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lvl10720-Turquoise
20-Turquoise
September 1, 2022
Solved

Co-planar or non-Co-planar with 4 points ?

Hi Everyone.
From the following :

Co-planar.PNG

Co-planar or non-Co-planar with the 4 points ?
Thanks in advance for your time and help.
Best Regards.
Loi.

 

terryhendicottAnswer
21-Topaz II
September 1, 2022

Hi,

A small program that takes the first three points expressed as vectors and calculates the equation of that plane defined by those three points.

Program then calculates the distance from the fourth point represented as a vector from the plane of the other three.

If the distance is zero the four points are coplanar.  If there is a positive distance then points are not coplanar.

Capture.JPG

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5 replies

terryhendicott21-Topaz IIAnswer
21-Topaz II
September 1, 2022

Hi,

A small program that takes the first three points expressed as vectors and calculates the equation of that plane defined by those three points.

Program then calculates the distance from the fourth point represented as a vector from the plane of the other three.

If the distance is zero the four points are coplanar.  If there is a positive distance then points are not coplanar.

Capture.JPG

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    Werner_E
    Werner_E25-Diamond I
    25-Diamond I
    September 1, 2022
    @terryhendicott wrote:

    Hi,

    A small program that takes the first three points expressed as vectors and calculates the equation of that plane defined by those three points.

    Hmmm, and what if the first three points happen to lie on a straight line (colinear), but the fourth does not? In this case the four points would be coplanar, but your program returns an error because of a division by zero (the "normal vector" is the zero vector here).
    And even if all four points should be co-linear and they don't define a plane uniquely, the program would have to come to the result that they are of course also co-planar (even in an infinite way).

     

    BTW, is there a special reason why you don't use Werner_E_2-1662026082471.png ?

     

     

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      Werner_E
      Werner_E25-Diamond I
      25-Diamond I
      September 1, 2022

      Her is a function to check for coplanarity of a vector of point coordinates of arbitrary length. I hope that I got all special cases.
      This boolean function returns 1 if the points are coplanar and 0 otherwise.

      Werner_E_0-1662033528163.png

       

      "coplanar2" is to be preferred as it also deals with the numerical inaccuracies which may occur when dealing with real numbers.

      Werner_E_2-1662033826023.png

       

       

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