# OpenGL Problems with rotations

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Hi, i'm new here. I was looking for a good opengl forum, and i think this would be. I want to rotate the axes first 90 degree around the x axe, then 90 degree around y axe and then 90 degree around z axe. This is easy, and works fine in my program. But if I want to rotate 90 degree around the x axe, then 90 degree around z axe and then 90 degree around y axe, I have a problem. I use this: glRotatef(90,1,0,0); glRotatef(90,0,1,0); glRotatef(90,0,0,1); So the problem is the order in the matrix multiplication (always multiply the y axe matrix before z axe matrix). But I don't know how to do this only using glRotatef. (I have read about quaternions, euler angle, ... , but I want to do, if it is possible, only with glRotatef). Thanks

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Actually, if I'm not much mistaken, you've posted the code for rotations about the z, y and x-axes in that order, rather than the other way around. Since the matrices are post-multiplied, the last operation is essentially performed first on the vertices. That is, in your example, if, before your glRotate calls are performed, the transformation matrix is A, and we call your rotations B, C and D respectively, then the result after making the glRotate calls should be:

ABCD (A multiplied by B multiplied by C multiplied by D)

In matrix mathematics, this results in the operation D "taking effect" first when the matrix is applied to a vertex, followed by C, B and A, in that order.

(A note: this is the result of the matrix mathematics, as I recall, rather than OpenGL doing anything funny with the actual calls.)

PS: The English singular of "axes" is "axis", by the way - one axis, two axes. ^_^

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I know.

So you say that I have to change the order of glRotatef. I have tried and this is not the main problem.

I have a picture to show you the problem, but i don't know how to attach a picture here.

Thanks and thanks for the english correction.

[Edited by - zorro68 on May 7, 2008 8:18:48 AM]

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glRotatef(90,1,0,0);
glRotatef(90,0,1,0);
glRotatef(90,0,0,1);

This is doing what you wanted to do. It rotates X then Y then Z if you want X Z Y

This will do X,Z,Y
glRotatef(90,1,0,0);
glRotatef(90,0,0,1);
glRotatef(90,0,1,0);

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Quote:
 Original post by ThaumaturgeThat is, in your example, if, before your glRotate calls are performed, the transformation matrix is A, and we call your rotations B, C and D respectively, then the result after making the glRotate calls should be:ABCD (A multiplied by B multiplied by C multiplied by D)

No, that's not the order OpenGL uses. If A is the original matrix and you call a matrix function with a matrix B, the resulting matrix is BA, not AB. Your sequence will be DCBA.

Zorro68: I'm not quite sure what your problem is, but are trying to say that you wonder why the resulting rotation is different when you change the order? Or are you experiencing gimbal lock, which is what happens when you rotate so, that rotating around one axis no longer is possible?

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Quote:
Original post by SnotBob
Quote:
 Original post by ThaumaturgeThat is, in your example, if, before your glRotate calls are performed, the transformation matrix is A, and we call your rotations B, C and D respectively, then the result after making the glRotate calls should be:ABCD (A multiplied by B multiplied by C multiplied by D)

No, that's not the order OpenGL uses. If A is the original matrix and you call a matrix function with a matrix B, the resulting matrix is BA, not AB. Your sequence will be DCBA.

Err, well, Thaumaturge isn't wrong but right! OpenGL uses column vectors, and OpenGL does post-multiplication (i.e. on the right side) when glTranslate, glRotate, glScale, or glMultMatrix is invoked. Hence, in an abstract form, the sequence
glAnyTransformation(A);
glAnyTransformation(B);
glAnyTransformation(C);
glVertex(v);
means mathematically
v' := A * B * C * v
Although OpenGL computes that (due to the order matrices are supplied) as
v' := ( ( A * B ) * C ) * v
it is true that the parantheses have no mathematical effect. E.g. the form
v' := A * ( B * ( C * v ) )
will give the identical result! I've chosen this form because it shows best what's "logically" happens: It is C that is applied to v, and B that is applied to the already transformed vertex, and A that is applied to those already twice transformed vertex.

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You made me check the Spec! Serves me right for not refreshing my memory earlier.

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Thank you, Haegarr. ^_^

Zorro, in order to display an image, first upload it to an image host and then include the relevant code in html <img> tags.

If you use ImageShack, then I believe that the code given for an image under "sites" should work (without any additional tags).

