Subject:
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Re: Quick way to mirror-image a model?
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Newsgroups:
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lugnet.cad
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Date:
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Tue, 22 Jun 2004 21:32:55 GMT
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Viewed:
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3858 times
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In lugnet.cad, Carl Nelson wrote:
> In lugnet.cad, Don Heyse wrote:
> > Under Steve's scheme the exception matrix for 3045.dat would be
> > created by multiplying a mirror matrix by a rotate 90 matrix. This
> > would create a part that looks identical, but is in fact mirrored. So
> > I don't think you need more than one exception matrix per part. Look
> > at this. The second part looks similar, but is actually mirrored.
> > That's the exception matrix for MIRROR.INI (except for the -32 Z
> > offset).
> >
> > 1 2 0 0 0 1 0 0 0 1 0 0 0 1 3045.dat
> > 1 1 0 -32 0 0 0 -1 0 1 0 -1 0 0 3045.dat
> >
> > Here's Steve's method using homogeneous 4x4 matrices (because they
> > make the math pretty):
> >
> > Default = MD = (-1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1)
> > Exception = ME = (a, d, g, 0, b, e, h, 0, c, f, i, 0, x, y, z, 1)
> >
> > For a typical (left right symmetric) part ME = MD
> >
> > Current = MC = (A, D, G, 0, B, E, H, 0, C, F, I, 0, X, Y, Z, 1)
> > Mirror across an arbitrary plane = MP = (...)
> > see http://www.geocities.com/SiliconValley/2151/matrices.html
> > (or use a simple mirror across the xy, yz, or xz plane).
> >
> > For each part, calculate MF (final matrix) where:
> > Mirrored (with no mirrored parts) = MF = MP * MC * ME
>
> Steve, Don--thanks for the explanations; this now makes complete sense
> to me (finally!).
>
> For a reflection about the plane containing the Z & Y axes
> (left-to-right), the reflection matrix (Mp) should be:
>
> -1 0 0
> 0 1 0
> 0 0 1
>
> Then Mp * (part-file rotation matrix from LDraw file) * Mp works for
> most parts.
>
> Substitute the second Mp for the exception matrix for the exception
> parts. The exception matrix needs to rotate to proper orientation
> and unmirror the part--for 2357 (brick 2 x 2 corner), the rotation
> matrix is:
>
> 0 0 -1
> 0 1 0
> 1 0 0
>
> To unmirror, the C element should be -1.
Err, I'm not sure what you mean by unmirror. I got
(0 0 1 0 1 0 1 0 0 0 0 0) for a mirror.ini exception matrix, which
looks yours except for the sign of that one number.
> Works like a charm so far, and I haven't found any parts that
> aren't solvable by a single exception matrix yet.
Me neither.
> Anybody see a problem with the algorithm to generate the
> rotation matrix setting
> A = -A and C = -C every time? One should always be 0, right?
> > Unless the text parsing code is already written. Then it's the same.
> > I put the MLCAD.INI (minifig configurator) file parsing in CVS on the
> > sourceforge, and the proposed MIRROR.INI file uses the same format.
> > However if you want to convert to and from XML, that's ok with me.
>
> OK, I haven't done anything else about the config file, but I'll
> stick with text if everyone thinks that's a better idea.
>
> > Sounds like it could work.
>
> Now I just have to program it! ;-)
> I better get busy coding...
And generating the MIRROR.INI file. I did some corner parts, some
triangular wings, some minifig arms and legs, and some technic liftarms.
I also created a tiny C program to parse MIRROR.INI and use it to mirror
a file across the ZY plane. It seems to work so far. The source, ini,
and a windows command line executable is here:
http://ldglite.sf.net/mirwin.zip
If anyone wants to update MIRROR.INI for all 2500 parts, that'd be
fantastic.
Enjoy,
Don
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Message has 3 Replies:
 | | Re: Quick way to mirror-image a model?
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| (...) Unreflect is a better word--just undo the X coordinate swap that -1 0 0 0 1 0 0 0 1 does. I believe they're equivalent things--I'm doing a clockwise rotation, then negating the X coordinate swap, you're doing the opposite rotation. I think (...) (20 years ago, 23-Jun-04, to lugnet.cad)
| | | Re: Quick way to mirror-image a model?
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| (...) Dibs on Wings and files starting with 1! How hard would it be to support normal, self-referential reflections for patterned parts? So we could map all 973*.dat parts to themselves, with a default mirror. Steve (20 years ago, 23-Jun-04, to lugnet.cad)
| | | Re: Quick way to mirror-image a model?
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| (...) In mirror.ini, you noted: ; NOTE: I started using the Flags to keep track of which parts I checked. ; 0 = not checked. ; 1 = substitute part ; 2 = mirror across XY plane instead of default of ZY plane ; 3 = mirror and rotate a bit. ; 4 = (...) (20 years ago, 23-Jun-04, to lugnet.cad)
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Message is in Reply To:
| | Re: Quick way to mirror-image a model?
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| (...) Steve, Don--thanks for the explanations; this now makes complete sense to me (finally!). For a reflection about the plane containing the Z & Y axes (left-to-right), the reflection matrix (Mp) should be: -1 0 0 0 1 0 0 0 1 Then Mp * (part-file (...) (20 years ago, 22-Jun-04, to lugnet.cad)
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