3D distance and angle.

Bill,

the 3pxa_matrix function takes the arguments as follows:

(3pxa_matrix <origin point> <x direction vector> <y direction vector>
<additional rotation about x axis in degrees (zero if none)>)

assuming:
delta triangle on a plane with points a1 b1 c1.
main triangle on a plane (the same as delta triangle or other) with points
a2 b2 c2.
co-linear pts between delta triangle and main triangle are a1=a2 b1=b2.

now the first step is to create a matrix aligned with the delta triangle.
This is the triangle you wish to change.

syntax (line 1):
(3pxa_matrix a1 b1 c1 180)

notice that I flipped the matrix by 180 degrees about the x axis. This is
so that when we create the final matrix it will be facing the same direction
as the first and not inverted on the opposite direction. Draw it out on
paper, examine it and I'm sure you'll see why.

the next step is to transform the delta triangle's points thru the newly
created matrix (doorway). This puts the points at 0,0,0 and oriented with
the WCS.

syntax (line 2):
(setq
a1 (mtrans a1 0 1)
b1 (mtrans b1 0 1)
c1 (mtrans c1 0 1)
)

now it's time to set up the final matrix or doorway to our final position.
And that's simply creating a matrix along the alignment edge of the
triangles flat with the base triangle, since the base triangle is our
destination plane...

syntax (line 3):
(3pxa_matrix a2 b2 c2 0.0)

notice that I didn't flip this matrix about the x axis 180 degrees this
time. It only needs to be done once, and on either matrix, since both
matrix's would actually face each other had we not flipped one of them. If
we didn't flip one or the other it would mirror the delta triangle if I'm
not incorrect.

summary so far:
The first matrix (line 1) created a doorway for the delta triangles points
to a holding frame that is aligned with the WCS at 0,0,0 as the base. The
second matrix (line 3) created a doorway to transport those temporary points
in the holding frame to the matrix that's aligned with the plane of the base
triangle. That's the final destination of the points.

Now we transform the points thru the new doorway...

syntax (line 4):
(setq
a1 (mtrans a1 1 0)
b1 (mtrans b1 1 0)
c1 (mtrans c1 1 0)
)

to understand a little about the mtrans function, what it does is this.
(mtrans pt 0 1) means to transform pt from 0 (WCS) to 1 (matrix). (mtrans
pt 1 0) means to transform pt from 1 (matrix) to 0 (WCS). And I guess I'm
pretty sure you already knew that, but for anyone else that's reading.

So really, in concept all that we are doing is creating two doors to
transform the points from one place and orientation to another place and
orientation. And to do that, we need a start door (line 1) and an end door
(line 3) and we need to step thru the doors (lines 2 & 4).

Like dimensional doorways from one location and orientation in space to
another. Stargate?

I hope this helps, let me know and if it doesn't then I'll test a working
example and post that too.

Devin

 

Devin,
I was picking the triangles in the wrong order.

This works if I draw a new triangle with points returned by the mtrans function. But if I use (vla-transformby rec_1 ucs_matrix_array) it flings the triangle off in space.
There may be another step I need to do?

Thanks

Bill

 

BillZ,

In order to use the transformby function you have to create an inverse
matrix. Notice that the mtrans and trans functions have two arguments that
specify from and to (ie: (mtrans pt 0 1) & (mtrans pt 1 0)) this allows
either passing the pt thru the matrix or the inverse matrix. Also notice
that the transformby function doesn't allow these arguments. What we'll
have to do is establish two functions for (3pxa_matrix), one that creates a
matrix and the other that creates an inverse matrix.

let me work on it a bit and I'll come up with something soon.

Devin

 

Bill,

I went ahead and added the inverse matrix switch to the 3pxa_matrix
function, the inverse matrix is nothing more than the transposition of the
3x3 rotation matrix portion of the transformation matrix. Simply add any
value other than nil to the <inverse> argument to create an inverse matrix.
I don't know which matrix in your sequence would be the inverse. Either the
first or the second (guess you've got a 50/50 chance of getting it right the
first time , try and let me know.

