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arbitrary-axis rotation matrix

4 posts in this topic

Not sure if this is the right place to post this, but i am trying to build a 4X4 matrix that will rotate a 3D object around an arbitraty axis (x,y,z) The axis vector (x,y,z) need not be normalized. The angle a is measured in radians. If the rotation axis faces the user, the rotation will be counterclockwise. x --> Specifies the X component of the axis of rotation. y --> Specifies the Y component of the axis of rotation. z --> Specifies the Z component of the axis of rotation. a --> Specifies the rotation angle, in radians. I am working in C++ and i think i am close, but while the object rotates it changes shape. Any help would be great, thanks.

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This can be found various places online [Edit: e.g. Sneftel's link], but here's another reference you can check your code against:
    // Some values you'll need (note that x, y and z are
// the components of the unit-length input axis):

T s = sin(angle);
T c = cos(angle);
T omc = (T)1.0 - c;

T xomc = x * omc;
T yomc = y * omc;
T zomc = z * omc;

T xxomc = x * xomc;
T xyomc = x * yomc;
T xzomc = x * zomc;
T yyomc = y * yomc;
T yzomc = y * zomc;
T zzomc = z * zomc;

T xs = x * s;
T ys = y * s;
T zs = z * s;

// The matrix is then:

[ xxomc + c, xyomc + zs, xzomc - ys ]
[ xyomc - zs, yyomc + c, yzomc + xs ]
[ xzomc + ys, yzomc - xs, zzomc + c ]

// This is in row-vector form; simply transpose if you're using column vectors.

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Thank you both, I had tried that matrix before but it looks like i was forgetting to normalize the vector, now its works like a charm :).

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I got great help with my last question, and i have one last problem:

The alignment matrix aligns the model space Y axis with the specified
axis vector (x,y,z) (which need not be normalized). The rotation is
performed about the vector (a ^ b), where a is (0,1,0) and b is (x,y,z).

x --> Specifies the X component of the axis of alignment.
y --> Specifies the Y component of the axis of alignment.
z --> Specifies the Z component of the axis of alignment.

I am having some trouble building the 4X4 rotation matrix that preforms this action, any help would be great, Thanks.

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