gdalgorithms-list

[Algorithms] Rotation from 4 points

[Jose M. <jos...@ya...>]

Hi,

I'm trying to find the pitch, yaw and roll from a group of four points, but just can't do it wright!

The points are the corners of a box..

C
 \
  A--D
 /
B


For a unit box in the origin aligned with the XYZ axis, these are the coordinates of the points:

A(0, 0, 0)
B(0, 0, 1)
C(0, 1, 0)
D(1, 0, 0)


Well, the box may be at any rotation and position, but it's easy to get the points.

How to extract one of these informations:

1 - A quaternion representing the rotation
2 - The pitch, yaw and roll values or
3 - The angles for the rotated axis


Thank you!


Jose




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Re: [Algorithms] Rotation from 4 points

[<Pau...@sc...>]

-----BEGIN PGP SIGNED MESSAGE-----
Hash: SHA256

> How to extract one of these informations:
> 
> 1 - A quaternion representing the rotation

Hi there,

Just form the basis vectors and you have a matrix right away. Convert to 
quat. Done :)

I.e. Subtract your corner points from the 'central' point, and those are 
your basis vectors.

row 0 = D-A
row 1 = B-A
row 2 = C-A

Cheers, Paul.
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Re: [Algorithms] Rotation from 4 points

[Jose M. <jos...@ya...>]

!!!

Sure!

You are right, Paul!

Easy and clever solution, thank you !

Jose


--- Em ter, 19/1/10, Pau...@sc... <Pau...@sc...> escreveu:

> De: Pau...@sc... <Pau...@sc...>
> Assunto: Re: [Algorithms] Rotation from 4 points
> Para: "Game Development Algorithms" <gda...@li...>
> Data: Terça-feira, 19 de Janeiro de 2010, 9:15
> -----BEGIN PGP SIGNED MESSAGE-----
> Hash: SHA256
> 
> > How to extract one of these informations:
> > 
> > 1 - A quaternion representing the rotation
> 
> Hi there,
> 
> Just form the basis vectors and you have a matrix right
> away. Convert to 
> quat. Done :)
> 
> I.e. Subtract your corner points from the 'central' point,
> and those are 
> your basis vectors.
> 
> row 0 = D-A
> row 1 = B-A
> row 2 = C-A
> 
> Cheers, Paul.
> **********************************************************************
> This email and any files transmitted with it are
> confidential and intended 
> solely for the use of the individual or entity to whom they
> are addressed. 
> If you have received this email in error please notify pos...@sc...
> This footnote also confirms that this email message has
> been checked for 
> all known viruses.
> Sony Computer Entertainment Europe Limited
> Registered Office: 10 Great Marlborough Street, London W1F
> 7LP, United 
> Kingdom
> Registered in England: 3277793
> **********************************************************************
> P Please consider the environment before printing this
> e-mail
> 
> -----BEGIN PGP SIGNATURE-----
> Version: PGP Universal 2.9.1 (Build 287)
> Charset: US-ASCII
> 
> wsBVAwUBS1WTBnajGqjtoMHxAQhirwgAmWoIGhiqB3qxlkaXVwQR1Tt2btMcJr02
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> RoDic0ebhbgce8osQquHCEhLEqNtoiUZBxA9VGASHgo/5sKTNHuBM9L45qJUkEPj
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