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