(defun 3pxa_matrix ( origin xvector yvector xangle inverse
/
-x org -y -z xo yo zo xx yx zx xy yy zy xz yz zz numx
numy numz v a
)
(setq
;create new axis
xangle (dtor (sign xangle))
v (mapcar;magnify vector a factor of 100
'(lambda (a)
(* a 100.0)
)
(vector origin xvector)
)
yvector (vector_translate yvector v)
-y (axial_rotate yvector 180d origin xvector)
-x (axial_rotate origin 180d yvector -y)
org (midpoint yvector -y)
-y (axial_rotate -y xangle origin xvector)
-z (axial_rotate -y 90d origin xvector)
)
(setq
xo (car org)
yo (cadr org)
zo (caddr org)
xx (car -x)
yx (cadr -x)
zx (caddr -x)
xy (car -y)
yy (cadr -y)
zy (caddr -y)
xz (car -z)
yz (cadr -z)
zz (caddr -z)
numx (sqrt (+ (sqr (- xx xo)) (sqr (- yx yo)) (sqr (- zx zo))))
numy (sqrt (+ (sqr (- xy xo)) (sqr (- yy yo)) (sqr (- zy zo))))
numz (sqrt (+ (sqr (- xz xo)) (sqr (- yz yo)) (sqr (- zz zo))))
v (vector (list 0.0 0.0 0.0) origin)
)
(if
inverse
(setq
ucs_matrix
(list
(list (/ (- xx xo) numx) (/ (- yx yo) numx) (/ (- zx zo) numx) (car
v))
(list (/ (- xy xo) numy) (/ (- yy yo) numy) (/ (- zy zo) numy)
(cadr v))
(list (/ (- xz xo) numz) (/ (- yz yo) numz) (/ (- zz zo) numz)
(caddr v))
(list 0.0 0.0 0.0 1.0)
)
ucs_matrix_array (vlax-tmatrix ucs_matrix)
)
(setq
ucs_matrix
(list
(list (/ (- xx xo) numx) (/ (- xy xo) numy) (/ (- xz xo) numz) (car
v))
(list (/ (- yx yo) numx) (/ (- yy yo) numy) (/ (- yz yo) numz)
(cadr v))
(list (/ (- zx zo) numx) (/ (- zy zo) numy) (/ (- zz zo) numz)
(caddr v))
(list 0.0 0.0 0.0 1.0)
)
ucs_matrix_array (vlax-tmatrix ucs_matrix)
)
)
ucs_matrix
)

 

Oops forgot to inverse the translation matrix portion of the transformation
matrix. Here ya go, I'm going to run a test myself to make sure it works
for you. Don't use the inverse matrix switch with mtrans as it will give
unexpected results...

(defun 3pxa_matrix ( origin xvector yvector xangle inverse
/
-x org -y -z xo yo zo xx yx zx xy yy zy xz yz zz numx
numy numz v a
)
(setq
;create new axis
xangle (dtor (sign xangle))
v (mapcar;magnify vector a factor of 100
'(lambda (a)
(* a 100.0)
)
(vector origin xvector)
)
yvector (vector_translate yvector v)
-y (axial_rotate yvector 180d origin xvector)
-x (axial_rotate origin 180d yvector -y)
org (midpoint yvector -y)
-y (axial_rotate -y xangle origin xvector)
-z (axial_rotate -y 90d origin xvector)
)
(setq
xo (car org)
yo (cadr org)
zo (caddr org)
xx (car -x)
yx (cadr -x)
zx (caddr -x)
xy (car -y)
yy (cadr -y)
zy (caddr -y)
xz (car -z)
yz (cadr -z)
zz (caddr -z)
numx (sqrt (+ (sqr (- xx xo)) (sqr (- yx yo)) (sqr (- zx zo))))
numy (sqrt (+ (sqr (- xy xo)) (sqr (- yy yo)) (sqr (- zy zo))))
numz (sqrt (+ (sqr (- xz xo)) (sqr (- yz yo)) (sqr (- zz zo))))
v (vector (list 0.0 0.0 0.0) origin)
)
(if
inverse
(setq
ucs_matrix
(list
(list (/ (- xx xo) numx) (/ (- yx yo) numx) (/ (- zx zo) numx)
(sign (car v)))
(list (/ (- xy xo) numy) (/ (- yy yo) numy) (/ (- zy zo) numy)
(sign (cadr v)))
(list (/ (- xz xo) numz) (/ (- yz yo) numz) (/ (- zz zo) numz)
(sign (caddr v)))
(list 0.0 0.0 0.0 1.0)
)
ucs_matrix_array (vlax-tmatrix ucs_matrix)
)
(setq
ucs_matrix
(list
(list (/ (- xx xo) numx) (/ (- xy xo) numy) (/ (- xz xo) numz) (car
v))
(list (/ (- yx yo) numx) (/ (- yy yo) numy) (/ (- yz yo) numz)
(cadr v))
(list (/ (- zx zo) numx) (/ (- zy zo) numy) (/ (- zz zo) numz)
(caddr v))
(list 0.0 0.0 0.0 1.0)
)
ucs_matrix_array (vlax-tmatrix ucs_matrix)
)
)
ucs_matrix
)

 

No problem,
I'll be working on this thing, in varying capacities, right along.
I find this subject quite interesting.

thanks for the help.

