BorlandTalk.com Borland discussion newsgroups   Archives   FAQ   Search   Memberlist   Usergroups   Register   Profile   Log in to check your private messages   Log in  How does OpenGL work with matrices under the hood?          BorlandTalk.com Forum Index -> Delphi Graphics View previous topic :: View next topic   Author Message Paul Nicholls Guest Posted: Fri Apr 30, 2004 3:23 am    Post subject: How does OpenGL work with matrices under the hood? Hi all, pardon me if this is a silly question (tm)....<G> when using OpenGL and I want to roate some object (in object coordinates) and then translate it to some position I do this type of thing: glLoadIdentity; .... glTranslatef(ObjectX,ObjectY,ObjectZ) glRotatef(ObjectAngle,0,1,0); DrawObject. I am used to doing it this way, but why is it necessary for the translation to come before the rotation in the code? Mathematically the rotation should be done before the translation, right? Does OpenGL do something similar to this in the background? (ignore exact code, only look at what it is doing) ModelMatrix: TMatrix3d; ModelMatrixOperationsIndex: Integer; ModelMatrixOperationsStack: array[0..MaxModelMatrixOperations - 1] of TMatrix3d; procedure glRotatef(Angle,ax,ay,az: Single); overload; begin ModelMatrixOperationsStack[ModelMatrixOperationsIndex] := ArbitaryAxisRotationMatrix(Vector3d(ax,ay,az),Angle); Inc(ModelMatrixOperationsIndex); end; procedure glTranslatef(tx,ty,tz: Single); begin ModelMatrixOperationsStack[ModelMatrixOperationsIndex] := TranslationMatrix3d(tx,ty,tz); Inc(ModelMatrixOperationsIndex); end; procedure glBegin(...); begin while(ModelMatrixOperationsIndex> 0)do begin Dec(ModelMatrixOperationsIndex); ModelMatrix := MatrixMultiply(ModelMatrix,ModelMatrixOperationsStack[ModelMatrixOperationsI ndex]); end; ... end; procedure glVertex3f(x,y,z: Single); begin NewVertex := TransformVector(Vector3f(x,y,z),ModelMatrix); ... end; I am trying to understand why one needs to specify the matrix operations (rotation, translation, etc) around the other way... I am itching to know :) Thanks in advance, Paul Nicholls (Delphi 5/6 Professional) "See No Evil, Hear No Evil, EMail No Evil !" - Paul Nicholls [email]paul-nicholls (AT) hotmail (DOT) com[/email] Replace '-' with '_' to reply Back to top Paul Nicholls Guest Posted: Fri Apr 30, 2004 6:37 am    Post subject: Re: How does OpenGL work with matrices under the hood? "Soós Árpád" <sarpad (AT) webmail (DOT) hu> wrote Quote: I am used to doing it this way, but why is it necessary for the translation to come before the rotation in the code? It is not necessary. The different transformation orders mean different transformations. No magic here, just imagine it: rotation is always rotation around the origin. If you rotate first, it rotates the object around its center (assuming your object center is the origin locally) and then translates it to a new position. If you translate it first, the rotation will move it on a larger arc. As an example if you make an animation and rotate first, your object will spinning in a fixed place around its center, if you translate first, it will spin around a different point (determined by the translation amount), orbiting it. Regards Árpád I know that matrix transformations are NOT cummulative, it depends on the order they are done in, as you say. :) OK, lets talk about spinning an object in a fixed place around it's centre... It appears OpenGL wants the translation THEN the rotation instead of what I would have thought was needed, ie. the rotation THEN the translation... ie. glTranslatef(...); translation FIRST glRotatef(...); rotation SECOND instead of glRotatef(...); rotation FIRST glTranslatef(...); translation SECOND Can you explain why this appears so when doing the code? Cheers, Paul. Back to top Rene Tschaggelar Guest Posted: Fri Apr 30, 2004 6:39 am    Post subject: Re: How does OpenGL work with matrices under the hood? Paul Nicholls wrote: Quote: Hi all, pardon me if this is a silly question (tm).... when using OpenGL and I want to roate some object (in object coordinates) and then translate it to some position I do this type of thing: glLoadIdentity; ... glTranslatef(ObjectX,ObjectY,ObjectZ) glRotatef(ObjectAngle,0,1,0); DrawObject. I am used to doing it this way, but why is it necessary for the translation to come before the rotation in the code? Mathematically the rotation should be done before the translation, right? Depends. When an object is rotated, it first has to be moved to the origin, then it is rotated, and afterwards it is moved back. This because a rotation is always around the origin. Rene -- Ing.Buro R.Tschaggelar http://www.ibrtses.com Your newsgroups @ http://www.talkto.net Back to top Paul Nicholls Guest Posted: Fri Apr 30, 2004 7:04 am    Post subject: Re: How does OpenGL work with matrices under the hood? "Rene Tschaggelar" <ee123123wqe12 (AT) sd242323 (DOT) com> wrote Quote: Paul Nicholls wrote: Hi all, pardon me if this is a silly question (tm).... when using OpenGL and I want to roate some object (in object coordinates) and then translate it to some