How to get distance of vertices from an arbitrary plane in Python?

Question

I have an arbitrary oriented plane and an object "above" it.
I would like to calculate the distance from the plane for each vertex in that object.

Hopefully this screenshot illustrates the idea (the purple line would be the distance of one of the vertices):

I suppose some kind of a transformation of vertex global coordinates to the local orientation of the plane would be the way to go, however, I'm too new to Blender to know even what to search for (I did try searching for mentioned keywords but didn't find something I could figure out, unfortunately).

I know how to iterate trough vertices of an object and get global coordinates, no problems with that.

Edit:
As Chebhou suggested I tried using the mathutils.geometry.distance_point_to_plane(pt, plane_co, plane_no) but cannot get it to work.
For testing I'm using a 2x2x2 cube at (0,0,1) and 6x6x6 plane at (0,0,0):
The code is this (shortened for clarity):

point_location = thecube.location

planepoint_location_w = theplane.matrix_world * theplane.data.vertices[0].co

plane_normal = theplane.matrix_world * theplane.data.polygons[0].normal

distance = geometry.distance_point_to_plane(point_location, planepoint_location_w, plane_normal)
print("point_location = ", point_location)
print("planepoint_location_w = ", planepoint_location_w)
print("distance = ", distance)

The result for the cube and plane location as in the pic is OK (the point is 1 unit above the plane):

point_location =  <Vector (0.0000, 0.0000, 1.0000)>  
planepoint_location_w =  <Vector (-3.0000, -3.0000, 0.0000)>  
distance =  1.0

However, if I move the plane on Y axis to (0,1,0) the result is this (but should be the same as before):

point_location =  <Vector (0.0000, 0.0000, 1.0000)>
planepoint_location_w =  <Vector (-3.0000, -2.0000, 0.0000)>
distance =  2.1213202476501465

Obviously I'm doing something wrong - but what?

https://www.blender.org/api/blender_python_api_current/mathutils.geometry.html?highlight=plane#mathutils.geometry.distance_point_to_plane — Chebhou, May 04 '16 at 17:47
when you solve the problem write an answer, and if you need help just ask — Chebhou, May 04 '16 at 17:51
Thanks @Chebhou! It never occurred to me that there could be something like distance_point_to_plane! I'm looking into it ... — spacer, May 04 '16 at 21:08
@Chebhou, I'm almost there but I think I'm giving it wrong parameters - should the parameters be global or local to the plane? For example, should the plane_co (a point on the plane) be like theplane.data.vertices[0].co or should it be corrected for plane's rotation? — spacer, May 04 '16 at 21:56
( i think ) they are supposed to be global, and theplane.data.vertices[0].co will do after converting to global — Chebhou, May 04 '16 at 22:09
@Chebhou, OK, I'm converting it to global with theplane.matrix_world * theplane.data.vertices[0].co but it still does not work right. What about the plane_no (direction the plane is facing) parameter - is that supposed to be converted to global too? I'm doing it but no go. I'll edit the question and add the test code ... — spacer, May 04 '16 at 22:31
@Chebhou, I am doing that - I updated the question to show the test code. — spacer, May 04 '16 at 22:58

Chebhou · Accepted Answer · 2016-05-04T23:39:50.070

3

You can use the dedicated function :mathutils.geometry.distance_point_to_plane(pt, plane_co, plane_no) were you supply the plane normal and one point from it, and the point you want to calculate the distance to as in the following example :

import bpy
import mathutils

plane = bpy.context.scene.objects['Plane']
p1 = plane.matrix_world*plane.data.vertices[0].co
p2 = plane.matrix_world*plane.data.vertices[1].co
p3 = plane.matrix_world*plane.data.vertices[2].co
plane_no = mathutils.geometry.normal([p1, p2, p3])

obj = bpy.context.object
mat = obj.matrix_world

for v in obj.data.vertices:
    pt = mat*v.co
    d = mathutils.geometry.distance_point_to_plane(pt, p1, plane_no)
    print(round(d, 4))

edited May 04 '16 at 23:39

answered May 04 '16 at 22:56

Chebhou

19,533
51
98

Thanks but this does not produce correct result - run it on the test example from my edit (cube at (0,0,1) and plane at (0,1,0) and it should give distance of 0 for four bottom vertexes, but it does not ... – spacer May 04 '16 at 23:16
it seems that the converting to global is the problem – Chebhou May 04 '16 at 23:18
Yes, I just run a test that uses all 8 possible combinations of local & global parameters and none of them gives correct result! – spacer May 04 '16 at 23:19
see if this helps ? – Chebhou May 04 '16 at 23:21
Unfortunately not. – spacer May 04 '16 at 23:24
Wait, maybe it does work - I get results like 1.3648547108754573e-17 – spacer May 04 '16 at 23:25
can you give me the full script ? in my script you have to select the cube before running the script – Chebhou May 04 '16 at 23:27
OK, it does actually work! The very small results are probably internal rounding errors. – spacer May 04 '16 at 23:30
which one of them ? – Chebhou May 04 '16 at 23:31
1

The edit works. Just replace print(round(d, 4)) and it will show zeros correctly. – spacer May 04 '16 at 23:34
Can you, please, edit the answer and remove the first solution to make it "clean" and I'll accept it :) – spacer May 04 '16 at 23:38

score 0 · Answer 2 · answered May 05 '16 at 01:03

0

I have found why my attempt to convert plane's normal by using plane_normal = theplane.matrix_world * theplane.data.polygons[0].normal failed - it is because matrix_world gives 4x4 matrix and the normal is 1x3 vector.

Instead I should have used matrix_world.to_3x3():

plane_normal = theplane.matrix_world.to_3x3() * theplane.data.polygons[0].normal

and it would have worked.

answered May 05 '16 at 01:03

spacer

901
7
21

See here Above will work correctly only when the origin is on the poly. – batFINGER Oct 23 '18 at 10:05

How to get distance of vertices from an arbitrary plane in Python?

2 Answers2