RE: [Algorithms] Rotation about arbitrary axis

[Matthew D. <MD...@ac...>]

Hi Pierre,

I wrote some code for just that purpose not so long ago:

	inline void matrix::SetRotation (const vector &axis, f32 radians)
	{
		f32 s, c, t;
		Maths_SinCos(radians,s,c);			// Calculate
sin and cosine
		t = 1 - c;

		assert(axis.IsValid());

		f32 txy = t*(axis.x * axis.y);
		f32 tyz = t*(axis.y * axis.z);
		f32 txz = t*(axis.x * axis.z);

		f32 xs = axis.x * s;
		f32 ys = axis.y * s;
		f32 zs = axis.z * s;

		_14 = _24 = _34 = _41 = _42 = _43 = 0.0f;
		_44 = 1.0f;

		_11 = t*(axis.x*axis.x) + c;
		_22 = t*(axis.y*axis.y) + c;
		_33 = t*(axis.z*axis.z) + c;

		_12 = txy + zs;
		_13 = txz - ys;
		_21 = txy - zs;
		_23 = tyz + xs;
		_31 = txz + ys;
		_32 = tyz - xs;
	}

I'm sure you can adapt that code.  For 4x4 matrices just extend it:

A B C     A B C 0
D E F     D E F 0
G H I     G H I 0
          0 0 0 1

Best regards,
Matt.
 

> -----Original Message-----
> From: Pierre Terdiman [mailto:p.t...@wa...]
> Sent: Monday, August 21, 2000 17:58
> To: gda...@li...
> Subject: [Algorithms] Rotation about arbitrary axis
> 
> 
> Hi,
> 
> Since I needed a piece of code to do that I searched the web 
> and found:
> http://www.iuk.tu-harburg.de/hypgraph/modeling/mod_tran/3drota.htm
> 
> I used the final matrix at the bottom of the page, but it 
> seems to fail when
> the arbitrary axis actually is the Z axis. The third column 
> gets erased
> where it should at least contain a 1. This is obvious when 
> looking at the
> provided matrix, since the third column of the third row 
> depends on the
> rotation angle - and of course if the input axis already is 
> the Z axis, it
> shouldn't.
> 
> Now, it sounds normal regarding the underlying method 
> (mapping the rotation
> axis to Z, etc). But I wonder whether there's an easy way to 
> perform a real
> arbitrary rotation about any arbitrary axis without using 
> different code
> paths according to the input axis.
> 
> I think it can probably be done by introducing quaternions or better,
> angle-axis, in the story. But err.... maybe there's something simpler.
> 
> Pierre
> 
> 
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