position I do this type of thing: glLoadIdentity; ... glTranslatef(ObjectX,ObjectY,ObjectZ) glRotatef(ObjectAngle,0,1,0); DrawObject. I am used to doing it this way, but why is it necessary for the translation to come before the rotation in the code? Mathematically the rotation should be done before the translation, right? Depends. When an object is rotated, it first has to be moved to the origin, then it is rotated, and afterwards it is moved back. This because a rotation is always around the origin. Rene If the object is already at the origin, how come I have to specify the translation THEN the rotation when using OpenGL? Is OpenGL putting the individual matricies on a stack, and then popping them off and multiplying one at a time with the current model matrix? This would explain why OpenGL seems to want the transformations specified in the opposite order... Back to top Paul Nicholls Guest Posted: Fri Apr 30, 2004 7:05 am    Post subject: Re: How does OpenGL work with matrices under the hood? "Soós Árpád" <sarpad (AT) webmail (DOT) hu> wrote Quote: It appears OpenGL wants the translation THEN the rotation instead of what I would have thought was needed, ie. the rotation THEN the translation... Transformations are not executed separately but a single composite transformation matrix is created using them. This is calculated by multiplying them. You must specify the individual transformation matrices in the order of multiplication which is opposite of the order they are applied. So I am correct in thinking that OpenGL needs the transformations specified in the opposite order what they will be applied? Back to top Alan Garny Guest Posted: Fri Apr 30, 2004 9:06 am    Post subject: Re: How does OpenGL work with matrices under the hood? "Paul Nicholls" <.> wrote Quote: I am trying to understand why one needs to specify the matrix operations (rotation, translation, etc) around the other way... You have kind of answered your own question with the code snippet you provided us. Indeed, you first translated, then rotated, and *finally* drew your object. Can't you see the pattern here? Things are coded in reverse order... Think about it... Now as to the reason, I must confess I don't know or can't remember it, but I wouldn't be surprised if it is mentioned somewhere in the Red Book... Alan. Back to top John Guest Posted: Fri Apr 30, 2004 10:49 am    Post subject: Re: How does OpenGL work with matrices under the hood? "Paul Nicholls" <.> wrote Quote: Mathematically the rotation should be done before the translation, right? Remember, though, you are constructing an operator, not applying to the object. Let's say A, B and C are operators, V is a vector. What's the new vector if we apply first operation A, _then_ B, _then_ C? It's: C * (B * (A* V)) Which means (since our operators are transitive but non-commutative): (C*B*A)*V So to construct the combined operator, you multiply them in reverse to the order that the vector would experience. Back to top Paul Nicholls Guest Posted: Sun May 02, 2004 11:04 pm    Post subject: Re: How does OpenGL work with matrices under the hood? "Soós Árpád" <sarpad (AT) webmail (DOT) hu> wrote Quote: So I am correct in thinking that OpenGL needs the transformations specified in the opposite order what they will be applied? Yes. See: http://www.dcc.unicamp.br/~lmarcos/courses/mc603/redbook/chapter03.html#name2 Thanks, that was very helpful :-) Cheers, Paul. Back to top Paul Nicholls Guest Posted: Sun May 02, 2004 11:05 pm    Post subject: Re: How does OpenGL work with matrices under the hood? "John" <John (AT) home (DOT) com> wrote Quote: "Paul Nicholls" <.> wrote Mathematically the rotation should be done before the translation, right? Remember, though, you are constructing an operator, not applying to the object. Let's say A, B and C are operators, V is a vector. What's the new vector if we apply first operation A, _then_ B, _then_ C? It's: C * (B * (A* V)) Which means (since our operators are transitive but non-commutative): (C*B*A)*V So to construct the combined operator, you multiply them in reverse to the order that the vector would experience. Ok, I think this makes sense now :-) Cheers, Paul. Back to top Paul Nicholls Guest Posted: Sun May 02, 2004 11:06 pm    Post subject: Re: How does OpenGL work with matrices under the hood? "Alan Garny" <someone (AT) somewhere (DOT) com> wrote Quote: "Paul Nicholls" <.> wrote I am trying to understand why one needs to specify the matrix operations (rotation, translation, etc) around the other way... You have kind of answered your own question with the code snippet you provided us. Indeed, you first translated, then rotated, and *finally* drew your object. Can't you see the pattern here? Things are coded in reverse order... Think about it... Now as to the reason, I must confess I don't know or can't remember it, but I wouldn't be surprised if it is mentioned somewhere in the Red Book... Alan. Thanks Alan, after looking at a link that was provided it does indeed say in the Red Book :-) Cheers, Paul. 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