Question

How do a find quaternion rotation from local and world coordinate systems?

Asked by: ImNotJimboJones

I am working with OpenGL, in the planning stages of a generic class describing 3D objects. I am trying to design the orientation control and have run into the following issue...

I'm not sure yet whether I will physically store an object's orientation based on rotation, or forward/up vectors, but in either case, I want to be able to get and set the object's orientation in terms of both.

I can't seem to figure out how to find quaternion (or axis/angle or Euler angle) rotation given forward/up vectors.

Regardless of chosen base reference, I will need this conversion to implement rotational get/set as well as a pseudo-gluLookAt equivalent. If I store orientation based on forward/up vector, I will need to convert during setOrientation(Quaternion quat) and if I store orientation based on rotation, I will need to convert in order to reference local axes (the forward vector, etc).

I've looked at the mesa source for gluLookAt, but it was of little help. The implementation converts the forward/up vectors directly to a transformation matrix. I have, however, included it as reference (maybe someone knows how to get a quaternion from gluLookAt's resulting matrix?).

thanks in advance for any insight.

void GLAPIENTRY
gluLookAt(GLdouble eyex, GLdouble eyey, GLdouble eyez,
	  GLdouble centerx, GLdouble centery, GLdouble centerz,
	  GLdouble upx, GLdouble upy, GLdouble upz)
{
   GLdouble m[16];
   GLdouble x[3], y[3], z[3];
   GLdouble mag;
 
   /* Make rotation matrix */
 
   /* Z vector */
   z[0] = eyex - centerx;
   z[1] = eyey - centery;
   z[2] = eyez - centerz;
   mag = sqrt(z[0] * z[0] + z[1] * z[1] + z[2] * z[2]);
   if (mag) {			/* mpichler, 19950515 */
      z[0] /= mag;
      z[1] /= mag;
      z[2] /= mag;
   }
 
   /* Y vector */
   y[0] = upx;
   y[1] = upy;
   y[2] = upz;
 
   /* X vector = Y cross Z */
   x[0] = y[1] * z[2] - y[2] * z[1];
   x[1] = -y[0] * z[2] + y[2] * z[0];
   x[2] = y[0] * z[1] - y[1] * z[0];
 
   /* Recompute Y = Z cross X */
   y[0] = z[1] * x[2] - z[2] * x[1];
   y[1] = -z[0] * x[2] + z[2] * x[0];
   y[2] = z[0] * x[1] - z[1] * x[0];
 
   /* mpichler, 19950515 */
   /* cross product gives area of parallelogram, which is < 1.0 for
    * non-perpendicular unit-length vectors; so normalize x, y here
    */
 
   mag = sqrt(x[0] * x[0] + x[1] * x[1] + x[2] * x[2]);
   if (mag) {
      x[0] /= mag;
      x[1] /= mag;
      x[2] /= mag;
   }
 
   mag = sqrt(y[0] * y[0] + y[1] * y[1] + y[2] * y[2]);
   if (mag) {
      y[0] /= mag;
      y[1] /= mag;
      y[2] /= mag;
   }
 
#define M(row,col)  m[col*4+row]
   M(0, 0) = x[0];
   M(0, 1) = x[1];
   M(0, 2) = x[2];
   M(0, 3) = 0.0;
   M(1, 0) = y[0];
   M(1, 1) = y[1];
   M(1, 2) = y[2];
   M(1, 3) = 0.0;
   M(2, 0) = z[0];
   M(2, 1) = z[1];
   M(2, 2) = z[2];
   M(2, 3) = 0.0;
   M(3, 0) = 0.0;
   M(3, 1) = 0.0;
   M(3, 2) = 0.0;
   M(3, 3) = 1.0;
#undef M
   glMultMatrixd(m);
 
   /* Translate Eye to Origin */
   glTranslated(-eyex, -eyey, -eyez);
 
