Multi-Object Queries

from geo3d.query import distance_between_points, minimize_points_to_points_distance, distances_plane_to_points
from geo3d import Point, Plane, Vector

Point-to-Point Distance

The distance between points can be queried as

pointA = Point([1,2,3])
pointB = Point([1,2,6])
distance_between_points(pointA, pointB)

3.0

Plane-to-Points Distance

The distance from a plane to an array of points, positive along the plane normal vector.

plane = Plane(
    normal=Vector([0,0,-1]),
    point=Point([1,2,0])
)
points = [[1,2,3], [1,2,6]]
distances_plane_to_points(plane, points)

array([-3., -6.])

Transformation minimizing group-to-group distance

For two point groups, find the transformation – applied to the first group – that minimizes the RMS distance between the corresponding points in the two groups:

Here, we extract a rotation of 90 degrees between the point groups, that is, groupA needs to be rotated by 90 degrees to coincide with groupB.

groupA = [[1,0,0], [0,1,0], [-1,0,0], [0,-1,0], [0,0,1], [0,0,-1]]
groupB = [[0,1,0], [-1,0,0], [0,-1,0], [1,0,0], [0,0,1], [0,0,-1]]
minimize_points_to_points_distance(groupA, groupB)

rotation matrix	Fixed angles (xyz, extr., deg.)	Euler angles (xyz, intr., deg.)	translation
-0.00000000 -1.00000000 0.00000000 1.00000000 -0.00000000 -0.00000000 0.00000000 0.00000000 1.00000000	θx 0.00000 θy -0.00000 θz 90.00000	θx 0.00000 θy 0.00000 θz 90.00000	x 0.00000 y 0.00000 z 0.00000