Bill

 

BillZ,

Looking back (when I researched matrices and transforming them) I remember
that the process of applying the translation vector to the point your
transforming was different depending on which way you were going (ie:
ucs->wcs or wcs->ucs). The transformby function only applies it in one
direction, so the inverse matrix may need to be defined differently. Let me
look into it some more and I'll see what I can come up with.

Devin

 

BillZ,

I fixed it, you have to trick the program by moving the object from the
origin pt to 0,0,0 then perform the inverse transformby then perform the
normal transformby. Look at the sequence of the delta command, also I
changed the 3pxa_matrix function a little...

(defun c:delta ( / obj ent )
(setq obj (vlax-ename->vla-object (setq ent (car (entsel "\nSelect object
to transform: ")))))
(princ "\nSelect common edge...")
(setq morig (getpoint "\nSelect origin point: "))
(setq mxv (getpoint morig "\nSelect xvector direction: "))
(princ "\nDelta triangle plane...")
(setq myv (getpoint morig "\nSelect yvector direction: "))
(princ "\nBase triangle plane...")
(setq nyv (getpoint morig "\nSelect yvector direction: "))
(3pxa_matrix morig mxv myv 180.0 t)
(vla-move obj (vlax-3d-point morig) (vlax-3d-point (list 0 0 0)))
(vla-transformby obj ucs_matrix_array)
(3pxa_matrix morig mxv nyv 0.0 nil)
(vla-transformby obj ucs_matrix_array)
)

(defun 3pxa_matrix ( origin xvector yvector xangle inverse
/
-x org -y -z xo yo zo xx yx zx xy yy zy xz yz zz numx
numy numz v a
)
(setq
;create new axis
xangle (dtor (sign xangle))
v (mapcar;magnify vector a factor of 100
'(lambda (a)
(* a 100.0)
)
(vector origin xvector)
)
yvector (vector_translate yvector v)
-y (axial_rotate yvector 180d origin xvector)
-x (axial_rotate origin 180d yvector -y)
org (midpoint yvector -y)
-y (axial_rotate -y xangle origin xvector)
-z (axial_rotate -y 90d origin xvector)
)
(setq
xo (car org)
yo (cadr org)
zo (caddr org)
xx (car -x)
yx (cadr -x)
zx (caddr -x)
xy (car -y)
yy (cadr -y)
zy (caddr -y)
xz (car -z)
yz (cadr -z)
zz (caddr -z)
numx (sqrt (+ (sqr (- xx xo)) (sqr (- yx yo)) (sqr (- zx zo))))
numy (sqrt (+ (sqr (- xy xo)) (sqr (- yy yo)) (sqr (- zy zo))))
numz (sqrt (+ (sqr (- xz xo)) (sqr (- yz yo)) (sqr (- zz zo))))
)
(if
inverse
(setq v (vector origin (list 0.0 0.0 0.0)))
(setq v (vector (list 0.0 0.0 0.0) origin))
)
(if
inverse
(setq
ucs_matrix
(list
(list (/ (- xx xo) numx) (/ (- yx yo) numx) (/ (- zx zo) numx) 0.0)
(list (/ (- xy xo) numy) (/ (- yy yo) numy) (/ (- zy zo) numy) 0.0)
(list (/ (- xz xo) numz) (/ (- yz yo) numz) (/ (- zz zo) numz) 0.0)
(list 0.0 0.0 0.0 1.0)
)
ucs_matrix_array (vlax-tmatrix ucs_matrix)
)
(setq
ucs_matrix
(list
(list (/ (- xx xo) numx) (/ (- xy xo) numy) (/ (- xz xo) numz) (car
v))
(list (/ (- yx yo) numx) (/ (- yy yo) numy) (/ (- yz yo) numz)
(cadr v))
(list (/ (- zx zo) numx) (/ (- zy zo) numy) (/ (- zz zo) numz)
(caddr v))
(list 0.0 0.0 0.0 1.0)
)
ucs_matrix_array (vlax-tmatrix ucs_matrix)
)
)
ucs_matrix
)

 

Devin,
Worked good first time!
I'm ready to leave for vacation and have another project to do when I get back so I'll have to test it more when I get back.
It should be a good start for what I wanted.

