Geometric tool

The Geometric Tool contains several functions to process COP data.

Plane Functions

This library contains several functions related to 3D planes:

• Build a plane from Three Points
• Fit a plane from COP data
• Compute the distance between a point and a plane
• Get the movement to align a given plane parallel to Z plane

This function could be used to orientate a COP parallel to the plane Z = 0. After that, when getting a ZMap from this oriented COP, the projection will be perpendicular to the desired plane.

The following pictures describes the problem to control a hole on an arbitrarely plane. If we directly generate the ZMap, the hole appears elliptical due to the projection. However, after aligning the plane to Z axis, the projection of the hole is perfectly circular. So, 2D tools can be used to measure the diameter in pixels units. In addition, the ZMap factors allows the user to convert this pixels units to metric values. Moreover, this example shows the robustness of the algorithm to cope with some points not belonging to the main plane.

Plane Fitting for ZMap orientation

COP	Generated ZMap	Generated ZMap after COP orientation

Please, look Advantages of ZMap to get more information about the advantages of rotating a COP before computing the ZMap.

Applications

The plane fitting could be use in different applications

• Planarity control: The ZMap after orientation is directly a measure of planarity. In addition, the function distanceToPlane could be use to get more accurate results
• Control angles between several planes: When the plane equation is known, a simple dot product can be used to compute the angle between two different planes.
• Align ZMap to Z axis to combine with 2D tools

Sphere Functions

• Fit a Sphere on a list of points This function determines the radius and the center of a sphere that best fits the list of points assuming that all points belong to the sphere.