Topic: ANGLE FORMED BY 2 PLANES so fast and infallible?

[SOFITO_SOFT]

Hi all:
For example, from 3 points (not coliniars) of each plane.
Any input is appreciated.

[Kerry]

depends  ..
In what plane do you want the angle expressed ?

Do you want the angle in the plane of the 3 points ?
or the angle in the current View ?
or the angle when viewed in World plan ?
How are the points defined  .. In world ordinates in in relation to the current UCS ?

See what happens here ... ask a question and someone will ask you at least 4 more

[Lee Mac]

This?

Code: [Select]

;; Angle Between Planes - Lee Mac 2010
;; Args: p1,p2,p3 - Points on First Plane
;;       p4,p5,p6 - Points on Second Plane

(defun AngleBetweenPlanes ( p1 p2 p3 p4 p5 p6 )
  (
    (lambda ( u v )
      (acos (/ (vxv u v) (* (norm u) (norm v))))
    )
    (v^v (mapcar '- p3 p2) (mapcar '- p2 p1))
    (v^v (mapcar '- p6 p5) (mapcar '- p5 p4))
  )
)

;; Vector Cross (Wedge) Product - Lee Mac 2010
;; Args: u,v - vectors in R^3

(defun v^v ( u v )
  (list
    (- (* (cadr u) (caddr v)) (* (cadr v) (caddr u)))
    (- (* (car  v) (caddr u)) (* (car  u) (caddr v)))
    (- (* (car  u) (cadr  v)) (* (car  v) (cadr  u)))
  )
)

;; Vector Dot Product - Lee Mac 2010
;; Args: u,v - vectors in R^n

(defun vxv ( u v )
  (apply '+ (mapcar '* u v))
)

;; Vector Norm - Lee Mac 2010
;; Args: v - vector in R^n

(defun norm ( v )
  (sqrt (apply '+ (mapcar '* v v)))
)

;; ArcCosine - Lee Mac 2010
;; Args: -1 <= x <= 1

(defun acos ( x )
  (if (<= (abs x) 1.0)
    (if (equal x 0.0 1e-8)
      (* pi 0.5)
      (atan (/ (sqrt (- 1.0 (* x x))) x))
    )
  )
)


[Kerry]

Lee, don't have time to play ..
Does that return the  Dihedral angle ?

I couldn't see the question intent exactly, but that may be it.

[Lee Mac]

Lee, don't have time to play ..
Does that return the  Dihedral angle ?

Correct, the angle between the normals 

[SOFITO_SOFT]

Hello:
Lee Marc is known about that question.
His program is perfect. You only need to add a verfificacion for 3 points of each plane (in UCS W) form a plane (not aligned).
A possible improvement is to ensure the 2 planes are the same. What angle are 2 planes overlap? The angle is not 0.0 ... Is Null? is infinite ? is not definided ? Thank you all.

[Lee Mac]

You only need to add a verfificacion for 3 points of each plane (in UCS W) form a plane (not aligned).

That is the caller's responsibility 

[SOFITO_SOFT]

Hello again:
Sorry ... Another second verfificacion: all the 3 points of each plan must be differents, else it cause a division by 0 and the resulting error.
So I added the word "infallible". The "truck" thickens with points taken from who knows where (other progarms / geometrics functions.)  Anyway, it's a good basis for a unfailing foolproof function. Thanks again. Health for the swamp people.

[Lee Mac]

This subfunction is for the calculation - IMO all error trapping should be in the calling function.

[Kerry]

soffit,
You will need to check that the 3 points in each plane are colinear (ie not in a straight line)
Then check that the planes are NOT coplanar (ie: that the normal (Z Direction) of one plane is not the same and does not negate the other plane.
Then you can run a routine similar to Lee's.

[Kerry]

Just to satisfy my curiosity,
How are you collecting these Points ??

[SOFITO_SOFT]

Hello:

Code: [Select]

;; Angle Between Planes - Lee Mac 2010
;; Args: p1,p2,p3 - Points on First Plane
;;       p4,p5,p6 - Points on Second Plane
;|
-  UPPER CASE CODE : ADDEMDUM VERIFICATION GEOMETRY CASES WITH SOLUTION BIZARRE BY SOFITO_SOFT :)
-  RETURN :
           nil                  = FAIL DATA... NO 2DPTS OR 3DPTS, CO-LINEAR PTS PLAN, nil PTS, VERY NEAR PTS
           0.0                  = PARALEL OR OVERLAP PLANS   !!! < REVISION
           >  0.0 REAL <  PI    = ONE OF 2 ANGLE INTER PLANS , ANOTER IS PI - RETURN
-  PARA PRUEBAS   
  ( ANGLEBETWEENPLANES  (G) (G) (G) (G) (G) (G) )
  ( DEFUN G (/) (GETPOINT) )
-  ORIGINAL
  (defun AngleBetweenPlanes ( p1 p2 p3 p4 p5 p6 )
  (
    (lambda ( u v )
      (acos (/ (vxv u v) (* (norm u) (norm v))))
    )
    (v^v (mapcar '- p3 p2) (mapcar '- p2 p1))
    (v^v (mapcar '- p6 p5) (mapcar '- p5 p4))
  )
)
|;

(defun AngleBetweenPlanes ( p11 p22 p33 p44 p55 p66 /

 P1  P2  P3  P4  P5  P6

)

; TOLER ES PUBLICA

( IF ( OR
       ( NOT TOLER )
       ( NOT ( NUMBERP TOLER ) )
     )
     ( SETQ TOLER 1E-8 )
)

