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Calculating Matrix by Vector

Started by No_Germs Feb 17, 2005 at 3:53 PM 2 replies 350+ views

Original Post

Feb 17, 2005 at 3:53 PM

suppose i have a normalized vector, and i want a matrix with one of its axes in the direction of the vector(i don't care where the other two axes will point to). how do i calculate the matrix?

Zakwayda

Feb 17, 2005 at 5:26 PM

I just answered this question in another post - here's what I wrote (slightly edited):

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What you need is an orthonormal basis. You want the direction vector to be one of these axes, let's say z. You can find the others by a) crossing z with an arbitrary vector to get an axis perpendicular to z, and b) crossing z and that vector to get the other vector. The only caveat is that an initial choice too close to z will produce a (more or less) null cross product. A nice workaround is to cross it with the axis it is most 'not aligned' with. Here's some code:

void Vector3::MakeOrthonormalBasis(Vector3& x, Vector3& y, Vector3& z, bool normalized) const{    // Find the principal axis most perpendicular to the vector    Vector3 axis;    if (fabsf(m_x) <= fabsf(m_y) && fabsf(m_x) <= fabsf(m_z))        axis.Set(1, 0, 0);    else if (fabsf(m_y) <= fabsf(m_x) && fabsf(m_y) <= fabsf(m_z))        axis.Set(0, 1, 0);    else        axis.Set(0, 0, 1);		    // Construct basis    z = *this;    if (!normalized)        z.Normalize();    z.Normalize();    x = z.UnitCross(axis);    y = z.Cross(x);}

(Note that this could actually be done a little more efficiently, but I'm not going to fix it right now.)

JohnBolton

Feb 17, 2005 at 5:32 PM

You are looking for how to implement a "look at" function. The technique is pretty simple:

You are looking for the basis vectors X, Y, and Z, given a vector V, to which Z is parallel.

Z = Normalize( V )
U = any unit vector != Z (usually it is the world's "up" vector)
X = Normalize( CrossProduct( U, Z ) )
Y = Cross( Z, X )

No_Germs

Feb 17, 2005 at 6:05 PM

it's all so simple now... Thanks a bunch :)

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