Quote:
 Originally posted by MARS_999glRotatef(90,1,0,0);glRotatef(90,0,1,0);glRotatef(90,0,0,1);This is doing what you wanted to do. It rotates X then Y then Z if you want X Z YThis will do X,Z,YglRotatef(90,1,0,0);glRotatef(90,0,0,1);glRotatef(90,0,1,0);

I'm pretty sure that the order is the opposite way around - respectively, I believe that those sets of calls would produce rotations about z, x and then y, and y, z, and then x.

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Thanks to all for a quickly answer.

But I (due to my bad english) don't explain you what is my problem. First at all, i say that i know the order of matrix, and what happend if you change this order. I know the gimbal lock problem, so I'm going to try to explain better:

I have 3 slices, one to rotate in the x axis, other to rotate in the y axis, and other for z axis.
If I move the slices in this order, first x , y and z (the program execute glRotatef(90,1,0,0), glRotatef(90,0,1,0), glRotatef(90,0,0,1);) and all works right.
But if I move the slices in this order, first x, z and y (the program execute the same, so the rotation is bad, I have to change the code).

So if I move the slices in different order, I have to change the code, and I need a code with glRotatef that always work.

I don't know if this is possible or not (with glRotatef) or if I need to implement quaternions or Euler angles or ....

Thanks and I hope you understand my problem.

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What I don't understand is that, if your rotating an object about its own local coordinates, which is what I assume your trying to do, those 3 rotations in any order is going to produce a similar affect? The main difference is going to be which faces are facing forward.

For instance if you have a square rotated about x, then y, then z at 90 degrees a piece, your always going to get the same square back, but by switching the order of rotations a different face will be front facing.

From your picture it looks to me that the rotations are working as they should, if you want it to produce a different result then you need to change the rotations.

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The picture lets me assume you want to rotate around local axes, while your code lets me assume you want to rotate around global axes. Perhaps your problem is to distinuish these 2 cases?

For this you must be aware that a transformation happens ever in its global co-ordinate frame. From your picture it seems me that you want to rotate around local axes. If so, you cannot simply use global axes! Instead, you have to figure out how the desired local axis is currently oriented in global space, and use that as argument to the glRotate function.

E.g. the y axis of your co-ordinate cross is
y = [ 0 1 0 ]T
in global space before any transformation. After a rotation by 90° around (global) x axis
y' := Rgx(90°) * y = [ 0 0 1 ]T
the result will point along the global z axis! See the difference: The global y axis is, of course, still [ 0 1 0 ]T w.r.t. the global space, but the local y axis is now [ 0 0 1 ]T w.r.t. the global space.

Now, rotating by glRotatef(90,0,1,0) around the (global) y axis will result in
yg" := Rgy(90°) * y' = [ 1 0 0 ]T
in a vector pointing along global x axis, while rotating around the "local" y axis using glRotate(90,0,0,1) results in
yl" := Rly(90°) * y' = [ 0 0 1 ]T
(doesn't change anything, because y axis rotated around y axis ;) ). Perhaps I've used a wrong sign anywhere, but the principle should became clear.

Using Euler angles means nothing else to use a specific order of a sequence of 3 glRotate invocations, each one with a defined axis. Several Euler triples exist; in principle your XYZ rotation is one of them. Using a quaternion means nothing more than to use a single glRotate, but with a "arbitrary" axis, i.e. where [ x y z ]T will typically differ all from 0. Although you can compute the belonging matrices by yourself, IMHO it doesn't effectively change anything significant here. So go with glRotate, but clarify which axes you want to rotate around.

[Edited by - haegarr on May 8, 2008 9:26:03 AM]

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haegarr, thanks for your explanation. I understand all you say, but there's something that I don't understand. I explain you:

The program always run this sentences continously:

glRotatef(rotx,1,0,0);
glRotatef(roty,0,1,0);
glRotatef(rotz,0,0,1);

so, as you say, when rotx=90, roty=0 and rotz=0, I have the local y axis pointing out of the screen [0 0 1], along the positive global z axis. Is it ok? (I think so)

Then I change the value of roty=90 (rotx=90,roty=90,rotz=0), so when I compute the three sentences glRotatef, I have to obtain the local y axis looking at the direction of positive x axis [1 0 0]. Is it ok? (I think so)

But I don't get this. If you show my picture you can see that I get a rotation around the global z axis (out the screen) so the local y axis doesn't move, and get the local y axis [0 0 1].

What's happend, or what is what i don't understand?

Pds: I understand that glRotatef always rotate around global axis, as you say.

