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MathGroup Archive 1998

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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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