Change coordinate system

[Macha]

I have a geometry sitting nicely in the default world coordinate system.

I have another 3 vectors defining another coordinate system.

How would I transform the geometry from one coordinate system to the other, so that it transforms and aligns appropriately?

I know I can do something with transformPrims() and hou.hmath.buildRotateAboutAxis or getTransformFromPointToPoint() but I'm not sure what, I get all confused.

Does anyone know how to do it, or where I can find good info about it?

If it helps. These are my new coordinate vectors:

v0 = [-0.508 -0.496 -0.703]

v1 = [-0.797 -0.036  0.602]

v2 = [ 0.324 -0.867  0.376]

Edited March 17, 2010 by Macha

[Mario Marengo]

I have a geometry sitting nicely in the default world coordinate system.

I have another 3 vectors defining another coordinate system.

How would I transform the geometry from one coordinate system to the other, so that it transforms and aligns appropriately?

If the vectors v_n are unit length and independent (like the orthogonal sets in your image), then I think the only missing ingredient would be the translation vector -- the position at the origin of the system you're transforming to (say, o₁) relative to the origin of the system you're transforming from; say o, both expressed in the same space of course). Then I believe the transform matrix (in a Houdini-friendly order), would be:

// translation vector
vector v3 = o1-o0;

// xfrom for points
matrix Mp = set( v0.x, v0.y, v0.z, 0,
                 v1.x, v1.y, v1.z, 0,
                 v2.x, v2.y, v2.z, 0,
                 v3.x, v3.y, v3.z, 1 );

// xfrom for vectors (strip translation)
matrix3 Mv = Mp;

// and for normals (strip translation and scaling)
matrix3 Mn = invert(Mv); 
transpose(Mn);

Then, to each element (point, vector, normal) that you want to transform, right-multiply it by the appropriate matrix -- eg p^' = p*Mp, or v^' = v*Mv, or n^' = n*Mn

(untested)

HTH,

Cheers.

[Macha]

Thanks Mario, I think I got it working!