Reconstruction of Geometrical shapes (least squares method)...

Quite often, methods are available to compute canonic shapes or registration moving matrix; but generally these mathematical "exact" ways are disappointing for many reasons:

Point clouds are oversampled collection of points, then it is difficult to know which point should be chosen to make computation. Often more than 100000 points are candidates and choosing right points is very difficult.

Points coming from measurement are rarely exact. A measurement error exists and the goal is to manage this error carefully.

Inside 3DReshaper the word "best" means the possibility to handle a great number of points, finding the "best" solution of your problem in the least squares sense and to answer questions like:

What is the best sphere, plane, registration etc. with this set of 1,000,000 points?

What is the max. or average error?

Could I obtain a better solution rejecting 10% or 20% of the points? But, which point to keep or to reject?

Three main commands are available in the construction menu:

Best Shape: this command computes the best shape from an entity (plane, cylinder, circle, sphere, line, rectangular and round slots...). The whole object is supposed to represent the shape; but you can discard the worst points.

Extract Shape: this command identifies in a point cloud, a mesh or a contour the relevant points for the shape extraction, using:

a nominal or reference shape corresponding to the shape to be extracted,

a clipping zone which defines the points used for the extraction. Thus, it is possible to remove chamfers or hole borders containing too many outliers.

Quick Plane and Quick Cylinder: this command directly extracts planes, contours, holes and cylinders from one or several points without a reference shape.

The computation is immediate, just clicking the preview button. These high level algorithms increase dramatically the point clouds processing speed and the model accuracy.

The function "Discretize" transforms the selected geometrical shape into a polyline and/or a mesh.

These geometrical shapes (lines, plane, cylinder, circle, sphere, slots...) can be used in different ways:

To export inside your CAD system using IGES and DXF interfaces so that you can make CAD models. These shapes can be used in association with sections;

To make geometrical constructions: projections and intersections;

To make some measurement (and reports): distance between two holes, or two planes, flatness of a plane, planarity...
The measuring information can be displayed through an inspection label. Tolerance as referential values can be customized to adjust the potential deviation, deflection or inclination between the best shape and the measured model.

To separate the points of a cloud according to the created or extracted geometrical shape.

See the demonstration video.

3D inspection and measuring.

Geometrical shape creation and extraction functions enable the 3D measuring or/and the reconstruction of a light 3D model from a point cloud.

The user can adjust the tolerance to reject worst points and to obtain the most accurate result. Besides, he can display the deviation information through an inspection label with customizable referential values.