Surface Fitting and Representation By Using 2D Least Squares Method in CAD Applications


This paper presents a general method for automatic surface fitting fromscattered range data and describes the implementation of three methods for fittingsurfaces: linear, quadratic and cubic. It uses a modified 2D least squares method tofitting, reconstructing and modeling several surfaces and statistical criteria tocompare the three approaches. The comparison is performed using amathematically defined data as real data obtained from the proposed models.The method can be used in a variety of applications such as reverse engineering,automatic generating of a CAD model, etc, and it has proven to be effective asdemonstrated by a number of examples using real data from mathematicalfunctions ( sine, cosine, exponential and cubic). By applying the proposedsurface fitting model the standard deviation was found to be (0.04-0.26), (0.02-0.07) and (0.0-0.12) mm for linear, quadratic and cubic fitting modelsrespectively.