
Re: Interpolated Plane from 4 points
Bjorn Hulman Jan 16, 2013 8:27 AM (in response to Mike Price)Will the points create a flat plane? If so, creating a plane from three of those points would intersect the 4th anyhow. If not, perhaps create a surface by creating a 3d sketch to join the points and insert a boundary surface, add a transparent material to it if you like.

Re: Interpolated Plane from 4 points
Mike Price Jan 16, 2013 8:29 AM (in response to Bjorn Hulman)The plane would be a geometry entity, so yes, it would be flat. The fourth point would not be located on the plane created by 3 of the points.
Therefore, that is why I need to interpolate a plane somehow.

Re: Interpolated Plane from 4 points
Kelvin Lamport Jan 16, 2013 8:40 AM (in response to Mike Price)Create two planes using two common points and one of the other points, and then create a midplane from those two planes.

Re: Interpolated Plane from 4 points
Bjorn Hulman Jan 16, 2013 9:07 AM (in response to Kelvin Lamport)That's an elegant solution.


Re: Interpolated Plane from 4 points
Chris Michalski Jan 16, 2013 8:41 AM (in response to Mike Price)what are your criteria? minimize the standard deviation from points to plane? With the 4 planes that those 4 points create you've got a lot of lattitude depending on functionality.

Re: Interpolated Plane from 4 points
Mike Price Jan 16, 2013 9:09 AM (in response to Chris Michalski)Kelvin, that gives me two planes that are not parallel.
Chris, I'm hoping to get all 4 points equidistant from the plane.
Imagine I have a rectangle 20mm x 10 mm. Call one corner 1 and rotate around to each one CW to get corners 2,3,4
Corner one will have a Z point of x mm, corner 2 will have Z point of y mm, etc.
So I have a rectangle with common x, y coordinates, but different Z coordinates.

Re: Interpolated Plane from 4 points
Chris Michalski Jan 16, 2013 9:57 AM (in response to Mike Price)If you choose 3 points and make a plane, then determine the distance from the 4th point perpendicular to this plane (x), then offset the plane by 1/2 of (x). Now each of your original 3 would be 1/2(x) away and the 4th would also be 1/2(x) away on the other side.
The problem is, this holds true for any 3 points you choose for your initial plane. There is no one answer, but a set of possible answers.



Re: Interpolated Plane from 4 points
Jim Sculley Jan 16, 2013 10:57 AM (in response to Mike Price)This is a linear algebra problem, not a modeling problem:
http://www.geometrictools.com/Documentation/LeastSquaresFitting.pdf
Section 3.
Jim S.

Re: Interpolated Plane from 4 points
Mike Price Jan 16, 2013 11:54 AM (in response to Jim Sculley)Hi Jim,
I've labeled this as the correct answer and understand, but I was hoping to "cheat" through 3d modeling to determine this plane.


