topic How to get angles from transformation matrix (same as returned by nentselp)? in Visual LISP, AutoLISP and General Customization Forum

How to get angles from transformation matrix (same as returned by nentselp)?

ShricharanaB — Thu, 13 Apr 2023 07:22:06 GMT

Hi,

I'm trying to insert some attachments to blocks (lets call them blockX) in the drawing which can be in any rotation but y axis of the block will always be parallel to the XY plane of WCS (even if nested) . These blocks are nested inside other blocks (lets call them blockY ) from 1 to 3 levels deep. BlockYs can be rotated along their Z axis in either in model space or in another block. Note that these attachments will be inserted into the model space not inside the blocks. Since I want to do this for all relevant blocks in the model space I cannot use nentselp / nentsel. I'm using (ssget "_X" ...).

I need the angle between x axis of blockX projected onto XY plane of WCS (no matter the level of nesting) θ, and angle between the x axis of blockX and the XY plane of WCS (no matter the level of nesting) γ . Shown in screenshot.

I'm currently getting the transformation matrix w.r.t WCS using the function 'get-tmatrix (by gile) ( which is same as the one returned by nentselp). But I don't know how to get the angles from this. Please help.

In the attached drawing file, the red line is the x axis of the respective blocks.

Thanks in advance!

Re: How to get angles from transformation matrix (same as returned by nentselp)?

_gile — Thu, 13 Apr 2023 08:05:38 GMT

Hi,

The angles you're looking for are called Euler angles.

The following routines computes the Euler angles from a transformation matrix such as the one returned by nentsel or nentselp with the two mainly used conventions: Proper Euler and Tait-Bryan.

The angles you're looking for seems to be Yaw and Pitch fromTait-Bryan angles.

;; gc:butLast ;; Returns the list but the last item ;; ;; Argument ;; l : a list (defun gc:butLast (l) (reverse (cdr (reverse l)))) ;; gc:GetNormal ;; Returns the unit vector of a vector ;; Retourne le vecteur unitaire d'un vecteur ;; ;; Argument ;; v : a vector (defun gc:GetNormal (v) ((lambda (l) (if (/= 0 l) (mapcar (function (lambda (x) (/ x l))) v) ) ) (distance '(0. 0. 0.) v) ) ) ;; TRP ;; Transposes a matrix -Doug Wilson- ;; ;; Argument ;; m : a matrix (defun trp (m) (apply 'mapcar (cons 'list m))) ;; gc:acos ;; Returns the arc cosine of an angle ;; ;; Argument ;; n : le angle cosine (defun gc:acos (n) (cond ((equal n 1. 1e-9) 0.) ((equal n -1. 1e-9) pi) ((< -1. n 1.) (atan (sqrt (- 1. (expt n 2))) n) ) ) ) ;; gc:asin ;; Returns the arc sine of an angle ;; ;; Argument ;; n : le angle sine (defun gc:asin (n) (cond ((equal n 1. 1e-9) (/ pi 2.)) ((equal n -1. 1e-9) (/ pi -2.)) ((< -1. n 1.) (atan n (sqrt (- 1 (expt n 2)))) ) ) ) ;; ProperEuler ;; Returns a list containing the the Euler angles in radians (precession, nutation and intrinsic rotation) ;; ;; Argument ;; m : a transformation matrix such as the one returned by nentsel or nentselp (defun ProperEuler (m / theta psi phi) (setq m (mapcar 'gc:GetNormal (if (= (length (car m)) 3) (mapcar 'gc:butlast (trp m)) (gc:butlast (mapcar 'gc:butlast m)) ) ) ) (setq theta (gc:acos (caddr (caddr m)))) (if (< (abs theta) 1e-7) (setq theta 0. psi 0. phi (atan (car (cadr m)) (cadr (cadr m))) ) (setq psi (atan (caddr (car m)) (- (caddr (cadr m)))) phi (atan (car (caddr m)) (cadr (caddr m))) ) ) (list psi theta phi) ) ;; TaitBryan ;; Returns a list containing the the Tait-Bryan angles in radians (yaw, pitch, roll) ;; ;; Argument ;; m : a transformation matrix such as the one returned by nentsel or nentselp (defun TaitBryan (m / a b c) (setq m (mapcar 'gc:GetNormal (if (= (length (car m)) 3) (mapcar 'gc:butlast (trp m)) (gc:butlast (mapcar 'gc:butlast m)) ) ) ) (setq b (- (gc:asin (car (caddr m))))) (cond ((< (abs (- b (* pi 0.5))) 1e-7) (setq b (* pi 0.5) a (atan (caddr (cadr m)) (cadr (cadr m))) c 0. ) ) ((< (abs (+ b (* pi 0.5))) 1e-7) (setq b (* pi -0.5) a (atan (- (caddr (cadr m))) (cadr (cadr m))) c 0. ) ) (T (setq a (atan (car (cadr m)) (car (car m))) c (atan (cadr (caddr m)) (caddr (caddr m))) ) ) ) (list a b c) )

Here's an testing command:

(defun c:EULERANGLES (/ block matrix) (while (not (and (setq block (nentsel "\nSelect a nested entity within a block: ")) (= (length block) 4) ) ) ) (setq matrix (caddr block)) (mapcar '(lambda (s v) (prompt (strcat "\n" s ": " (angtos v)))) '("precession" "nutation" "rotation") (ProperEuler matrix)) (mapcar '(lambda (s v) (prompt (strcat "\n" s ": " (angtos v)))) '("yaw" "pitch" "roll") (TaitBryan matrix)) (princ) )

Re: How to get angles from transformation matrix (same as returned by nentselp)?

ShricharanaB — Thu, 13 Apr 2023 08:57:25 GMT

I knew you were going to answer this! Are you the same Gile that has posted this theswamp.org ?

I seem to be getting the proper angles from the TaitBryan function. Thank you!

P.S: Is there any reference you can suggest where I can learn about the transformation matrix and the Euler angles and the relation between the two? I just can't seem to get these concepts into my head.