How to skew something (via XFORM)

[Anonymous]

Apologies to Katarina:

Her thread was sort of hijacked into a discussion of XFORM, so I have copied it into the GDL forum for further discussion of XFORM. Her original question on walls should be answered in the remaining thread in Working in ArchiCAD:

http://archicad-talk.graphisoft.com/viewtopic.php?t=26825

Sincerely,
Karl

------------------------------

Hello,

I am trying to create a wall that is slanted in two different directions, see the picture, but I haven’t been able to figure out how to do. I have looked at the complex profiles tool, but I have only managed to create a wall that is slanted at the same direction in both ends, not in opposite directions.

Anyone who knows how to do?

Regards,
Katarina

[Karl Ottenstein]

Peter wrote:
Is there any way I can obtain your XFORM object

Thanks again, Peter - object and PDF article are a zip download in the Depository link given. Unless I messed up the upload.

Cheers,
Karl

[Anonymous]

Hello Karl,
I downloaded the skewer.gsm object and the .PDF tutorial
from the depository. What I was referring to was not the
skewer.gsm object but an object you wrote a long time ago
that I thought was called "XFORM.gsm". This object demonstrated
the use of the XFORM transformation by setting the
XFORM command's parameters in various ways to show
how it deformed a PRISM_ command. Is this object also in
the Object Depository somewhere ?
Thanks,
Peter Devlin

[Karl Ottenstein]

Sorry I misunderstood. I don't remember writing an object like that, but I'm getting old and forgetful. I wonder you're thinking of Oleg?

Karl

[Anonymous]

Hello Karl,
I am sure it was you. Bellow is a quote from a post you wrote
back in 2004 in which you acknowledge my reference to that object
and it's author, you.

http://archicad-talk.graphisoft.com/viewtopic.php?p=14496&highlight=xform#14496

*************************************************************
"Peter Devlin wrote:
Karl Ottenstein wrote:
"Add a ROTX command into the script using a fresh angle parameter and you can then rotate the wall/window assembly as needed."

Would it not work better to use XFORM rather than ROTX as this transformation would shear both the wall and the window?

I am not sure about this but Karl would know.
I believe he was the one who wrote that excellent library part
that explained and demonstrated XFORM.

Just wondering,
Peter Devlin
**********************************************************

Thanks, Peter. XFORM would be better, especially if one wants the sills to be parallel to the ground. I was suggesting ROTX since it is so simple and something that everyone should know how to do.

I actually have a new little part called Skewer that I wrote for a contribution to David's in-progress GDL Cookbook 4 to explain and demonstrate XFORM. It lets you parametrically skew another library part in any and all axes. Everyone who gets the CB4 will get a copy. If ROTX doesn't give the result that Vincent needs, I'll ask David if he minds if I pre-release Skewer here.

Karl"
************************************************************

I hope you will remember because I thought it was great and
would like to have it again.
Thanks,
Peter Devlin

[Karl Ottenstein]

Wow, that seems like a long time ago. But, the part I mention there, skewer.gsm, is the part that is uploaded here...

Cheers,
Karl

[Anonymous]

Hello Karl,
You wrote:
"But, the part I mention there, skewer.gsm, is the part that is uploaded here.."
Yes it is but notice that you say:
"I actually have a new little part called Skewer"
The object I refer to was older than the "new little part called Skewer"

I am sorry you don't recall writing that other object.
Thank you for talking to me.
Regards,
Peter Devlin

[Karl Ottenstein]

Peter wrote:
Thank you for talking to me.

Of course! I did a Spotlight search and couldnt find anything else other than an early version of skewer (not parametric) called 'xform test'. Getting old and forgetful stinks.

Cheers,
Karl

[Anonymous]

Hello Karl,
I presently have at least three lib parts that use XFORM and to
make sure I was doing it right I copied the code out of your
object and pasted into my object, commented it out, and then
pasted again and changed the parameters I wanted and
used it to distort the elements I wanted.
Bellow is the snippet of code I copied. Maybe you will recognize it.
Notice your commented explanations for each parameter.

xform 1,0,0,0, !mulx 1,shear xz plane positive x, shear xy plane positive x
0,1,0,0, !shear zy plane positive z,muly 1, shear xy plane positive y
0,0,1,0 !shear zy plane positive z, shear zx plane positive z, mulz 1

I hope this looks familiar
Thanks,
Peter Devlin

[Karl Ottenstein]

Looks like something I would write. I'm guessing that I posted it to the old GDL talk list and do not have a copy of the original post. I found a bunch of posts from 2001 that I made concerning XFORM that included GDL script pasted in the post, but not the particular one you show. So, must be something I didn't save...

I'm going to move this thread over to the Libararies forum (apologies to the person who started it)...

Thanks,
Karl

[Karl Ottenstein]

Here's an old post, explaining XFORM...

	Subject: 	[GDLTalk] XFORM (was koordinates)
	Date: 	July 13, 2001 12:33:36 PM MDT
	To: 	        GDLTalk

> Following the coordinates thread, could anybody enlighten me on how
> XFORM is used?
>
> Laurent Godel


Hi Laurent,

Below is an explanation of XFORM in the form of an annotated 3D script.

Not sure if that is what you wanted?



