FitPlaneToPoints for colinear points does not result in 'inconclusive'

Scripting
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1

If you pass three or more colinear points or points in the same location to Plane.FitPlaneToPoints the FitPlaneResult shows “Success”. Shouldn’t that be “Inconclusive” instead?

from Rhino.Geometry import Plane, Point3d

pts = [Point3d(0,0,0),
       Point3d(1,1,1),
       Point3d(2,2,2)]
fitResult, plane = Plane.FitPlaneToPoints(pts)

print(fitResult)
2

Hi @trademacher

In any case the plane would be inconclusive/arbitrary as even with points scattered exactly on a plane, the orientation of the X and Y axes (rotation around the Z-Axis) can not be derived from the input points.
So any plane will be arbitrary.

The plane in your example is valid and contains the 3 points.

image

I visualized it with this:

from Rhino.Geometry import Plane, Point3d
import rhinoscriptsyntax as rs

pts = [Point3d(0,0,0),
       Point3d(1,1,1),
       Point3d(2,2,2)]
fitResult, plane = Plane.FitPlaneToPoints(pts)

print(fitResult)

rs.AddPoints(pts)

xid = rs.AddLine(plane.Origin, plane.Origin + plane.XAxis * 10)
yid = rs.AddLine(plane.Origin, plane.Origin + plane.YAxis * 10)
zid = rs.AddLine(plane.Origin, plane.Origin + plane.ZAxis * 10)

rs.ObjectColor(xid, [255, 0, 0])
rs.ObjectColor(yid, [0, 255, 0])
rs.ObjectColor(zid, [0, 0, 255])

Furthermore the method attempts to fit a plane, there is no mention of constructing a plane that contains all input points:

image

from Rhino.Geometry import Plane, Point3d
import rhinoscriptsyntax as rs
import random


pts = [Point3d(random.random(),random.random(),random.random()),
       Point3d(random.random(),random.random(),random.random()),
       Point3d(random.random(),random.random(),random.random()),
       Point3d(random.random(),random.random(),random.random()),
       Point3d(random.random(),random.random(),random.random()),
       Point3d(random.random(),random.random(),random.random()),
       Point3d(random.random(),random.random(),random.random()),
       Point3d(random.random(),random.random(),random.random())]
       
       
fitResult, plane = Plane.FitPlaneToPoints(pts)

print(fitResult)

rs.AddPoints(pts)

xid = rs.AddLine(plane.Origin, plane.Origin + plane.XAxis * 10)
yid = rs.AddLine(plane.Origin, plane.Origin + plane.YAxis * 10)
zid = rs.AddLine(plane.Origin, plane.Origin + plane.ZAxis * 10)

rs.ObjectColor(xid, [255, 0, 0])
rs.ObjectColor(yid, [0, 255, 0])
rs.ObjectColor(zid, [0, 0, 255])
3

Hi Willem,

thanks for your reply. I total agree with you. As long as you provide three or more points the FitPlaneToPoints method returns a valid and optimal (with respect to points deviation) plane. However, according to the documentation for line-aligned points and points in the same location the PlaneFitResult should be “Inconclusive=1” and not “Success=0”:

image
image1978×732 44.3 KB

So it’s not about the resulting plane. I struggle with the value of the fitResult.

1 Like
4

Ah I see,

Sorry did not read that documentation well enough.
However the wording “this might happen” indicates to me that it’s not always when points are co-linear but there are situations of co-linear points that trigger an inconclusive return…

I think only a McNeel developer can confirm or deny my conclusion.

-Willem