}

1:
2:
3:
4:
5:
6:
7:
8:
9:
10:
11:
12:
13:
14:
15:
16:
17:
18:
19:
20:
21:
22:
23:
24:
25:
26:
27:
28:
29:
30:
31:
32:
33:
34:
35:
36:
37:
38:
39:
40:
41:
42:
43:
44:
45:
46:
47:
48:
49:
50:
51:
52:
53:
54:
55:
56:
57:
58:
59:
60:
61:
62:
63:
64:
65:
66:
67:
68:
69:
70:
71:
72:
73:
74:
75:
76:
77:
78:
79:
80:

Select all Open in new window

This Question has been solved and asker verified All Experts Exchange premium technology solutions are available to subscription members.

Subscribe now for full access to Experts Exchange and get

Instant Access to this Solution

Plus...

30 Day FREE access, no risk, no obligation
Collaborate with the world's top tech experts
Unlimited access to our exclusive solution database
Never be left without tech help again

Subscribe Now

Asked On: 2009-08-21 at 12:59:57ID24672530
Tags: quaternion lookat orientation
,; rotation vector coordinate
,; quaternion
,; opengl
,; orientation
,; glulookat
,; rotation
Topics: 3D Game Programming
,; OpenGL Graphics & Game Programming
,; Algorithms
Participating Experts: 2
Points: 500
Comments: 8

Trusted by hundreds of thousands everyday for fast, accurate and reliable tech support.

"The time we save is the biggest benefit of Experts Exchange to Warner Bros. What could take multiple guys 2 hours or more each to find is accessed in around 15 minutes on Experts Exchange." Mike Kapnisakis, Warner Bros.
"Our team likes having a resource that is more secure than just using Google and most experts using this service really know their stuff. It's nice to look here first versus using Google." Dayna Sellner, Lockheed Martin
"Anytime that I've been stumped with a problem, 9 out of 10 times Experts Exchange has either the accepted solution or an open discussion of the potential solution to the problem." Kenny Red, eBay Inc.

See what Experts Exchange can do for you.

Got a question?

We've got the answer.

Experts Exchange has been collecting answers to technology questions since 1996…3 million and counting! If you have a question, chances are we already have your answer.

Screenshot of Experts Exchange Knowledgebase

Need individual assistance?

Our experts are ready to help.

If you can't find the exact answer you're looking for, ask our exclusive community of 50,000 experts. You’ll get a personalized answer from a trusted professional.

Want to learn from the best?

Read articles from industry experts.

Thousands of free tech tips, tricks, how-to’s and tutorials are available in our peer reviewed articles section. See for yourself how smart our experts are, no login required.

Working on a long term project?

Store your work and research.

Save solutions to your questions, answers you’ve discovered through searching plus helpful articles in your personal knowledgebase for easy future access.

Access the answers to your technology questions today.

Subscribe Now

30-day free trial. Register in 60 seconds.

What Makes Experts Exchange Unique?

Members of the expert community talk about why the experience at Experts Exchange is different than what you will find anywhere else.

Trusted by the world's most respected brands.

image of each brand's logo

Faithfully serving IT professionals since 1996.

Experts Exchange Logo

Try it out and discover for yourself.

Subscribe Now

30-day free trial. Register in 60 seconds.

Free Tech Articles

WARNING: 5 Reasons why you should NEVER fix a computer for free.
It is in our nature to love the puzzle. We are obsessed. The lot of us. We love puzzles. We love the challenge. We thrive on finding the answer. We hate disarray. It bothers us deep in our soul. W...
SCCM OSD Basic troubleshooting
SCCM 2007 OSD is a fantastic way to deploy operating systems, however, like most things SCCM issues can sometimes be difficult to resolve due to the sheer volume of logs to sift through and the dispe...
Migrate Small Business Server 2003 to Exchange 2010 and Windows 2008 R2
This guide is intended to provide step by step instructions on how to migrate from Small Business Server 2003 to Windows 2008 R2 with Exchange 2010. For this migration to work you will need the fo...
Create a Win7 Gadget
This article shows you how to create a simple "Gadget" -- a sort of mini-application supported by Windows 7 and Vista. Gadgets can be dropped anywhere on the desktop to provide instant information, ...
Outlook continually prompting for username and password
There have been a lot of questions recently regarding Outlook prompting for a username and password whilst using Exchange 2007. There are a few reasons why this would happen and I will try to cover t...
Backup Exchange 2010 Information Store using Windows Backup
There seems to be quite a lot of confusion around the ability to backup Exchange 2010 using the built in Windows Backup feature. This stems from the omission of this feature prior to Exchange 2007 s...

