rotating a point along an axis...

[Devin]

I can't remember who it was, but someone mentioned something about point transformations. What I want to do is rotate a point along an axis defined by two points a given angle.

Thanks for any help,

Devin

 

[BillZ]

Rotate3d method.

Syntax from the help file:

object.Rotate3D Point1, Point2, RotationAngle

I haven't used this yet but soon.

Bill

 

[Devin]

That's the stuff.  Thanks Bill!

 

Devin

 

[Mark Propst]

Are you talking about transforming a point coordinate or rotating a point entity(as in BillZ's answer)?

 

[Domenico Maria Pisano]

This is a "translation" from a C function defined in the "CAL" pseudo ALisp command . . .

(defun :SQR (n)
(if (> n 46340)
(* (float n) n)
(* n n)
)
)

(defun :VECTOR_MODULE (v / X Y Z)
(setq x (car v) y (cadr v) z (caddr v) )
(if (not z) (setq z 0.0))
(sqrt (+ (* z z) (* x x) (* y y) ) )
)

(defun :VECTOR_2P (pt1 pt2 / )
(if(equal pt1 pt2 1e-10)
nil
(mapcar (function(lambda (i j) (- j i))) pt1 pt2)
)
)

(defun :ROTATE_POINT_AROUND_AXIS (px angx p1 p2
/
CADDRP CADRP CARP COSA COSB COSC LEN LENXY
N P PZ SINA SINB SINC
)
(setq *EPS10* 1.0e-010)

(setq n VECTOR_2P p1 p2)
lenxy (sqrt (+ SQR (car n)) SQR (cadr n))))
)
(if (> lenxy *EPS10*)
(setq cosa (/ (car n) lenxy) sina (/ (cadr n) lenxy) ) (setq cosa 1.0 sina 0.0 ) ) (setq len VECTOR_MODULE n) cosb (/ (caddr n) len) sinb (/ lenxy len) cosc (cos angx) sinc (sin angx) p VECTOR_2P p1 px) carp (car p) cadrp (cadr p) caddrp (caddr p) px (+ (* cosa carp) (* sina cadrp)) cadrp (+ (* sina -1.0 carp) (* cosa cadrp)) carp px pz (+ (* cosb caddrp)(* sinb carp) ) carp (+(* -1.0 sinb caddrp)(* cosb carp)) caddrp pz px (-(* cosc carp) (* sinc cadrp)) cadrp (+(* sinc carp) (* cosc cadrp)) carp px pz (-(* cosb caddrp)(* sinb carp)) carp (+(* sinb caddrp)(* cosb carp)) caddrp pz px (-(* cosa carp)(* sina cadrp)) cadrp (+(* sina carp)(* cosa cadrp)) carp px ) (list (+ carp (car p1)) (+ cadrp (cadr p1)) (+ caddrp (caddr p1))
)

)

domenico

 

[Devin]

Thanks Domenico,

That is going to come in handy, the only thing now is how to get the angle of three 3d points. angle: p1 p2 p3.

Devin

 

[Devin]

Hi Joe,

I thought that the angle command is only good for angles about the x axis. I need to find the absolute angle between < p1 p2 p3 allowing for all three axis. Will this still work?

Thanks,

Devin

 

[Joe Burke]

Devin,

Sorry, I didn't read the messages carefully. @delta is a 2D function. I did think that seemed like too simple an answer.

Joe

 

[Domenico Maria Pisano]

.. . . try this and let me know if it works well . . .

(defun :VECTOR_2P (pt1 pt2 / )
(if(equal pt1 pt2 1e-10)
nil
(mapcar (function(lambda (i j) (- j i))) pt1 pt2)
)
)

(defun :ACOS (x)
;
(cond
((equal x -1.0 1e-06) (setq x -1.0) )
((equal x 1.0 1e-06) (setq x 1.0) )
((> x 1.0) (setq x nil ) )
((< x -1.0) (setq x nil ) )
)
(if x
(atan (sqrt (- 1.0 (expt x 2.0))) x)
nil
)
)

(defun :VECTOR_SCALAR_PRODUCT (v1 v2)
(+ (* (car v1)(car v2)) (* (cadr v1)(cadr v2)) (* (caddr v1)(caddr v2)) )
)

(defun :VECTOR_MODULE (v / X Y Z)
(setq x (car v) y (cadr v) z (caddr v) )
(if (not z) (setq z 0.0))
(sqrt (+ (* z z) (* x x) (* y y) ) )
)

; returns intenal angle (radiants) for 3 3d points
(defun :ANG2D_3P3D_I (p1 px p3 / V1 V3)
(setq v1 VECTOR_2P px p1))
(if v1
(setq v3 VECTOR_2P px p3))
)
(if v3
(if (not (equal v1 v3 1e-12))
ACOS
(/
VECTOR_SCALAR_PRODUCT v1 v3)
(* VECTOR_MODULE v1) VECTOR_MODULE v3) )
)
)
0.0
)
nil
)
)

domenico

 

[BillZ]

Also:
Here is a program that came with AutoCAD (R10 I think). Called Spiral. Will Make a 2d or 3d spiral with giver parameters. It so simple that I can't understand it but have always thought that it must contain the math needed to figure a 3d point around an axis.

HTH

Bill

 

[Devin]

Thanks Domenico,

It will be a little time before I can put them into play. Hopefully short. I'm trying to make a function to create a ucs given three points. The vla functions for adding the ucs require a base pt, x-direction-vector and y-direction-vector. I think that the three points have to be perpendicular. But the points I need to supply aren't perpendicular so I must make them that way, via your functions.

If I have three points defining an x-y axis, how do I get a fourth point up
1.0 units in the z direction? I think that would give me the axis for the 3drotate of the point. Perhaps we can create this function together.

Thanks, you've been a big help!

Devin

 

[Domenico Maria Pisano]

If you will use my routenes, you will not need no UCS manipulation. My code works (if it works . . . but I think that it works . . .) in the current UCS. It is not an "ACAD" solution but a "mathematical" one.

ciao

domenico

 

[Devin]

You're stronger in math than I. I'll need to use the ucs and projection lines and entities into the current ucs. Sorry for my lack of math skill. I'll use what you've given me.

Thanks,

Devin