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# 3DPoints on same plane

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Basic question: how to know if 3 or more points are in same plane on space?

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3 points will always lie in a plane, won''t they?
Not sure what you mean.

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The plane''s equation is: A x + B y + C z + D = 0

Vector (A,B,C) is the plane''s geometric normal and can be easily computed using a cross-vector multiplication with 3 points and then solve for D. Introducing the fourth point in the equation above will equate to zero (0) if it is to lie on the plane. I leave it to you to fix the tolerance needed for this to be true.

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quote:
Original post by Tybalt
3 points will always lie in a plane, won''t they?
Not sure what you mean.

Of course, no! They can form a line

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if they form a line then that''s the case when the 3 points are on the same plane .

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I wrote:
"I leave it to you to fix the
tolerance needed for this to
be true."

Of course, there are several ways the equation will break down leading to more complex algorithmics:

a) all points are equal
b) points are co-linear
c) floating-point imprecisions
c1) points are too far away from the origin
c2) points are almost co-linear
c3) points are almost equal (too close)
d) bad selection of 3 out of 3+N points

Regardless of the scenario, you will have to find the set of reasonnable assumptions that will make your code work at optimum speed. I can''t make that decision for you.

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3 points will always lie on a plane, since three points are needed to actually create and define a plane. The line situation is a special case: they still lie on a same plane, but they don't define a specific one.

Edit: unless you mean to check if some arbitrary point lies on another, arbitary plane, independently defined by it's normal and D offset. In that case, you can use the plane equation, as cbenoi1 mentioned.

[edited by - Yann L on February 7, 2003 10:28:10 AM]

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think he wants to know how to decide wether the plane of the 3 points is equal to another given plane

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