Applying a Transform relative to a Plane coordinate system

Hi everyone,

Let's say I have computed a Transform based on the composition of several translations and rotations. And now I would like to apply this Transform to an object, e.g. a Plane, a Curve, a BRep, etc. But instead of applying this transformation in World coordinates, I would like to perform it relative to another Plane's coordinate system. Is there a direct way of doing this directly?

Also, I have noticed the Transform.ChangeBasis(plane p0, plane p1) in C# is inverted? Meaning, p0 is actually target plane and p1 is origin plane? See attached image for this code:

private void RunScript(Plane x, Plane y, Brep z, ref object A, ref object B, ref object C)
{
    Transform tt = Transform.ChangeBasis(x, y);

    z.Transform(tt);

    A = z;
    B = tt;
}

Thanks.

Attachments:

JLX_2014-11-24_20-46-33_S7.png, 49 KB

Replies to This Discussion

Permalink Reply by Mateusz Zwierzycki on November 24, 2014 at 7:08pm

I think you're looking for PlaneToPlane

http://4.rhino3d.com/5/rhinocommon/?topic=html/M_Rhino_Geometry_Tra...

... and if you want to apply the same transformation in different place :

You have planes :

A = worldXY
B = transformation relative to A
C = plane to apply the transformation from
D = B oriented to C

Dim transAC as rhino.geometry.transform = rhino.geometry.transform.planetoplane(A,C)

B.transform(transAC)

D = B 'just for clarity here

Dim targetTransformation as rhino.geometry.transform = rhino.geometry.transform.planetoplane(C,D)

now the targetTransformation is (I think) the one you asked for.

Sorry for VB, but I think the code is simple enough.

Permalink Reply by Garcia del Castillo on November 25, 2014 at 9:14am

Hi Mateus,

Thanks for your reply. This is close to what I am looking for, but not exactly.

What I am looking for is a way to apply a precalculated Transform to an object, but instead of using World coordinates, using the relative coordinates of a Plane. Let me break it down into an example:

- I have a Transform T (e.g. translating in Z direction one unit).

- I have a reference Plane P (e.g. a XZ plane somewhere in space).

- I have a Geometry G (e.g. a Box).

Now, what I would like to do is to apply Transform T to Geometry G, using Plane P as the coordinate system. In the example above, the box would move one unit in the world -Y direction (which is Plane P's Z direction).

Permalink Reply by David Rutten on November 25, 2014 at 10:24am

In that case you first compute a PlaneToPlane transformation, and you multiply it with your precalculated transform. Multiplying transform matrices has the effect of combining them, but the order is important (and I can never remember what order is the correct one).

Function OrientTransformation(precomputed as Transform, plane As Plane) As Transform

Dim orient As Transform = Transform.PlaneToPlane(Plane.WorldXY, plane)

Return orient * precomputed

End Function

I didn't test the above code, I'm not sure if the multiplication is in the correct order.

Permalink Reply by Garcia del Castillo on November 25, 2014 at 10:50am

Hi David,

Thanks for your response. The problem with that solution is that the resulting transform also incorporates the change of basis, i.e. the necessary translations + rotations to go from WorldXY to the reference Plane.

What I am looking for is using the target Plane just as a reference, and if the Transform is a for example a translation of one unit in Z direction, instead of basing that Transform on World coordinates, using the Plane's position and orientation for this Transform. Maybe what I am asking doesn't make sense algebraically, I am not sure anymore...

Let me create an example of what I am looking at and post it here.

Permalink Reply by Garcia del Castillo on November 25, 2014 at 1:12pm

Here goes an example of what I am trying to achieve, but with Translation transforms implemented only.

Attachments:

plane_based_transform.gh, 15 KB

Permalink Reply by Daniel Hambleton on November 25, 2014 at 1:37pm

You just need to apply the inverse Plane to Plane transformation afterwards, i.e

T' = A*T*Ainv

Or in c# (also attached):

Transform p2p = Transform.PlaneToPlane(Plane.WorldXY, plane);
Transform p2pI;
p2p.TryGetInverse(out p2pI);

geo.Transform(p2p);
geo.Transform(xform);
geo.Transform(p2pI);

A = geo;

Multiplying those transforms before applying them will reduce computation time...

Attachments:

TransformRemap.gh, 6 KB

Permalink Reply by Garcia del Castillo on November 25, 2014 at 1:59pm

Ok, so that's what matrix similarity means in geometrical terms... Nice!

http://en.wikipedia.org/wiki/Matrix_similarity

I would add to this that, if the Transformation matrix only includes rotations and translations, a faster implementation of the inverse matrix can be applied by doing

Ainv = [ Rt, -Rt*d; 0, 1]

where Rt is the transpose of the 3x3 rotational part and d is the 3x1 translation one.

Thanks a lot Daniel, that was super helpful.

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