Cloud Class Webinars

Avoiding Bugs in Microsoft Access
Alison Balter takes and in-depth look at avoiding bugs in Access. In this webinar you will learn about using the immediate window to debug your applications, invoking the debugger, using breakpoints to troubleshoot, stepping through code, setting the next statement to execute, ...
Top 10 Best New Features in Visio 2010
Scott Helmers gives live demonstrations of the top 10 new features in Visio 2010. This webinar will teach you how to create compelling diagrams by adding shapes to the page with a single click, linking the shapes in a diagram to data in Excel (or SQL Server, or SharePoint), ...
IT Consultant Business Secrets Revealed
Michael Munger, Experts Exchange tech pro and IT consultant, pulls back the curtain on his very successful businesses and answers question on every IT consultant and business owner should know about. He shares secrets on what he did to solve the 5 most common problems in IT, ...
Disaster Recovery and Business Continuity
Quest CTO, Mike Billon, gives an overview of the steps involved in building a dunamic disaster recovery plan. Through case studies and an examination of software/hardware tooles for monitoring and testing, you'll gain a better understandin of where you are, where you want ...
Organize Your Visio Diagrams with Containers and Lists
Scott Helmers uses cross functional flowcharts, wireframe diagrams, data graphic legends and seating charts to teach you: how to ustilize all three new structured diagram components in Visio 2010, the best practices for organizeing shapes in previous version of Visio, how to organize ...
How to Us Objects, Properties, Events and Methods in Microsoft Access
Alison Dalter gives an in-depbth look at objects, properties, events and methods in Microsoft Access. In this webinar you will learn about using the object browser, referring to objects, working with properties and methods, working with object variables, understanding the ...

Watch More

Join the Community

Give a Little. Get a Lot.

Join the community of experts here and help other tech pros by answering question in your area of expertise. You can earn FREE access to all Experts Exchange's premium features and resources.

Join the Community

Answers

by: ikeworkPosted on 2009-08-22 at 02:56:42ID: 25158068

Hi ImNotJimboJones,

If you have the forward/up vectors, then you have practically the 3x3 orientation matrix, you just need the cross-product of both, then you have the right vector

right-vector -> 1. column
up-vector -> 2. column
forward-vector -> 3. column

This page is about the conversion:

http://www.euclideanspace.com/maths/geometry/rotations/conversions/matrixToQuaternion/index.htm

Below is the source for the matrix-quaternion conversion:

ike

void gqFromM33( quaternion qResult, matrix33 const m )
{
    real tr,s;
    real q[4];
    int i,j,k;
 
    int nxt[3] = { 1, 2, 0 };
 
    tr = m[0][0] + m[1][1] + m[2][2];
 
