Math Is Fun Forum

entone

Member

Registered: 2008-03-27

Posts: 3

Plane Equation

Hi,
Given two planes A and B, each of them are in the form of Parallelogram with known vertices.

Eg. For plane A there are four points(p1,p2,p3, and p4) as the four vertices of the parallelogram. And also there are for plane B.

I want to check whether a given point, eg.(6,10,3), is in between  of these two planes or not. How can i do this? can you give me a step by step solution or example how to solve this.

Regards,

mathsyperson

Moderator

Registered: 2005-06-22

Posts: 4,900

Re: Plane Equation

I'm not sure what you mean by 'in between'. Are the planes restricted to being parallel to each other? If they're not, I can't think how a point could be between them.

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Why did the vector cross the road?
It wanted to be normal.

John E. Franklin

Member

Registered: 2005-08-29

Posts: 3,588

Re: Plane Equation

If you want to just do a really rough check, you can average all 8 points to
get the middle point between the two parallelograms.  Then see if your
point of interest is within a certain radius from that middle.
The radius is half the distance between the centers of each parallelogram.
Those 2 centers are just the average of their 4 points.
And the distance formula is "distance" = squareRootOf(xDifference^2 + yDifference^2 + zDifference^2)

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igloo myrtilles fourmis

entone

Member

Registered: 2008-03-27

Posts: 3

Re: Plane Equation

yes they are parallel.
Now i want to kno how to write a plane equation from the above vertices(vertices of plane A and B) in the form of plane equation Ax+By+Cz+D=0. After getting equation for two planes is there any way to check the given point is between of these two plane or not?

Regards,

entone

Member

Registered: 2008-03-27

Posts: 3

Re: Plane Equation

For more information the points are:

(10,10,10), (50,10,15),(55,20,10),(15,20,5)-----Plane A.

(20,10,0), (60,10,5),(65,20,0),(25,20,-5)-------Plane B.

John E. Franklin

Member

Registered: 2005-08-29

Posts: 3,588

Re: Plane Equation

use these equations to get A,B,C, and D.
http://local.wasp.uwa.edu.au/~pbourke/geometry/planeeq/
Now the A, B, C will be the same for both planes.
Your D values will be the limits for your
determination of being between the planes.
When you get a point to check,
then calculate Ax + By + Cz and if it is in between
your 2 values of D, then you are between the planes!!!!
I hope I'm right, since I just learned this a bit.

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igloo myrtilles fourmis

entone

Member

Registered: 2008-03-27

Posts: 3

Re: Plane Equation

Thank you very much