3D Transformations?

I wrote a working Quaternion lib, and I have some matrix commands written in Blitz. I want to do 3D transformations like Blitz3D does for child-parent relationships (but in BlitzPlus).

Given 3 float values for x,y, and z position of a point, say a vertex in a mesh, and an x,y,z,w quaternion rotation, what is the adjusted point position. In other words, what would it's position be in world coordinates?

Function Tranform(x#,y#,z#,qx#,qy#,qz#,qw#)

End Function

If you want the quat lib it's at www.leadwerks.com/code/userlibs/maths3d

This SHOULD work, according to the book I am using, but doesn't, which is not all that surprising:

Ax,y,z is the 3D point and x,y,z,w is the quat rotation.

Should I be storing full 4x4 matrices, or just a quat and a position for each entity?

Any words of wisdom from THE MAN?

Function TransformPoint(Ax#,Ay#,Az#,x#,y#,z#,w#)

;Create a temporary 3x3 matrix
mat11#=1-2*y^2-2*z^2
mat12#=2*x*y+2*w*z
mat13#=2*x*z-2*w*y 
mat21#=2*x*y-2*w*z
mat22#=1-2*x^2-2*z^2
mat23#=2*y*z+2*w*x
mat31#=2*x*z+2*w*y
mat32#=2*y*z-2*w*x
mat33#=1-2*x^2-2*y^2

;Multiple the position and temp matrices as if they were two complete matrices
newx#=Ax*mat11+Ay*mat21+Az*mat31
newy#=Ax*mat12+Ay*mat22+Az*mat32
newz#=Ax*mat13+Ay*mat23+Az*mat33

;Store values for retrieval
FillVector newx,newy,newz,0
End Function

Sorry man my linear algebra is a little rusty at the moment :)

Got the conversions for Quaternions to matrices in B3D.

I guess my question now is should I store a full 4x4 matrix, a 4x3 matrix, or just a 3-value position and 4-value quaternion?

Function QuatAsMatrix#(x,y,z,w)
mat00#=1-2*x^2-2*z^2
mat01#=-(2*z*y+2*w*x)
mat02#=2*w*z-2*x*y
mat10#=-(2*z*y-2*w*x)
mat11#=1-2*y^2-2*x^2
mat12#=2*x*z+2*w*y
mat20#=-(2*x*y+2*w*z)
mat21#=-(2*w*y-2*x*z)
mat22#=1-2*z^2-2*y^2
End Function