation filter. And the whole 3x3 matrix makes no sense to me. Sorry, I'm 30 years out of college. This is a hobby project for a calculator I'll give away free. Can someone clue me in?

[JKSH]

3 hours ago, Gan Uesli Starling said:

all I find is Math/Geometry/3D Rot (direct and euler) which both take ARRAYS for their input, and a 3X3 ARRAY for it's command... How can I use it instead to deal with a single point (anywhere) relative to the system origin?

I presume you mean the 3D Cartesian Coordinate Rotation VIs. The NI documentation has a decent description of what they do: https://zone.ni.com/reference/en-XX/help/371361R-01/gmath/3d_cartesian_coordinate_rotation_euler/

These are polymorphic VIs. By default, they take an array of coordinates. If you just want to rotate a single point, select the "Scalar" version of the VI (Put the subVI on your block diagram, then Right-click > Visible Items > Polymorphic VI Selector)

 

3 hours ago, Gan Uesli Starling said:

a 3X3 ARRAY for it's command. I do not grok this concept at all. What's going on?....

And the whole 3x3 matrix makes no sense to me.

The 3x3 matrix is the transformation matrix, which is a concept described in linear algebra. There are different types of transformations: Translation, rotation, shearing, scaling, etc.

In a nutshell: Think of your 3D point-coordinates as a 3x1 matrix (also called a column vector). If you multiply a column vector by a 3x3 matrix, you will get a new column vector. That new vector will contain your "transformed" point-coordinates.

Edited September 3, 2020 by JKSH