How to trans WCS to OCS ?

Can someone show me the mathematical expressions about translating WCS to OCS ?
I need calculate the value in OCS when I know the value in WCS . I use this in the C++ program :-]
Can somebody help me ?
Thanks,
ifiew

 

Somehow I don't think this is what you're after, but here it is just the
same:

(setq point (list 1.0 2.0 3.0))
(trans point 0 1) ; converts it from the WCS to your current modelspace UCS
(trans point 0 2) ; converts it from the WCS to the current viewport's UCS
(trans point 0 3) ; converts it from the WCS to the current paperspace UCS
-doug

 

ifiew,

That's a fun question... ;-)

Joe Burke

See the following posted 8/3/2003.

 

Hi Bill,

That looks like John's latest version. Thanks for posting it.

I've used it. I'm sure it works as expected transforming a point WCS to OCS.

Joe Burke

 

You're welcome.

I found it in my archives and shook the cobwebs off it.

My translation testing has ceased for now since I ran into an accumlative accuracy problem in my unfold mesh tests.

But I am sure this is the latest version.

Bill

 

I'm looking for the same thing (see my posting DXF Codes 10 210 Formula). Unfortunately I always see the same types of answers....in AutoLISP. Of course, this doesn't help since we are working outside of AutoCAD. I'm still waiting for some assistance on my posting.

 

Did you happen to look at the lisp file posted by BillZ?

If you had, you might've seen in the header that Larry & John included
multiple references that would be beneficial to you.

If you haven't, I'd suggest doing so.........

 

In addition to what Jeff said... you should look on the web for tutorials written by
game programmers. Game software relies heavily on matrix and vector math. Which is
totally independent of any lisp functions available under ACAD.

BTW, an attitude like someone owes you an answer will almost always return zero
results.

Joe Burke

 

I've got it .
For example:
0
CIRCLE
5
93
100
AcDbEntity
8
0
100
AcDbCircle
10
-2.895377203008716
20
22.18318099539349
30
54.07639973511205
40
4.513139999999999
210
0.1433730436417575
220
-0.2456260747668692
230
0.9587032918226155
The center Point value (-2.895377203008716,22.18318099539349,54.07639973511205)is in OCS .
The value in WCS is-0.467296,-6.54411,58.1523)
When I know the circle center in WCS , and I want to write it in a *.dxf file , I must know the value in OCS .
First : Calculate the OCS .
We know the x , y , z axis in WCS is:
Wx (1,0,0) Wy (0,1,0) Wz (0,0,1)
The origin of the OCS and WCS is the same .
The z axis of OCS is the value of the "210 " "220" "230"
We always call it N , Here we are looking for the arbitrary X and Y axes to go with the normal N . They will be called Ax and Ay. N could also be called Az (the Z axis of OCS) .
N (0.1433730436417575,-0.2456260747668692,0.9587032918226155)

We calculate Ax first .
if ( |Nx| < (1/64) && |Ny| < (1/64) )
Ax = Wy × N (where “׆is the cross-product operator).
else
Ax = Wz × N

Scale Ax to unit length.
I got Ax (0.86364,0.50411,0) .

The method of getting the Ay vector is as follows:
Ay = N × Ax. Scale Ay to unit length.
I got Ay (-0.483867,0.827974,0.28449422547) .

So , the OCS matrix is
matrixO :
Axi Ayi Ni
Axj Ayj Nj
Axk Ayk Nk

The center Point value in WCS is
matrix1 : [x0,y0,z0]

The value in OCS is matrix1*matrixO
Axi Ayi Ni
[ x0 y0 z0 ] × Axj Ayj Nj = [ x y z ]
Axk Ayk Nk

The result is the value in OCS ,also is the value below "10" "20" "30" in the dxf files.

In this example:
x0 = -0.467296
y0 = -6.54411
z0 = 58.1523
and
x = -2.895377203008716
y = 22.18318099539349
z = 54.07639973511205

So the key is got the OCS matrix .