Regards,

Karl



------------> Copy and paste the following into a 3D Script <---

! XFORM Overview and Demo

! Karl Ottenstein

! July 13, 2001



! Laurent asked about how the XFORM command is used in GDL.  This object

! gives an overview, demo, and some references to textbooks at the end.



! Representing a point as a vector (x, y, z), one can apply matrix algebra

! in order to move (translate), scale, or rotate that point.  According to

! Foley and van Dam (ref at end), the concept of homogeneous coordinates

! originated in geometry in 1946 by E. Maxwell at Cambridge.  Homogeneous

! coordinates, and their transformations, extend a point vector with an

! additional scale factor - so (x, y, z) becomes (x, y, z, 1)



! The homogeneous transformation matrix for translation only is:

!   1   0   0   0

!   0   1   0   0

!   0   0   1   0

!   dx  dy  dz  1

!

! So, with dx, dy, dz as 2, 4, 6 [original said "3, 6, 9" - no idea where that came from], similar to ADD 2, 4, 6:

!   1   0   0   0

!   0   1   0   0

!   0   0   1   0

!   2   4   6   1

!

! Multiply a point (x, y, z, 1) in homogenous coordinate space

! (the extra 1) with the above matrix:  pt * M and you get

! (x+2, y+4, z+6, 1) - a "translated" (shifted) point.

!

! Read DOWN the matrix columns as entering data for the XFORM, and

! leave off the last column of the 4x4 matrix above.



        XFORM 1, 0, 0, 2,

                0, 1, 0, 4,

                0, 0, 1, 6

! Make an asymmetric block in order to see what's going on

BLOCK 1, 4, 8



        DEL 1



! The homogeneous transformation matrix for scaling only is:

!   sx  0   0   0

!   0   sy  0   0

!   0   0   sz  0

!   0   0   0   1

!

! So, with sx, sy, sz as 2, .5, .5, similar to MUL 2, 0.5, 0.5

! you have:

!   2   0   0   0

!   0   0.5 0   0

!   0   0   0.5 0

!   0   0   0   1

!

! Multiply a point (x, y, z, 1) in homogenous coordinate space

! by the above matrix:  pt * M and you get

! (x*2, y*0.5, z*.05, 1)

!

! Read DOWN the matrix columns as entering data for the XFORM, and

! leave off the last column of the 4x4 matrix above.



        XFORM 2, 0, 0, 0,

                0, 0.5, 0, 0,

                0, 0, 0.5, 0

! Make a sphere in order to see what's going on

SPHERE 3



        DEL 1



! Before we proceed to rotation - let's combine translation and scaling,

! using the same numbers as above.  Notice that the XFORM below replaces

! one ADD and one MUL at this point:



! Translate and scale together

        XFORM 2, 0, 0, 2,

                0, 0.5, 0, 4,

                0, 0, 0.5, 6

! Make a sphere in order to see what's going on

SPHERE 3



        DEL 1



!The transformation matrix for rotation "a" degrees about the Z axis is:

!   cos(a)  sin(a)  0       0

!   -sin(a) cos(a)  0       0

!   0       0       1       0

!   0       0       0       1

!For "a" degrees about the X axis:

!   1       0       0       0

!   0       cos(a)  sin(a)  0

!   0       -sin(a) cos(a)  0

!   0       0       0       1

!And, for "a" degrees about the Y axis:

!   cos(a)  0       -sin(a) 0

!   0       1       0       0

!   sin(a)  0       cos(a)  0

!   0       0       0       1



! So...let's rotate a block

! about the Y axis 30 degrees...same as ROTY 30



ang = 30

cosa = cos(ang)

sina = sin(ang)



        XFORM cosa, 0, sina, 0,

                0, 1, 0, 0,

                -sina, 0, cosa, 0

! Make an asymmetric block in order to see what's going on

BLOCK 1, 4, 8



        DEL 1

END

!

! Note that the matrices are combined by multiplying them together,

! giving a new 4x4 transformation matrix. Any number of transformations

! can be combined into one final matrix - represented by a single

! GDL XFORM.  Email me if you want me to post an explanation and

! example.

!

! This is probably not that useful for most GDL programmers, but

! would be very handy for API developers.  (Picture an add-on where the

! user has sliders to rotate, scale and translate an object.  The final

! settings could be saved as a single XFORM.)



! References

!

! These books are dated, as am I.  No doubt there are newer editions,

! and even other, newer books out there now.  Two of them were

! classics, and I expect still are.

!

! Foley, J. D. and van Dam, A. Fundamentals of Interactive Computer

! Graphics.  Addison-Wesley (1982) 664 pages.  This was THE book to

! have - there must be a newer edition.

! ISBN for this edition 0-201-14468-9.

!

! Giloi, Wolfgang K. Interactive Computer Graphics.

! Prentice-Hall (1978) 354 pages.

!

! Harrington, Steven.  Computer Graphics: A Programming Approach.

! McGraw-Hill (1983) 448 pages.

!

! Newman, William M. and Sproull, Robert F. Principles of

! Interactive Computer Graphics, 2nd Edition.

! McGraw-Hill (1979) 541 pages.  This was the bible for graphics

! when I was in school.

!

! Karl Ottenstein, July 2001.