Thanks Again!

Bill

 

Bill,

use the following modified functions...

(defun c:delta ( / obj ent )
(setq obj (vlax-ename->vla-object (setq ent (car (entsel "\nSelect object
to transform: ")))))
(princ "\nSelect common edge...")
(setq morig (getpoint "\nSelect origin point: "))
(setq mxv (getpoint morig "\nSelect xvector direction: "))
(princ "\nDelta triangle plane...")
(setq myv (getpoint morig "\nSelect yvector direction: "))
(princ "\nBase triangle plane...")
(setq nyv (getpoint morig "\nSelect yvector direction: "))
(3pxa_matrix morig mxv myv 180.0 t)
(vla-move obj (vlax-3d-point morig) (vlax-3d-point (list 0 0 0)))
(vla-transformby obj ucs_matrix_array)
(3pxa_matrix morig mxv nyv 0.0 nil)
(vla-transformby obj ucs_matrix_array)
)

(defun 3pxa_matrix ( origin xvector yvector xangle inverse
/
-x org -y -z xo yo zo xx yx zx xy yy zy xz yz zz numx
numy numz v a
)
(setq
;create new axis
xangle (dtor (sign xangle))
v (mapcar;magnify vector a factor of 100
'(lambda (a)
(* a 100.0)
)
(vector origin xvector)
)
yvector (vector_translate yvector v)
-y (axial_rotate yvector 180d origin xvector)
-x (axial_rotate origin 180d yvector -y)
org (midpoint yvector -y)
-y (axial_rotate -y xangle origin xvector)
-z (axial_rotate -y 90d origin xvector)
)
(setq
xo (car org)
yo (cadr org)
zo (caddr org)
xx (car -x)
yx (cadr -x)
zx (caddr -x)
xy (car -y)
yy (cadr -y)
zy (caddr -y)
xz (car -z)
yz (cadr -z)
zz (caddr -z)
numx (sqrt (+ (sqr (- xx xo)) (sqr (- yx yo)) (sqr (- zx zo))))
numy (sqrt (+ (sqr (- xy xo)) (sqr (- yy yo)) (sqr (- zy zo))))
numz (sqrt (+ (sqr (- xz xo)) (sqr (- yz yo)) (sqr (- zz zo))))
)
(if
inverse
(setq v (vector origin (list 0.0 0.0 0.0)))
(setq v (vector (list 0.0 0.0 0.0) origin))
)
(if
inverse
(setq
ucs_matrix
(list
(list (/ (- xx xo) numx) (/ (- yx yo) numx) (/ (- zx zo) numx) 0.0)
(list (/ (- xy xo) numy) (/ (- yy yo) numy) (/ (- zy zo) numy) 0.0)
(list (/ (- xz xo) numz) (/ (- yz yo) numz) (/ (- zz zo) numz) 0.0)
(list 0.0 0.0 0.0 1.0)
)
ucs_matrix_array (vlax-tmatrix ucs_matrix)
)
(setq
ucs_matrix
(list
(list (/ (- xx xo) numx) (/ (- xy xo) numy) (/ (- xz xo) numz) (car
v))
(list (/ (- yx yo) numx) (/ (- yy yo) numy) (/ (- yz yo) numz)
(cadr v))
(list (/ (- zx zo) numx) (/ (- zy zo) numy) (/ (- zz zo) numz)
(caddr v))
(list 0.0 0.0 0.0 1.0)
)
ucs_matrix_array (vlax-tmatrix ucs_matrix)
)
)
ucs_matrix
)

 

oh, and have fun on your vacation

 

Better yet.
Thanks.

Bill

 

Bill,

I thought maybe I should expand a little on what I did to make it work...

A transformation from a 4x4 transformation matrix is done by first
multiplying the 3x3 matrix by the point to be transformed and after that
applying the translation vector at the far right of the 4x4 matrix to the
point. That's the steps to transforming to a matrix. To transform from a
matrix you must first subtract the translation vector and after that
multiply the pt to be transformed by the transposition of the 3x3 rotation
matrix. To understand a transposition of a 3x3 matrix look at the
following:

simple 3x3 matrix...

1 2 3
4 5 6
7 8 9

and that same matrix transposed...

1 4 7
2 5 8
3 6 9

As you can see the transposition is simply the matrix mirrored along a line
from the top left to the bottom right of the matrix. The interesting
property of the transposition is that when you multiply a vector by the
transposition matrix it actual reverses the rotation.

HTH,

Devin

 

Very interesting.
I will look at this more closely as time permits.

Thanks

Bill