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# instead of glRotatef build a matrix

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10 replies to this topic

### #1Delfi  Members

Posted 23 April 2011 - 01:40 PM

I'm not very skilled with math, but i'm wondering what does glRotatef do internally?

I have some legacy code which does some math i don't really understand and sends values to glRotatef. I am implementing a physics engine to go with this legacy code and i need a 4x4 matrix instead of that output, i don't really understand how the rotation along a vector glrotatef thing works, but i just need a resulting matrix - which if i multiplied with glMultMatrixf instead of glrotatef would result in same working output.

Thanks.
Projects: Top Down City: http://mathpudding.com/

### #2mrchrismnh  Members

Posted 23 April 2011 - 01:56 PM

I'm not very skilled with math, but i'm wondering what does glRotatef do internally?

I have some legacy code which does some math i don't really understand and sends values to glRotatef. I am implementing a physics engine to go with this legacy code and i need a 4x4 matrix instead of that output, i don't really understand how the rotation along a vector glrotatef thing works, but i just need a resulting matrix - which if i multiplied with glMultMatrixf instead of glrotatef would result in same working output.

Thanks.

Try the Euler matrices for x,y,and z axes; glMultMatrixf(euler_y_mat_with_desired_angle); will get you spin around the y axis, and you can also multiply them together for multi-axis transforms taking care to avoid locks.
"It's like naming him Asskicker Monstertrucktits O'Ninja" -Khaiy

### #3Aks9  Members

Posted 23 April 2011 - 01:57 PM

If you need just a matrix, here it is:

	|	x^2*(1-c)+c	x*y*(1-c)-z*s	x*z*(1-c)+y*s	0	|
R = 	|	y*x*(1-c)+z*s	y^2*(1-c)+c	y*z*(1-c)-x*s	0	|
|	x*z*(1-c)-y*s	y*z*(1-c)+x*s	z^2*(1-c)+c	0	|
|	0		0		0		1	|


[x, y, z] - a vector about which the rotation should be done

c - cos(alpha)

s - sin(alpha)

alpha - rotation angle

### #4Nanoha  Members

Posted 23 April 2011 - 02:15 PM

May be of some use to you:
http://en.wikipedia.org/wiki/Rotation_matrix
Most are 3x3, just add 0, 0, 0, 1 column/row vectors in the 4th colum/row to get it 4x4.
The http://en.wikipedia.org/wiki/Rotation_matrix#General_rotations section shows you euler angles

Interested in Fractals? Check out my App, Fractal Scout, free on the Google Play store.

### #5Delfi  Members

Posted 23 April 2011 - 02:19 PM

Ok thanks, based on that i wrote this function (sorry for pascal syntax):

function CreateGlRotateMatrix(angle, x, y, z: single) : TMatrix;
var
axis: TVector3f;
b, c, ac, s: single;
begin
result:= IdentityHmgMatrix;

c:= cos(angle);
s:= sin(angle);

result[0,0] := (x*x) * (1-c)+c;
result[1,0] := x*y * (1-c)-z*s;
result[2,0] := x*z * (1-c)+y*s;

result[0,1] := y*x * (1-c)+z*s;
result[1,1] := (y*y) * (1-c)+c;
result[2,1] := y*z * (1-c)-x*s;

result[0,2] := x*z * (1-c)-y*s;
result[1,2] := y*z * (1-c)+x*s;
result[2,2] := (z*z) * (1-c)+c;

end;


The results aren't what it's supposed to be:

I replaced: glRotatef(Angle * 180 / Pi, Axis[0], Axis[1], Axis[2]);

With:

rotang:= CreateGlRotateMatrix( Angle * 180 / Pi, Axis[0], Axis[1], Axis[2]);
glMultMatrixf(@rotang[0,0]);

The results make a total mess when objects are rendered, none of rotations look correctly, did i get the matrix array addressing right? in delphi the matrix order are row-col based.
Projects: Top Down City: http://mathpudding.com/

### #6Brother Bob  Moderators

Posted 23 April 2011 - 02:20 PM

[x, y, z] - a vector about which the rotation should be done

A normalized vector. I guess you knew that already, but just making sure everyone knows it as well .

### #7Aks9  Members

Posted 23 April 2011 - 02:57 PM

A normalized vector. I guess you knew that already, but just making sure everyone knows it as well .

Yes, I've forgotten to say that. glRotatef auto-normalizes that vector. In our code, we should take care of normalization.

Also, be aware that GL assumes column-major order of matrices. If normalization doesn't help alone, transpose your matrix.