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I think you still don't consider all aspects. Let's see ...
Still using column vectors and right handed co-ordinate systems:

Quote:
 Original post by zorro68so, as you say, when rotx=90, roty=0 and rotz=0, I have the local y axis pointing out of the screen [0 0 1], along the positive global z axis. Is it ok? (I think so)

Yes, its okay, because the mathematical equivalent is
v' := Rx(90°) * Ry(0°) * Rz(0°) * [ 0 1 0 ]T
== Rx(90°) * I * I * [ 0 1 0 ]T
== Rx(90°) * [ 0 1 0 ]T
== [ 0 0 1 ]T

Quote:
 Original post by zorro68Then I change the value of roty=90 (rotx=90,roty=90,rotz=0), so when I compute the three sentences glRotatef, I have to obtain the local y axis looking at the direction of positive x axis [1 0 0]. Is it ok? (I think so)

Nope. Because the mathematical equivalent is
v' := Rx(90°) * Ry(90°) * Rz(0°) * [ 0 1 0 ]T
== Rx(90°) * Ry(90°) * I * [ 0 1 0 ]T
== Rx(90°) * Ry(90°) * [ 0 1 0 ]T
== Rx(90°) * [ 0 1 0 ]T
== [ 0 0 1 ]T

Keep in mind that (as already written in one of the previous answers) mathematically
A * B * C == ( A * B ) * C == A * ( B * C )
is all the same.

I suggest you: Don't think in code with stuff like this! Think in mathematical terms, and then translate that to code.

[Edited by - haegarr on May 8, 2008 11:14:14 AM]

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I see what you say (I see better with maths).

So if I think in math terms, the solution of my problem is to multiply the three matrix before apply to the scene. (ok?)

But how can I do this with glRotatef function only?

PD: I have to do this in my paintGL() functions that is always running.

Thanks very much.

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Quote:
 Original post by zorro68So if I think in math terms, the solution of my problem is to multiply the three matrix before apply to the scene. (ok?)

Err, not primarily; I'm not sure whether I understood you correctly here, so my following explanation may be superfluous, but what should I do ;) Make yourself clear what happens step-by-step. Assume you use the pseudecode sequence
glRotate(A);
glRotate(B);
glBegin(...);
glVertex3(v);

Now, glLoadIdentity() prepares OpenGL's matrix stack:
M := I

The 1st rotation glRotate(A) then causes
M := I * A
being on the stack.

The 2nd rotation glRotate(B) then causes
M := I * A * B
being on the stack.

Applying that to the vertex glVertex3(v) then means
v' := M * v = I * A * B * v

Now, the sequence of invocations has computed this actually as
( ( I * A ) * B ) * v
but, as already said several times, it is mathematically absolutely the same as
I * ( A * ( B * v ) )
or any other (syntactically correct) arrangement of parantheses!

In other words, using glRotate has definitely build up the matrix as a whole internally before the first vertex is transformed by it, but it plays no role for the result (only for the performance). You could use quaternions, multiply them together, convert the result to a matrix, and use glMultMatrix; whatever ... it'll change nothing.

Unfortunately, I still have no real clue what you are desired to reach. So I tell you again what's going wrong, but am not able to hint in the correct direction. I'm pretty sure that the results you want to reach are possible using glRotate (it must be since glRotate does nothing more than converting into a rotation matrix and multiply that). Could you perhaps illustrate in detail what should happen? And why are you forced to use that specific sequence of rotations?

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I have no clue what he the OP is trying to do, but I have tried the rotations you asked for and found the cube will end up back at the starting point after you move the axes in the order you wanted.

To check this yourself grab a dice, mark all 6 sides as front, back, left, right, bottom, top. Now keep the front facing you to start with, rotate X,Z,Y mind you you need to rotate in a CW direction when you do this. You will be back at the front facing you after all three have moved. Is this what you want?

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If you are trying to implement a rotation user interface, do not use Euler angle.

Using Euler angle is a bad idea.

By the way, this is going to help...
http://www.gamedev.net/community/forums/topic.asp?topic_id=463800

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u can use eular angles no problems, what u shouldnt do though is perform several glRotatef(..) commands in a row as this will often end in gimbal lock
see the matrix faq

http://www.j3d.org/matrix_faq/matrfaq_latest.html

Q33. How do I combine rotation matrices?
Q34. What is Gimbal Lock?

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Quote:
 Original post by zedzu can use eular angles no problems, what u shouldnt do though is perform several glRotatef(..) commands in a row as this will often end in gimbal lock

How are you using Euler angles w/o performing several glRotates in row (or, as an equivalent, compose the matrix by yourself)? Euler angles means ever a composition of consecutive rotations.

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Quote:
 Original post by haegarrIn other words, using glRotate has definitely build up the matrix as a whole internally before the first vertex is transformed by it, but it plays no role for the result (only for the performance). You could use quaternions, multiply them together, convert the result to a matrix, and use glMultMatrix; whatever ... it'll change nothing.