    // check the diagonal
    if( tr > REAL(0.0) )
    {
        s = gsqrt( tr + REAL(1.0) );
 
        qResult[3] = s * REAL(0.5);
 
        s = REAL(0.5) / s;
 
        qResult[0] = ( m[1][2] - m[2][1] ) * s;
        qResult[1] = ( m[2][0] - m[0][2] ) * s;
        qResult[2] = ( m[0][1] - m[1][0] ) * s;
    }
    else
    {
        // diagonal is negative
 
        i = 0;
 
        if( m[1][1] > m[0][0] ) i = 1;
        if( m[2][2] > m[i][i] ) i = 2;
 
        j = nxt[i];
        k = nxt[j];
 
        s = gsqrt( ( m[i][i] - ( m[j][j] + m[k][k] ) ) + REAL(1.0) );
 
        q[i] = s * REAL(0.5);
 
        if( s != REAL(0.0) ) s = REAL(0.5) / s;
 
        q[3] = ( m[j][k] - m[k][j] ) * s;
        q[j] = ( m[i][j] + m[j][i] ) * s;
        q[k] = ( m[i][k] + m[k][i] ) * s;
 
        qResult[0] = q[0];
        qResult[1] = q[1];
        qResult[2] = q[2];
        qResult[3] = q[3];
    }
}

1:
2:
3:
4:
5:
6:
7:
8:
9:
10:
11:
12:
13:
14:
15:
16:
17:
18:
19:
20:
21:
22:
23:
24:
25:
26:
27:
28:
29:
30:
31:
32:
33:
34:
35:
36:
37:
38:
39:
40:
41:
42:
43:
44:
45:
46:
47:
48:
49:
50:
51:

Select all Open in new window

by: InteractiveMindPosted on 2009-08-22 at 03:13:26ID: 25158100

Is this not what you're trying to achieve?
http://www.gamedev.net/reference/programming/features/quatcam/page3.asp

I'm not absolutely clear what you mean by "find quaternion (or axis/angle or Euler angle) rotation given forward/up vectors". Do you mean that you're given the forward/up vectors of the camera, and you wish to rotate the scene using quaternions (so as to give the effect that the camera is at an angle)?

by: InteractiveMindPosted on 2009-08-22 at 03:14:15ID: 25158101

Sorry, looks like ike understands it.

by: ikeworkPosted on 2009-08-22 at 03:50:24ID: 25158203

>> I am working with OpenGL, in the planning stages of a generic class describing 3D objects.
>> I'm not sure yet whether I will physically store an object's orientation based on rotation, or forward/up vectors, but in either case

I recommend you to store a 4x4 matrix in each of your 3D objects. Then you have the orientation/scaling and translation (position) of your objects in a generic way and well defined in terms of math. You can pass that matrix to OpenGL before rendering your object, its just one call of glMultMatrix.

http://www.opengl.org/sdk/docs/man/xhtml/glMultMatrix.xml

I would not recommend to implement the conversions from axis-angle/euler/quaternions in the setter/getter-methods of your 3D-Object-class. The conversion/multiplication should be done in a math-library, that supports this classes. Then you just pass it to your 3D object-class and the math-library does its work, something like this:

void Your3DObject::rotate(const quaternion &q)
{
// rotate the objects matrix by this quaternion
this->transform = this->transform * q;
}

Tell us if you need more help on designing such a class and math-library :)

ike

by: ikeworkPosted on 2009-08-22 at 04:04:25ID: 25158237

>> Sorry, looks like ike understands it.

No prob IM :) As I understand it, its about how to design the 3D-objects (camera/meshes) and what datatypes actually to store in them and how to manipulate the 3D attributes of such objects, via euler-angles, quaternions, matrices etc.. But lets see what ImNotJimboJones thinks about it

by: ImNotJimboJonesPosted on 2009-08-29 at 20:21:10ID: 25216251

Sorry for the delayed response... thanks everfor the input.

>> I would not recommend to implement the conversions from axis-angle/euler/quaternions in the setter/getter-methods of your 3D-Object-class...

I have already started working on a math lib to contain all needed computations and conversions. That is how I came to realize my question :)

>> I recommend you to store a 4x4 matrix in each of your 3D objects.

I do plan on applying transformations with glMultMatrix. Do you think I should store only a 4x4 matrix for each object and only make conversions (to extract rotation, location, etc) when requested? I was originally thinking that I would store a vertex location, a quaternion orientation, and a 4x4 transformation matrix that would be updated whenever location or orientation were.

