Bài báo trình bày giải thuật nội suy theo phương pháp nội tiếp lớn nhất(MI) và ngoại tiếp bé nhất(MC). Chúng tôi dùng các phương pháp nội suy này để xây dựng phần mềm cho CMM(máy đo tọa độ) trong trường hợp của đường tròn, mặt cầu và mặt trụ. | TẠP CHÍ PHÁT TRIỂN KH&CN, TẬP 13, SỐ K4 - 2010 MAXIMUM- INSCRIBED AND MINIMUM- CIRCUMSCRIBED FITTING FOR CO-ORDINATE MEASURING MACHINE Thai Thi Thu Ha(1), Nguyen Hong Phuoc (1) University of Technology, VNU-HCM (2) Digital Control and System Engineering Lab, VNU-HCM (Manuscript Received on July 09th, 2009, Manuscript Revised December 29th, 2009) ABSTRACT: This paper describes algorithms that fit geometric shapes to data sets according to maximum- inscribed (MI) and minimum- circumscribed (MC) fit. We use these fits to build the CMM’s (Coordinate Measuring Machine) software in cases of circle, sphere and cylinder. For each case, we obtain the fit by two methods: first, by (relative easy) least squares fit method and then refine by MI and MC fit method. Although, the later method is substantially more complicated than the former one, Its results are used to make comparision with the the results of least squares method in order to give more options in the CMM software. In the near future we will continue to develop MI and MC fit with an effective algorithm- Simulated Annealing algorithm. solve the fitting problem. There are four fitting 1. INTRODUCTION algorithms which are commonly used in CMM This paper summarizes works carried out in Coordinate Measuring are Least Squares Fit, Minimum Circumscribed Machine Fit, Maximum Inscribed Fit and Chebyshev Fit Manufacturing project. The aim of our project (Minimum Zone Fit). Table 1 describes the was to introduce the reference algorithm to applicability to basic geometric shapes. Table 1. Applicability to geometric shapes. Least- Min- Min- Max- Square Zone Circumscribe Inscribe d d s Line X X Plane X X Circle X X X X Sphere X X X X Cylinder X X X X Cone X X Trang 5 Science & Technology Development, Vol 13, 2010 Coordinate measuring machine (CMM) software has long used least-squares fit calculations to construct resolved geometry representations of measured features. .