Yes you are right.

Quote:
 Original post by MARS_999To check this yourself grab a dice, mark all 6 sides as front, back, left, right, bottom, top. Now keep the front facing you to start with, rotate X,Z,Y mind you you need to rotate in a CW direction when you do this. You will be back at the front facing you after all three have moved. Is this what you want?

I'm going to explain you what I need?

Quote:
 Original post by ma_htyIf you are trying to implement a rotation user interface, do not use Euler angle.Using Euler angle is a bad idea.

I have read this. By the way, thanks for the gimbal lock discussion.

Quote:

It's a very good summarized in maths.

I thought the rotation problem was a closed theme (in maths and in opengl), but I can see that there's a lots of doubts.

I'm going to explain what I am doing and what is my problem. I'm programming a molecular viewer with opengl. I have seen other molecular viewer and when you click with the mouse into the scene and move the mouse you rotate all the scene (in my case, the molecule). But I have seen that all of them has a problem, if you rotate the scene with the mouse you can see the rotation of the scene and it seems that is all ok. But you are rotating the scene sometimes around global axis and sometime around local axes. This is the same effect that I am having when I use, three times, glRotatef function. Due to the matrix order multiplication, it seems that you are rotating the scene sometime around its local axes and sometime around its global axes. (Show what I'm trying to say in the picture)

What I am trying to program is that when I click and move the mouse (left click + left-right move around x axis, left click + top-down move around y axis, right click + left-right move around z axes, and right click + top-down zoom the scene) or move the slices the scene seems to rotate ALWAYS around the global axes, or seems to rotate ALWAYS around the local axes. But not a mix of them.

I hope you understand me. If not, show me and I'll try again.

Pd: My main problem is that I cannot explain in English like I would like.

Thanks to all of you.

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ATM I think your desire is not 100% possible to be realized (but perhaps someone else from the cummunity will contradict). However, I furthur think you've several more-or-less good options to work around:

(a) Make the user clear that s/he is varying an Euler angle like set-up with the 3 sliders. This solution doesn't touch the math, but is IMHO user unfriendly, since the user shouldn't be burdened with such stuff.

(b) Rotate the molecule by the currently dragged slider always as an incremental rotation around the local axis, but decompose the resulting orientation back into its 3 angles, and adapt the sliders accordingly. This allows you to still show the absolute angles (but only w.r.t. the equivalent rotations of a defined order). DCC packages often offer this way.

(c) Don't use absolute angles but relative ones. I.e. remake the GUI so that pulling a slider's knob changes its belonging angle incrementally around the local axis, but releasing the knob lets it snap back to the neutral position. The molecule, on the other hand, is left as is. So at most one slider knob is outside of 0, and that only temporarily. This simulates a kind of turn table but with sliders, so restricting the kinds of rotation axes (see below).

(d) Drop the usage of slides totally, and go with the tool approach (e.g. turn table like). I.e. manipulate the model directly inside the view, not indirectly and beneath it. Besides the tool idea, this is similar to (c), but also allows for more or less arbitrary rotation axes.

(e) One of (b) or (c) above but using global axes.

Other options may exist, too. I personally would prefer the tool approach. But that is the opinion of a programmer of a 3D DCC editor, not of a chemist :)

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Quote:
 Original post by zorro68...But I have seen that all of them has a problem, if you rotate the scene with the mouse you can see the rotation of the scene and it seems that is all ok. But you are rotating the scene sometimes around global axis and sometime around local axes....

This is a typical defect introduced by mapping Euler angle to the user interface directly. As long as you are using Euler angle honestly, there is no way you can solve this problem.

Why don't you give up Euler angle and use Axis-angle instead? If you are using Axis-angle correctly, there will not be such a problem. Well well, you are probably going to make a lengthy statements to defend your idea (that's what had happened repeatedly whenever there is discussion about Euler angle user interface).

