Plane-Line intersection (Little contest)


#1

The intersection between a plane and a line is a point.
The challenge is discovering the way of calculating that point with Blender tools, using some geometric reasoning.
Exercising to bypass sucky Blender booleans.


#2

my first google-result:
http://astronomy.swin.edu.au/~pbourke/geometry/planeline/

ofcourse, an understanding of the dot-product is needed…


#3

I mean
- calculated with Blender tools,
- no scripts involved,
- with some geometric reasoning behind.

Example file.


#4

Alvarus, Sunday is supposed to be a day of rest :).

I’ve been working on this for a couple of hours now and still no nearer a solution. Do you have an answer? I know how to get the position of the point using trig and the results from turning the edge length and edge angles buttons on, but from your posts I’m pretty sure that’s not the way to do it that you’re thinking of and anyway it’s not very elegant.

Back to the grindstone.

A


#5

Yes, I have it.
And It is an easy answer.


#6

the newest version of wings can do it via the intersect command. you could poke around the developer forums over there or if you’re really brave you could have a look at the source code.

i’ve used the intersect command myself for manual booleans, so i can vouch for its efficacy.


#7

I mean calculated with Blender editing tools.
It is not an exact result (we would need some maths and coding to do that) but quite an aceptable one, a very good approacching and backed by geometric logic.
Use your 3D brain, not your eyes.
And I’m not pulling your leg.:slight_smile:

  [img]http://img17.imageshack.us/img17/562/sinnombre36jr.jpg[/img]

#8

I mean calculated with Blender editing tools.

yes i understood you. i was suggesting the answer may be found elsewhere.

edit: ok i reread this thread. it seems you already know the answer. in that case, please tell! it must have something to do with local or normal space and scaling? maybe?


#9

how about this:

  1. extend the edge(s) containing the vert(s) through the plane to be intersected.

  2. subdivide or loop cut the edge(s).

  3. switch from bounding box to 3d cursor mode. snap the 3d cursor to the vert that is below the plane to be intersected. select the middle vert. hit s and begin scaling. the vert will now slide along the edge, maintaining the straightness of the edge. repeat for remaining verts. it’s best to select the face before this step, and hit shift s and select side view. it will make eyeballing the intersection easier.

  4. all that remains is to delete the extra verts below the plane of intersection.

having written all this, it would probably be easier to use the knife tool on something so simple, however this method will work for more complex intersections.

this method is inspired by the wings3d intersect command.

i doubt this is what you had in mind since it is not 100% accurate.


#10

alvarus, i just checked out your two aircraft wips. they’re bloody fantastic! do you ever go here: www.military-meshes.com ?


#11

Hi, TroutMaskReplica,
Your method is quite accurate, the key is the view aligned with the intersecting plane (step 3). I think is an acceptable one, since IMO for an exact result we would need some coding and maths.

 However, my method is quite diferent. I recommend practising it first only with a line:
 In an ortho [b]Side View[/b] (therefore a perpendicular one), calculate the projection of the line onto the plane:
 [img]http://img75.imageshack.us/img75/5329/17pa1.jpg[/img]
 
 Then, in a ortho [b]Front View[/b], we have a two lines.
 [img]http://img158.imageshack.us/img158/866/25oi.jpg[/img]
 
 Finally, choose a vertice as pivot and scale the line untill the opposite vertice is on the intersection.
 [img]http://img306.imageshack.us/img306/7066/36ak.jpg[/img]
 
 That's all. We have found the damn intersection ([experiment6.zip](http://forums.cgsociety.org/attachment.php?attachmentid=77011&stc=1))

TroutMaskReplica, I'm already participating in [b]M&M[/b] forums as [b]Alvaro [/b](the same avatar as here). You can find my recent works in the [b]3D Aviation Hanger [/b]forum. Thank you.

#12

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