[Code] Skew Transformation from axes

TIG

Thanks.
PS: Use [code] rather than [ruby:1g3n3drk] to keep indents etc.
I edited the OP...

eneroth3

Thanks TIG!

fredo6

Thanks for posting. Good to know. I think I may have come across this case some time ago, but did not think of encapsulate it as a Transformation, which is an elegant solution.

One small remark: you can check the orientation of 2 vectors by
(xaxis*yaxis) % zaxis > 0
which is equivalent, but faster than
xaxis*yaxis).angle_between(zaxis) < 90.degrees

Fredo

eneroth3

@fredo6 said:

Thanks for posting. Good to know. I think I may have come across this case some time ago, but did not think of encapsulate it as a Transformation, which is an elegant solution.

One small remark: you can check the orientation of 2 vectors by
(xaxis*yaxis) % zaxis > 0
which is equivalent, but faster than
xaxis*yaxis).angle_between(zaxis) < 90.degrees

Fredo

Thanks!

I had the feeling there had to be a more idiomatic way but didn't know it. It's at times like these I wish I had studied more math. There is no math at my school of architecture despite it being a part of the faculty of engineering at the university . All I know about cross products and matrices have I learned by making plugins and I don't think I've ever used a dot product before .

Well, at least I'm making progress. Before I even know of cross multiplication I used to offset the origin point in one axis and apply a 90 degree rotation transformation using the other axis to get a new point that I then could subtract the origin from to get a perpendicular vector.

fredo6

...and there is the magic formula by thomthom to check if two faces are coplanar (actually have parallel planes)

face1.normal % face2.normal > 0.9999999991

Fredo

eneroth3

@fredo6 said:

...and there is the magic formula by thomthom to check if two faces are coplanar (actually have parallel planes)

face1.normal % face2.normal > 0.9999999991

Fredo

That's a nice one! When making my upright extruder I first tried the samedirection? method but it has some issues with the precision and see faces as co-planar sometimes when they aren't (just as the built in Soften Edges feature). Instead I looped the vertices on one face and used classify_point on the other face to see if any vertex position were considered not on plane. In the future I'll use this instead!

icehuli

@fredo6 said:

...and there is the magic formula by thomthom to check if two faces are coplanar (actually have parallel planes)

face1.normal % face2.normal > 0.9999999991

Fredo

I have never known this operator "%" on vectors. Fredo, could you explain to me how it works....

Dan Rathbun

@icehuli said:

I have never known this operator " %" on vectors....., could you explain to me how it works....

Geom::Vector3d#%()
is an alias for the dot() method, ie:
Geom::Vector3d#dot()

@unknownuser said:

(https://en.wikipedia.org/wiki/Dot_product)":dlvmfrbf]
Geometrically, it is the product of the Euclidean magnitudes of the two vectors and the cosine of the angle between them. The name "dot product" is derived from the centered dot " · " that is often used to designate this operation; the alternative name "scalar product" emphasizes that the result is a scalar (rather than a vector).

fredo6

Dot product is 0 if the vectors are perpendicular.
It is 1 if they have the same direction (assuming they are normalized) and -1 for opposite direction.

Fredo

Dan Rathbun

@fredo6 said:

"assuming they are normalized"

Does normalizing first remove any variance that could throw off the comparison (with -1, 0 or 1) afterward ?

Or would it be safer to use:
vec1.perpendicular?(vec2)
vec1.parallel?(vec2) && vec1.samedirection?(vec2)
vec1.parallel?(vec2) && ! vec1.samedirection?(vec2)

I also wonder about ThomThom's magic comparison.

Is it the same on 64-bit SketchUp ?

I mean why 10 decimal places ? Is it SketchUp's internal tolerance ?

Ie, (0.001 x 0.001 x 0.001) ... which is 9 decimal places.

sdmitch

If you have a component instance that has been skewed, how do you determine which axis is skewed?

thomthom

@fredo6 said:

...and there is the magic formula by thomthom to check if two faces are coplanar (actually have parallel planes)

face1.normal % face2.normal > 0.9999999991

Fredo

hm... this must be something from and old version of CleanUp? It was never reliable. What I do now is take all the vertices of the faces and generate a best-fit plane - then I check if each of the vertices is on the plane.

fredo6

Well, I think I found it it an old post!. And it seems to work fine for the purpose.

Indeed there are alternate methods, the problem being to detect the false positive, that is faces that would be co-planar by the formula, but would not in the model drawn by Sketchup.

Fredo

Dan Rathbun

@thomthom said:

@fredo6 said:

...and there is the magic formula by thomthom to check if two faces are coplanar (actually have parallel planes)
face1.normal % face2.normal > 0.9999999991

hm... It was never reliable.

I was hoping you'd answer the questions I posed (above) in this post:
http://sketchucation.com/forums/viewtopic.php?f=180%26amp;t=65068%26amp;view=unread#p597160

fredo6

Face.normal returns a normalized vector.

thomthom

@fredo6 said:

Well, I think I found it it an old post!. And it seems to work fine for the purpose.

Indeed there are alternate methods, the problem being to detect the false positive, that is faces that would be co-planar by the formula, but would not in the model drawn by Sketchup.

Fredo

Checking the plane might in some cases yield false for some cases where SU is able to merge. But this is rare. Comparing normal had the opposite of yielding true in cases where SU would not be able to merge.

thomthom

@dan rathbun said:

@thomthom said:

@fredo6 said:

...and there is the magic formula by thomthom to check if two faces are coplanar (actually have parallel planes)
face1.normal % face2.normal > 0.9999999991

hm... It was never reliable.

I was hoping you'd answer the questions I posed (above) in this post:
http://sketchucation.com/forums/viewtopic.php?f=180%26amp;t=65068%26amp;view=unread#p597160

As Fredo mentions, face.normal already return a unit vector. The issue is that comparing vectors is too unreliable in edge cases.

Dan Rathbun

So what is the solution here?

Is it some extra text in the API docs explaining how best to test for face coplanarity ?

Or would it be a new API method for the Sketchup::Face class:
face.coplanar_with?(other_face)
or a module method?:
Geom::faces_coplanar?(face1,face2)

thomthom

No sure where it would fit in the docs. Maybe we can add a Wiki section on the GitHub repo that host the new docs.

This scenario is so common though that a face.coplanar_with?(other_face) might be a nice addition.