I have been participated in those discussions too many times. Therefore, even if you are decided to defend your idea anyway, I am not going to join your discussion. Instead, I give you the source code of what a correctly designed Axis-angle user interface should look like (i.e. almost the ArcBall).
/////////////////////////// glutTest13.cpp//// Created by Gary Ho, ma_hty@hotmail.com, 2007//#include <stdio.h>#include <stdlib.h>#include <math.h>#include <GL/glut.h>#define PI 3.14159265358979323846ffloat v0[3], v1[3];float mo[16] = { 1,0,0,0, 0,1,0,0, 0,0,1,0, 0,0,0,1 };float clamp( float x, float a, float b );float dot( const float *a, const float *b );float norm( const float *a );void vassign( float *a, float x, float y, float z );void vassign( float *a, const float *b );void cross( float *a, const float *b, const float *c );void normalize( float *a );void display();void mousebutton(int button, int state, int x, int y );void mousemove(int x, int y);void main( int argc, char **argv ){  glutInitDisplayMode( GLUT_DOUBLE | GLUT_RGB | GLUT_DEPTH );  glutInitWindowSize( 512, 512 );  glutCreateWindow( "test09" );  glutDisplayFunc( display );  glutMouseFunc( mousebutton );  glutMotionFunc( mousemove );  glutMainLoop();}void display(){  GLint viewport[4];    glGetIntegerv( GL_VIEWPORT, viewport );  glEnable( GL_DEPTH_TEST );  glEnable( GL_LIGHTING );  glEnable( GL_LIGHT0 );  glClear( GL_COLOR_BUFFER_BIT | GL_DEPTH_BUFFER_BIT );  glMatrixMode(GL_PROJECTION);    glLoadIdentity();    gluPerspective( 45, double(viewport[2])/viewport[3], 0.1, 10 );    glMatrixMode(GL_MODELVIEW);    glLoadIdentity();    gluLookAt( 0,0,3, 0,0,0, 0,1,0 );    glMultMatrixf( mo );    glutSolidTeapot(1);  glutSwapBuffers();}void mousebutton(int button, int state, int x, int y ){  vassign( v0, 2.0*x/512-1, -2.0*y/512+1, 1 );  normalize(v0);}void mousemove(int x, int y){  float axis[3], angle;  vassign( v1, 2.0*x/512-1, -2.0*y/512+1, 1 );  normalize(v1);  if( v0[0]==v1[0] && v0[1]==v1[1] && v0[2]==v1[2] )    return;  cross(axis,v0,v1);  normalize(axis);  angle = acosf( clamp(dot(v0,v1),-1,1) );  vassign( v0, v1 );  glPushMatrix();    glLoadIdentity();    glRotatef( angle*180/PI, axis[0], axis[1], axis[2] );    glMultMatrixf( mo );    glGetFloatv( GL_MODELVIEW_MATRIX, mo );  glPopMatrix();  glutPostRedisplay();}float clamp( float x, float a, float b ){ return x<a ? a : (x<b?x:b); }float dot( const float *a, const float *b ){ return a[0]*b[0]+a[1]*b[1]+a[2]*b[2]; }float norm( const float *a ){ return sqrtf(dot(a,a)); }void vassign( float *a, float x, float y, float z ){ a[0]=x; a[1]=y; a[2]=z; }void vassign( float *a, const float *b ){ a[0]=b[0]; a[1]=b[1]; a[2]=b[2]; }void cross( float *a, const float *b, const float *c ){  a[0] = b[1]*c[2] - c[1]*b[2];  a[1] = -b[0]*c[2] + c[0]*b[2];  a[2] = b[0]*c[1] - c[0]*b[1];}void normalize( float *a ){  float l = norm(a);  a[0]/=l; a[1]/=l; a[2]/=l;}

This user interface is probably the implementation you wanted.

Euler angle? Forget it, it is not going to work. If you insist to use Euler angle, find a rotation matrix in the above program, convert it to Euler angle for storage and then convert the Euler angle to rotation matrix for computation. Just make sure you are not doing any calculation using Euler angle (beside storage), everything will be fine. Is it sound more comforting?

[Edited by - ma_hty on May 9, 2008 3:24:30 PM]

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I 'm learning how to create game by using opengl with c/c++ coding, so here is my fist game. In video description also have game contain in Dropbox. May be I will make it better in future.
Thanks.

• So I've recently started learning some GLSL and now I'm toying with a POM shader. I'm trying to optimize it and notice that it starts having issues at high texture sizes, especially with self-shadowing.
Now I know POM is expensive either way, but would pulling the heightmap out of the normalmap alpha channel and in it's own 8bit texture make doing all those dozens of texture fetches more cheap? Or is everything in the cache aligned to 32bit anyway? I haven't implemented texture compression yet, I think that would help? But regardless, should there be a performance boost from decoupling the heightmap? I could also keep it in a lower resolution than the normalmap if that would improve performance.
Any help is much appreciated, please keep in mind I'm somewhat of a newbie. Thanks!

• Hi,
I'm trying to learn OpenGL through a website and have proceeded until this page of it. The output is a simple triangle. The problem is the complexity.
I have read that page several times and tried to analyse the code but I haven't understood the code properly and completely yet. This is the code: