Product quality is a main concern in today manufacturing. It is a fundamental requirement for companies to be competitive. To assure such quality, a dimensional inspection to verify geometric property of a product has to be carried out. High speed non contact scanners help this task, by both speeding up acquisition speed and increasing accuracy through a more complete description of the surface. The algorithms for the management of the measurement data play a critical role in ensuring both the measurement accuracy and speed. One of the most fundamental parts of the algorithm is procedure for fitting substitute geometry to the cloud of points. This article addresses this challenge. Three relevant geometries are selected as case studies: non-linear least-square fitting of circle, sphere and cylinder. These geometries are chosen with consideration of their common use in practice; for example the sphere is often adopted as reference artifact for performance verification of coordinate measuring machine (CMM) and cylinder is the most relevant geometry for pin-hole relation as an assembly feature to construct a complete functioning product.In this article, an improvement of the initial point guess for Levenberg-Marquardt (LM) algorithm by employing Chaos Optimization (CO) method is proposed. This causes a performance improvement in the optimization of a non-linear function fitting the three geometries. The results show that, with this combination, higher quality of fitting results in term of smaller norm of the residuals can be obtained while preserving the computational cost. Fitting a "incomplete-point-cloud", which is a situation where the point cloud do not cover a complete feature e.g. from half of the total part surface, is also investigated. Finally, a case study about fitting a hemisphere is presented.