Topic: Coordinates in the triangle

[velasquez]

I have problem to calculate the coordinates of the point "xpto" in the triangle.
Can someone help me?

Tanks.

[Lee Mac]

"Cheating" with trans:

Code - Auto/Visual Lisp: [Select]

1. (defun tpt ( p1 p2 p3 / v )
2.     (setq v (mapcar '- p3 p1))
3.     (trans (cons (car (trans p2 0 v)) (cdr (trans p1 0 v))) v 0)
4. )
5.  

Assumes points are in WCS; compatible with UCS planes parallel to WCS plane only.

[Marc'Antonio Alessi]

"Cheating" with trans:

Code - Auto/Visual Lisp: [Select]

1. (defun tpt ( p1 p2 p3 / v )
2.     (setq v (mapcar '- p3 p1))
3.     (trans (cons (car (trans p2 0 v)) (cdr (trans p1 0 v))) v 0)
4. )
5.  

Assumes points are in WCS; compatible with UCS planes parallel to WCS plane only.

  Grande.

[ribarm]

Another convoluted though and untested...

Code - Auto/Visual Lisp: [Select]

1. (defun c:test ( / v^v projp2pp xpto p1 p2 p3 pt )
2.  
3.   (defun v^v ( u v )
4.     (list
5.       (- (* (cadr u) (caddr v)) (* (caddr u) (cadr v)))
6.       (- (* (caddr u) (car v)) (* (car u) (caddr v)))
7.       (- (* (car u) (cadr v)) (* (cadr u) (car v)))
8.     )
9.   )
10.  
11.   (defun projp2pp ( p p1 p2 / v nv n )
12.     (setq v (mapcar '- p2 p1))
13.     (setq nv (v^v (mapcar '- p p1) (mapcar '- p p2)))
14.     (setq n (v^v v nv))
15.     (inters p (mapcar '+ p n) p1 p2 nil)
16.   )
17.  
18.   (defun xpto ( p1 p2 p3 / pp )
19.     (setq pp (projp2pp p2 p1 p3))
20.     (mapcar '+ p1 (mapcar '- p2 pp))
21.   )
22.  
23.   (initget 1)
24.   (setq p1 (trans (getpoint "\nP1 : ") 1 0))
25.   (initget 1)
26.   (setq p2 (trans (getpoint "\nP2 : ") 1 0))
27.   (initget 1)
28.   (setq p3 (trans (getpoint "\nP3 : ") 1 0))
29.   (setq pt (xpto p1 p2 p3))
30.   (entmake (list '(0 . "POINT") (cons 10 pt)))
31.   (princ)
32. )
33.  

[roy_043]

Interesting stuff, no doubt. But I don't understand. I see a green and a yellow line that are not parallel to any of the magenta lines.

[velasquez]

Interesting stuff, no doubt. But I don't understand. I see a green and a yellow line that are not parallel to any of the magenta lines.

Hello Roy

The yellow line and a green line are to show the location of the coordinates that I need to find. The angle between these lines is always 90 degrees.

[roy_043]

Interesting stuff, no doubt. But I don't understand. I see a green and a yellow line that are not parallel to any of the magenta lines.

Hello Roy

The yellow line and a green line are to show the location of the coordinates that I need to find. The angle between these lines is always 90 degrees.

I guessed as much. But the other contributors have made the assumption that the green line is parallel to a magenta line. Conclusion: your image is quite confusing.

[Stefan]

"Cheating" with trans:

Code - Auto/Visual Lisp: [Select]

1. (defun tpt ( p1 p2 p3 / v )
2.     (setq v (mapcar '- p3 p1))
3.     (trans (cons (car (trans p2 0 v)) (cdr (trans p1 0 v))) v 0)
4. )
5.  

Assumes points are in WCS; compatible with UCS planes parallel to WCS plane only.

Nicely done Lee, direct and concise...
This one works for any 3d points

Code - Auto/Visual Lisp: [Select]

1.     (setq v (mapcar '- p3 p1)
2.           p1 (trans p1 0 v)
3.           p2 (trans p2 0 v)
4.     )
5.     (trans (list (car p2) (cadr p2) (caddr p1)) v 0)

[velasquez]

I'm sorry if the picture was confusing.
The functions always return the coordinate of p2, I need to find out the coordinate of the xpto point.
Remembering that I always have p1 p2 and p3. I posted a drawing showing some triangle situations.

Tanks.

[ribarm]

So...
Cyan line is not parallel to p1p3 line?
Then how do you get cyan?

[kirby]

There are an infinite number of rays from P1 and P2 that are perpendicular to each other.  You need to add another constraint (eg. ray from P1 is parallel to X axis, etc.)

[velasquez]

The point you need to calculate is always the projection from point p1 to the projection of point p2 at an angle of 90 degrees.

[ribarm]

Men, like Kirby explained, there are infinite number of possibilities of such projections - you don't say at which orientation is either cyan or perpendicular projection... Just create half circle from p1 to p2... All points on that half circle could be xpto point + half circle can rotate in 3d around p1 p2 axis which makes it sphere of infinite xpto points on its surface...

[velasquez]

Men, like Kirby explained, there are infinite number of possibilities of such projections - you don't say at which orientation is either cyan or perpendicular projection... Just create half circle from p1 to p2... All points on that half circle could be xpto point + half circle can rotate in 3d around p1 p2 axis which makes it sphere of infinite xpto points on its surface...

Hello Ribarm,

Please note the drawing I posted, what I need is to learn to calculate the coordinate of the point described as xpto, in relation to the x and y axes.
Using the id command at the end of the green line will show this.

I'm sorry but I can not show it better.

Thanks

[Lee Mac]

Nicely done Lee, direct and concise...
This one works for any 3d points

Thanks Stefan, in hindsight that makes more sense. 

Interesting stuff, no doubt. But I don't understand. I see a green and a yellow line that are not parallel to any of the magenta lines.

The yellow line and a green line are to show the location of the coordinates that I need to find. The angle between these lines is always 90 degrees.

I assumed that P3-P1 was parallel to P2-XPTO; without this assumption, any point on the circle with diameter P1-P2 meets your criteria -



Hence there would be infinite solutions, as kirby correctly notes.