This document aims at characterizing and giving more details about fixtures used in test modules, in order to clarify the philosophy of feature testing.
Six point clouds with simple shapes have been drawn in order to describe basic geometric patterns. There are respectively lines, planes, spheres, vertical tubes, walls and roofs.
The simple geometric shape is the 1D-line.
Defined only over x-axis, it does not imply any 2D or 3D characteristic. Regarding the point cloud decomposition, one has only one high eigenvalue denoting the distribution of points over the x-axis. Other eigenvalues are negligible (hence the two less important vectors do not appear on the figure). The eigenvector that corresponds to the highest eigenvalue is oriented along the line.
Considering a plane-shaped point cloud, one has to expect a strong 2D spreading around x- and y- axis.
By depicting the point cloud eigenvectors, this characteristic is confirmed, as the third eigenvalue looks negligible. The two main eigenvectors draw a 2D-space along the x-y plane, and both vectors are of comparable importance.
The sphere is the archetypal 3D point cloud, with a equal repartition of values along the three axis.
Drawing eigenvectors provides a view of the three dimension balanced importance: one has three orthogonal vectors of comparable length.
The vertical tube is a particular case of 1D-line, where points are spreading along the z-axis, instead of the x-axis.
As for the line case, one has only one significant eigenvalue, that is associated with a fairly vertical eigenvector.
This particular fixture will be used for highlighting verticality.
The wall fixture is a particular case of the plane. Walls may generally be
defined with only two coordinates (z, plus x, y or a linear combination
of x and y), one can resume the point cloud information by a 2D
representation. Hence the wall is a 3D structure that has a line-shaped
projection over the xy-plane.
Indeed, there are only two significant eigenvalues in such cases, and eigenvectors draw a 2D-plane that follows the point spatial distribution.
The roof-shaped point clouds come as a last base fixture. This is a
3D-structure composed of two sloping planes; its projection over the xy-plane
represents a plane.
There is no "negligible" eigenvalue, strictly speaking. However the third eigenvalue is significantly smaller than the first ones. Third 3D-shaped type of point cloud will be characterized by a particular set of geometric features (as an example: verticality coefficient of roofs are close to 0).
It has to be noted that depending on the point cloud resolution, such pattern may be rare.