Least Square Fitting with Correction Factor of Circle and Ellipse

• Main Authors: Chih-Hsiang Chang, 張智祥
• Other Authors: 黃溪泉
• Format: Others
• Language: zh-TW
• Published: 2007
• Online Access: http://ndltd.ncl.edu.tw/handle/34816868471264649343

碩士 === 國立中興大學 === 機械工程學系所 === 95 === Conic includes ellipse, hyperbola and parabola. In engineering application, curve fitting from a set of measured data at discrete points for the ellipse (including circle) are widely desired. Furthermore, since the ellipse gas closed boundary, its application is also much expanded. There application arise in computer graphics, statistics, metrology, astronomy, etc. In practice, the measured data on the manufactured part are normally obtained by using a coordinate measuring machine (CMM), which is a device with a probe moving in a particular direction and identifies the coordinates of the points on the surface. Each measurement data the information is not necessarily expected, it might be better data can be, measurement error or a lack of precision caused. Each one of these experiments, many of the needs of their time, spirit and money. Mapping project areas such as Auto CAD for the second curve, Rendering process must be based on parameters related to the use of vector technology, But the formula is expressed in the details and information (including the center, radius, focus, major axis, minor axis, Vertex, etc.) will not be given. This study , the quadratic equation is derived parameters of all relative information, however, fitting for the process is the use of quadratic equations by each graphic geometric characteristics, such as a circle posed by the data, first use the Least Square method find out every parameters, and then every data points calculate distances form the center to the data and radii ratio by radius, finally bring each data point into the quadratic equation and decide which data point to correct the center or radius by iterative computation or not. This study argues that center and radius can be improved and close to the theoretical value. Then final the curve fitting for each quadratic is derived with these optimal data points.