Transforming polygons from 1 3D Coordinate system to another

• To: mathgroup at smc.vnet.net
• Subject: [mg15285] Transforming polygons from 1 3D Coordinate system to another
• From: Andrew Bushnell <andy at anisci.com>
• Date: Thu, 31 Dec 1998 04:39:39 -0500
• Organization: Concentric Internet Services
• Sender: owner-wri-mathgroup at wolfram.com

```[Mathematica solutions only.  Others to the submitter vial email.  - moderator]

Any help appreciated...

Ok, here goes...

I need help in converting (or mapping) an arbitrary coplanar polygon

(with a minimum of 3 vertices) from its original position to a target

polygon (or plane) defined by 3 vertices.

An example might help...

take a right-handed coordinate system...

Y
|
|
|_____ X
/
/
Z

Lets say we have a polygon located at (3,0,0) with a normal of (1,0,0)

- this example is for easy numbers but the polygon's normal could be

oriented any which way.

/ C(3,1,0)
Y          / |
|       D / -|-----> N (1,0,0)
|         |  |B(3,0,0)
|_________|  |___X
/          | /
/           |/
Z           A(3,0,1)

(again for simplicity) We want to transform this polygon so that its

normal is aligned with the Y axis. The point A is moved to the origin

(0,0,0)and the edge AB is aligned with the +Z axis. The Body of the

polygon will therefor be on the XY plane.

Somehow (I think) I need to define a 4x4 matrix that represents the

coordinate system convertion and use this to convert all the original

polygon coordinates into the new location/orientation.

Someone told me that converting the coordinate values into "Vector

Basis" was the was to go ???? :^)

Could you help.

Tx

Andy

```

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