 ( IF ( AND
 
         ( SETQ P1  (FUERZ_PUNTO3D P11))  ; PRUEBA PUNTOS Y 2D -> 3D (Z=0.0)
         ( SETQ P2  (FUERZ_PUNTO3D P22))
         ( SETQ P3  (FUERZ_PUNTO3D P33))
         ( SETQ P4  (FUERZ_PUNTO3D P44))
         ( SETQ P5  (FUERZ_PUNTO3D P55))
         ( SETQ P6  (FUERZ_PUNTO3D P66))
                           
         ( > (DISTANCE P1 P2) TOLER )     ; PRUEBA DISTINTOS
         ( > (DISTANCE P2 P3) TOLER )
         ( > (DISTANCE P4 P5) TOLER )
         ( > (DISTANCE P5 P6) TOLER )
         
         ( COLIN_3PUNTO P1 P2 P3 )        ; PRUEBA EXISTEN INTERS.-> NO CO-LINEALES
         ( COLIN_3PUNTO P4 P5 P6 )         
         
      )                           ; AND
 
  ( ABS
   (
    (lambda ( u v )
      (acos (/ (vxv u v) (* (norm u) (norm v))))     ; <- CODIGO MAGISTRAL !! :)
    )
    (v^v (mapcar '- p3 p2) (mapcar '- p2 p1))        ; <- CODIGO MAGISTRAL !! :)
    (v^v (mapcar '- p6 p5) (mapcar '- p5 p4))        ; <- CODIGO MAGISTRAL !! :)
   )
  )
 
 
 ) ; IF


)                ; DEFUN

(DEFUN ES_PUNTO (PUNTO /

)
  (AND (LISTP PUNTO)
        ( OR
           ( = 2 (LENGTH PUNTO) )
           ( = 3 (LENGTH PUNTO) )
        )
        (APPLY
  (FUNCTION AND)
  (MAPCAR (FUNCTION NUMBERP) PUNTO)
        )
       
  )
)

 

(DEFUN FUERZ_PUNTO3D (PUNTO /

)
  (IF (AND
        (LISTP PUNTO)       
(ES_PUNTO PUNTO)
      )
    (IF (CADDR PUNTO)
      (LIST (FLOAT (CAR PUNTO)) (FLOAT (CADR PUNTO)) (FLOAT (CADDR PUNTO)))
      (LIST (FLOAT (CAR PUNTO)) (FLOAT (CADR PUNTO)) 0.0)
    )   
  )
)


(DEFUN COLIN_3PUNTO (V11 V22 V33 /

V1  V2  V3

)

  (IF
    (AND
      (SETQ V1  (FUERZ_PUNTO3D V11))
      (SETQ V2  (FUERZ_PUNTO3D V22))
      (SETQ V3  (FUERZ_PUNTO3D V33))
      (NOT (EQUAL 0.0 (DISTANCE V1  V2 ) TOLER))
      (NOT (EQUAL 0.0 (DISTANCE V1  V3 ) TOLER))
      (NOT (EQUAL 0.0 (DISTANCE V2  V3 ) TOLER))
    )

     (INTERS V1  V2  V1  V3 )

  )
)


;; Vector Cross (Wedge) Product - Lee Mac 2010
;; Args: u,v - vectors in R^3

(defun v^v ( u v )
  (list
    (- (* (cadr u) (caddr v)) (* (cadr v) (caddr u)))
    (- (* (car  v) (caddr u)) (* (car  u) (caddr v)))
    (- (* (car  u) (cadr  v)) (* (car  v) (cadr  u)))
  )
)

;; Vector Dot Product - Lee Mac 2010
;; Args: u,v - vectors in R^n

(defun vxv ( u v )
  (apply '+ (mapcar '* u v))
)

;; Vector Norm - Lee Mac 2010
;; Args: v - vector in R^n

(defun norm ( v )
  (sqrt (apply '+ (mapcar '* v v)))
)

;; ArcCosine - Lee Mac 2010
;; Args: -1 <= x <= 1

(defun acos ( x )
  (if (<= (abs x) 1.0)
    (if (equal x 0.0 1e-8)
      (* pi 0.5)
      (atan (/ (sqrt (- 1.0 (* x x))) x))
    )
  )
)
I think that now is almost indestructible. The points are passed to other functions, such as "inters line / plan", "inters cone / line " "interes plan / planXY ", etc. It has given me many problems here. I want to do this in the picture. Thank you all for your interest.

[SOFITO_SOFT]

I have not much practice on this. 
[img=http://img337.imageshack.us/img337/5544/follonazodebarras2.th.jpg]

[Kerry]

Just for fun, try with these planes

Code: [Select]

(setq p1 '(-1000. 0. 0.)
      p2 '(0. 0. 0.)
      p3 '(0. 500. 100.)
      p4 '(1000. 0. 0.)
      p5 '(0. 0. 0.)
      p6 '(0. 500. 100.)
)

Code: [Select]

(setq p1 '(-1000. 200. 0.)
      p2 '(0. 0. 0.)
      p3 '(0. 500. 100.)
      p4 '(1000. 200. 100.)
      p5 '(0. 0. 0.)
      p6 '(0. 500. 100.)
)

[Kerry]

Lee, don't have time to play ..
Does that return the  Dihedral angle ?

Correct, the angle between the normals 

No, The dihedral angle is between faces, not between normals.