### #8Delfi  Members

Posted 23 April 2011 - 03:08 PM

Ok, i tried normalizing the vector & transposing / not transposing but still no luck, here's new function i have:

function CreateGlRotateMatrix(angle, x, y, z: single) : TMatrix;
var
axis: TVector3f;
b, c, ac, s: single;
invLen : Single;
begin

invLen:= RSqrt(x * x + y * y + z * z);
x:= x * invLen;
y:= y * invLen;
z:= z * invLen;

result:= IdentityHmgMatrix;

c:= cos(angle);
s:= sin(angle);

result[0,0] := (x*x) * (1-c)+c;
result[1,0] := x*y * (1-c)-z*s;
result[2,0] := x*z * (1-c)+y*s;

result[0,1] := y*x * (1-c)+z*s;
result[1,1] := (y*y) * (1-c)+c;
result[2,1] := y*z * (1-c)-x*s;

result[0,2] := x*z * (1-c)-y*s;
result[1,2] := y*z * (1-c)+x*s;
result[2,2] := (z*z) * (1-c)+c;

//  vectorgeometry.TransposeMatrix(result);

end;


I can show some screenshots of the working (glrotatef) & non-working results (CreateGlRotateMatrix) if that would help in any way clear the situation on what's wrong with it.
Projects: Top Down City: http://mathpudding.com/

### #9Jan-Lieuwe  Members

Posted 23 April 2011 - 03:10 PM

	c:= cos(angle);
s:= sin(angle);


The results aren't what it's supposed to be:

I replaced: glRotatef(Angle * 180 / Pi, Axis[0], Axis[1], Axis[2]);

With:

rotang:= CreateGlRotateMatrix( Angle * 180 / Pi, Axis[0], Axis[1], Axis[2]);
glMultMatrixf(@rotang[0,0]);

The results make a total mess when objects are rendered, none of rotations look correctly, did i get the matrix array addressing right? in delphi the matrix order are row-col based.

cos/sin take radians while glRotatef takes degrees. So you don't need the radians to degrees conversion (* 180 / PI) when calling your own function.

### #10Aks9  Members

Posted 23 April 2011 - 03:22 PM

The results aren't what it's supposed to be:
I replaced: glRotatef(Angle * 180 / Pi, Axis[0], Axis[1], Axis[2]);

With:
rotang:= CreateGlRotateMatrix( Angle * 180 / Pi, Axis[0], Axis[1], Axis[2]);

Hey, I just noticed the way you pass angles... glRotatef() takes angle in degrees not in radians!!!

Previous two lines are not identical, because the angles are not the same.

### #11Delfi  Members

Posted 23 April 2011 - 03:50 PM

Ok, thanks to everyone, here's the final working version:

function CreateGlRotateMatrix(angle, x, y, z: single) : TMatrix;
var
axis: TVector3f;
b, c, ac, s: single;
invLen : Single;
begin

invLen:= RSqrt(x * x + y * y + z * z);
x:= x * invLen;
y:= y * invLen;
z:= z * invLen;

result:= IdentityHmgMatrix;

c:= cos(angle);
s:= sin(angle);

result[0,0] := (x*x) * (1-c)+c;
result[1,0] := x*y * (1-c)-z*s;
result[2,0] := x*z * (1-c)+y*s;

result[0,1] := y*x * (1-c)+z*s;
result[1,1] := (y*y) * (1-c)+c;
result[2,1] := y*z * (1-c)-x*s;

result[0,2] := x*z * (1-c)-y*s;
result[1,2] := y*z * (1-c)+x*s;
result[2,2] := (z*z) * (1-c)+c;

end;


This finally matches the game's map files to build a proper matrix, it uses this with some "odd" quaternion conversion routine, which i couldn't reproduce with any other quaternion to matrix algorythm on the internet:

	// preprocess quarternion rotations
X := rx;
Y := ry;
Z := rz;
W := -rw;
S := Sqrt(1.0 - W * W);

// divide by zero
if not (S = 0) then
begin
Axis[0] := X / S;
Axis[1] := Y / S;
Axis[2] := Z / S;
Angle   := 2 * geometry.ArcCos(W);

if not (Angle = 0) then begin

rotang:= CreateGlRotateMatrix( Angle * 180 / Pi, Axis[0], Axis[1], Axis[2]);
glMultMatrixf(@rotang[0,0]);

//glRotatef(Angle * 180 / Pi, Axis[0], Axis[1], Axis[2]);

end;
end;


But this only works on game file quaternions. If i use this on the game's quaternions from the memory i get some strange results, i'll post that as another question if i can't figure it out soon :S

Edited by Delfi, 23 April 2011 - 03:53 PM.

Projects: Top Down City: http://mathpudding.com/

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Guest, the last post of this topic is over 60 days old and at this point you may not reply in this topic. If you wish to continue this conversation start a new topic.