As for my original question:
I am going to look through the code that you posted for matrix -> quaternion and see if I can combine that with the GluLookAt code to create a streamlined function. I'll repost when I get things working (or fail miserably haha).

by: ImNotJimboJonesPosted on 2009-08-29 at 22:30:04ID: 25216446

I created and tested my function. Everything works great. I'd still like to get your opinion about my previous post, however.

by: ikeworkPosted on 2009-08-30 at 02:03:26ID: 25216846

>> Do you think I should store only a 4x4 matrix for each object and only make conversions (to extract rotation, location, etc) when requested?

Definetely I would store the 4x4 matrix. Probably it will be useful to store the inverse 4x4 matrix too, to transform objects like rays or bounding boxes into the space of the 3D-Object, to make hit tests or something.

I would cache the orientation, only if I come to a point, where I really need it very often, but for starters I wouldnt store it.
Usually you dont need the orientation seperated that often.
However, if you need the orientation, I would rather extract a 3x3 matrix from the 4x4 matrix, there is actually the rotation stored and its just 3 memcpy's.
Quaternion math is usually not as efficent as matrix-multiplications.
However, Q's are very useful for rotation-interpolation, i.e. for camera paths or skeleton-animation and they use less memory. But nowadays memory is quite cheap, so that souldnt be an issue.

So if you need the orientation from your 3D-object seperated, you better extract the 3x3 matrix, rather than to compute euler-angles or quaternions.
Btw. extracting the position is very easy too, just copy the last column of the 4x4 matrix, it is the position.

Would be very interesting to hear from you how it is going :)

20120131-EE-VQP-002

3 Ways to Join

30-Day Free Trial

For individual users
Instant access to solutions
Ask your tech questions
Start your 30-day Free Trial

Business Accounts

Perfect for organizations
Multiple users
Save over 36%
Create a Business Account

Answer for Membership

Earn free access
Showcase your knowledge
No credit card required
Sign Up to Answer

The Experts

98% positive feedback on 31,087 answers since March 2000. angeliii is a Microsoft Most Valuable Professional for his work with MS SQL Server & Develoment.

He has also proven his knowledge of Visual Basic Programming, PHP Scripting and Oracle Databases.

The Experts

97% positive feedback on 10,752 answers since July 2000. lrmoore has more than 18 years experience in the networking industry.

The six-time Mircosoft MVPs specialties include firewalls, virtual private networking, and network management.

Testimonials

"...and excellent source for support... Kind of like having your very own IT dept." Electriciansnet

Testimonials

"I was apprehensive at signing up at first. However... it has already made my life as an IT administrator much easier." JaCrews

Testimonials

"WOW! You guys have great, active, and knowledgeable people on here." moore50

Business Clients

In the Press

"If you’ve got a question... Experts Exchange can supply an answer.”

In the Press

"...an invaluable aid for both IT professionals and those who require tech support."

In the Press

"where IT professionals provide quick answers on just about any topic"

Business Account Plans

Loading Advertisement...

Question

How do a find quaternion rotation from local and world coordinate systems?

Subscribe now for full access to Experts Exchange and get

Instant Access to this Solution

Trusted by hundreds of thousands everyday for fast, accurate and reliable tech support.

See what Experts Exchange can do for you.

Got a question?

We've got the answer.

Need individual assistance?

Our experts are ready to help.

Want to learn from the best?

Read articles from industry experts.

Working on a long term project?

Store your work and research.

What Makes Experts Exchange Unique?

Trusted by the world's most respected brands.

Faithfully serving IT professionals since 1996.

Related Solutions

Free Tech Articles

Cloud Class Webinars

Join the Community

Give a Little. Get a Lot.

Answers

3 Ways to Join

The Experts

The Experts

Testimonials

Testimonials

Testimonials

Business Clients

Business Clients

In the Press

In the Press

In the Press