## New Release of OptoInspect3D Inline Version 2.4

OptoInspect3D Inline Version 2.4 was released in July and is now available. This new version includes a number of functional and performance improvements and several new features. One of the most important new features is the improved numerical stability and accuracy of the Minimum Zone computations using Chebyshev approximation methods.

### The key new features and improvements in Version 2.4:

- Improved numerical stability and precision for Chebyshev approximation methods
- Chebyshev(Minimum Zone)- best fit 3D line
- Minimum Enclosing Cylinder [new feature]
- Minimum Enclosing Planes [new feature]
- Algorithm for the calculation of a 3D convex hull [new feature]
- Improved speed of Least-squares (Gauss) approximation methods
- Iterative Closest Point: improved performance and stability for meshes (Least-Squares and Chebyshev)
- Iterative Closest Point: rotation center can optionally be fixed at the origin

## Shape evaluation using the “minimum zone“

The “minimum zone“ is often used in metrology for the evaluation of the shape of a specific geometry. In this context, the “minimum zone” is defined as the smallest possible area or distance between two geometrical objects, which enclose the shape (surface) that is to be investigated from both sides. To evaluate the cylindricity of an object – for example – two parallel concentric cylinders with a minimum and maximum radius are positioned in such a way, that the shape is completely contained in the area between the two cylinders and that the area between the two cylinders is as small as possible (cf. picture). If the “minimum zone” is small, this means that the shape is close to a cylinder.

Analogously, the planeness, roundness or straightness of geometrical shapes can be evaluated. For planeness – for example – the “minimum zone” is defined as the distance between two planes, for roundness as the distance between two concentric spheres.

## „Minimum Zone“ with Chebyshev

To get an accurate description and evaluation of the geometrical shapes it is important to have a „minimum zone“ that is as small as possible and closely resembles the geometric shape. With OptoInspect3D Inline the smallest possible “minimum zone” can be constructed easily. In the following, we take the example of a cylindricity analysis. As a first step, a best fit cylinder has to be generated for the measured point cloud. This best fit cylinder is commonly created by minimizing the sum of the squares of differences between the point cloud and the cylinder (the least-squares / Gauss method). However, OptoInspect3D Inline provides the alternative to minimize the maximum distance between the best fit cylinder and the pointcloud (Chebyshev method). In this case, the „minimum zone“ constructed with the Chebyshev best fit cylinder is by design minimal (and smaller than that produced by the Gauss method). Indeed, the “minimum zone” computed with the Gauss method is not the smallest region that is needed for evaluating the shape. This is why the “minimum zone” with Chebyshev should always be used for evaluating geometrical shapes (for example when investigating whether a bolt would fit inside a bore hole).