Learn how to a build a cloud-first strategyRegister Now

x
?
Solved

How to calculate an absolute position/rotation given a relative position/rotation and a parent position/rotation vector and vice versa?

Posted on 2006-06-23
9
Medium Priority
?
1,405 Views
Last Modified: 2008-01-16
I'm making an application where I need to be able to calculate an absolute position/rotation given a relative position/rotation and a parent position/rotation it is relative to. The order of rotation will be X, Y then Z. I also need to be able to go the opposite way. That is finding a relative position/rotation given an absolute position/rotation and a parent position/rotation. What is the most efficient and easiest way to integrate this in an application that uses position and rotation vectors (radians) to store object placements?

If I'm not too wrong I can rotate it by X by multiplying the relative position X with cos(rotation x) and relative position Y with cos(rotation x). Not sure about Y and Z rotation though. I'm thankful for any solution :).
0
Comment
Question by:imnotapro
  • 3
  • 3
7 Comments
 
LVL 25

Expert Comment

by:InteractiveMind
ID: 16971014
Absolute parent position: vector P.


To rotate a vector around an axis by an angle 'a', you multiply the vector with the appropriate matrix:


Rotate around X axis:

[ 1     0        0    0 ]
[ 0  cos a  sin a  0 ]
[ 0 -sin a  cos a  0 ]
[ 0     0        0    1 ]

Rotate around Y axis:

[ cos a  0 -sin a   0 ]
[    0     1    0      0 ]
[ sin a   0  cos a  0 ]
[    0     0    0      1 ]

Rotate around Z axis:

[ cos a  sin a  0  0 ]
[-sin a  cos a  0  0 ]
[    0        0    1  0 ]
[    0        0    0  1 ]


You need to watch out for what is known as "Gimbal lock", where one or more of the rotations have no effect due to the order in which you perform the rotation.

To find the angle between two vectors around each axis, treat each vector as being 3 different 2D vectors, and use the dot product:

For vectors u and v:

u dot v = u.x * v.x + u.y*v.y + .. = |u| * |v| * Cos a

Therefore:

a = arccos( u dot v / (|u| * |v|) )
0
 

Author Comment

by:imnotapro
ID: 16975294
I get the logic in what you're saying, but I think I need an example. Say the parent position vector is called p (p.x p.y and p.z). The parent rotation vector is called pr (pr.x pr.y and pr.z). Then we have a child position vector that is relative to the parent position and rotation (c.x c.y and c.z) and a child rotation vector cr (cr.x cr.y and cr.z). I know nothing about matrices. How would you step for step go to find the child absolute position and rotation (a.x a.y a.z and ar.x ar.y ar.z)?

Also say we have the child absolute position/rotation (a and ar) and the parent absolute position/rotation (p and pr). Any example on how to find the child relative position/rotation (c and cr)?

I'm a programmer and I'm not very experienced on vector math and matrix math so I need it step for step :). Thanks!
0
 
LVL 25

Expert Comment

by:InteractiveMind
ID: 16975303
I'll be happy to provide an example; but, what do you mean by "rotation vector" ?
0
Industry Leaders: We Want Your Opinion!

We value your feedback.

Take our survey and automatically be enter to win anyone of the following:
Yeti Cooler, Amazon eGift Card, and Movie eGift Card!

 

Author Comment

by:imnotapro
ID: 16975943
A vector with 3 floats defining the rotation of the mesh in radians. One for X axis, one for Y and one for Z. Ie  pi/2,0,0 is 90 degrees along the X axis.
0
 
LVL 25

Accepted Solution

by:
InteractiveMind earned 1000 total points
ID: 16976074
Oh, ok.

Well, to multiply a vector with a matrix, you must first extend the vector to a 4x1 matrix, giving the 4th element (w) the value of 1.

So the vector V, becomes:

[ V.x ]
[ V.y ]
[ V.z ]
[   1  ]

(This is just another notation for what you've used above:  (V.x, V.y, V.z, 1)).


To then multiply this with a 4x4 matrix (which all of the transformation matrices are), let's take the following matrix as an example:

[ a  b  c  d ]
[ e  f   g  h ]
[ i   j   k  l  ]
[ m n  o  p ]

You multiply each row with the vectors column, and sum those components. So you get the following as the result:

[ a*V.x  + b*V.y + c*V.z + d ]
[ e*V.x  + f*V.y  + g*V.z + h ]
[ i*V.x   + j*V.y  + k*V.z + l  ]
[ m*V.x + n*V.y + o*V.z + p ]

And with the transformation matrices, the last row in that result can be neglected. So your new, transformed vector, becomes just:

[ a*V.x  + b*V.y + c*V.z + d ]         // x component
[ e*V.x  + f*V.y  + g*V.z + h ]        // y component
[ i*V.x   + j*V.y  + k*V.z + l  ]        // z component

And that's your transformed vector! :)
0
 

Author Comment

by:imnotapro
ID: 16979158
Okay, I've written up some code using the example you provided and I'm about to test it once I have a way of doing this the other way around. To get the relative position using parent position, parent rotation and child absolute position/rotation I guess I have to unrotate the child first using the absolute rotation of the child and the absolute rotation of the parent? Would it work taking the difference between those rotations (child absolute rotation minus parent absolute rotation), make them negative and then rotate them using what you said above?
0
 
LVL 1

Assisted Solution

by:lawyerboy780
lawyerboy780 earned 1000 total points
ID: 17113123
I'm confused.  Can anything be absolutely located if all or any  attempts at imposing order result in a systemic increase in chaos?  You know the entropy is inversely related to enthalpy thing?
0

Featured Post

Upgrade your Question Security!

Add Premium security features to your question to ensure its privacy or anonymity. Learn more about your ability to control Question Security today.

Question has a verified solution.

If you are experiencing a similar issue, please ask a related question

Introduction On a scale of 1 to 10, how would you rate our Product? Many of us have answered that question time and time again. But only a few of us have had the pleasure of receiving a stack of the filled out surveys and being asked to do somethi…
When we purchase storage, we typically are advertised storage of 500GB, 1TB, 2TB and so on. However, when you actually install it into your computer, your 500GB HDD will actually show up as 465GB. Why? It has to do with the way people and computers…
Finds all prime numbers in a range requested and places them in a public primes() array. I've demostrated a template size of 30 (2 * 3 * 5) but larger templates can be built such 210  (2 * 3 * 5 * 7) or 2310  (2 * 3 * 5 * 7 * 11). The larger templa…
I've attached the XLSM Excel spreadsheet I used in the video and also text files containing the macros used below. https://filedb.experts-exchange.com/incoming/2017/03_w12/1151775/Permutations.txt https://filedb.experts-exchange.com/incoming/201…
Suggested Courses

810 members asked questions and received personalized solutions in the past 7 days.

Join the community of 500,000 technology professionals and ask your questions.

Join & Ask a Question