Print ISSN: 1681-6900

Online ISSN: 2412-0758

### Keywords : Surface Fitting

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

Tahseen F. Abbas; Omar A. Raheem; Abdulwahab N. Abbas

Engineering and Technology Journal, 2011, Volume 29, Issue 7, Pages 1425-1437

This paper presents a general method for automatic surface fitting from
scattered range data and describes the implementation of three methods for fitting
surfaces: linear, quadratic and cubic. It uses a modified 2D least squares method to
fitting, reconstructing and modeling several surfaces and statistical criteria to
compare the three approaches. The comparison is performed using a
mathematically 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 as
demonstrated by a number of examples using real data from mathematical
functions ( sine, cosine, exponential and cubic). By applying the proposed
surface 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 models
respectively.

##### A New Method For Three Dimensional Cubic Bezier Surface Reconstruction Based On Matching The Surface Framework

Wissam K. Hamdan

Engineering and Technology Journal, 2010, Volume 28, Issue 8, Pages 1654-1671

Numerous efforts have been directed to convert the physical model ( in-hand
model) to a computer model. This work is dedicated for the cubic Bezier surface
reconstruction based on finding the positions of the sixteen control points that form the
surface of the product. The idea is based on inverse progressive search (IPS) method
rather than the approximate surface fitting method already used in previous researches.
The presented method is based on three successive steps:(a) converting the continuous
coordinate measuring machine (CMM) data to discrete data,(b) estimating the
positions of the 12 boundary control points and (c) estimating the positions of the 4
intermediate control points to generate the intended surface. To show the feasibility of
the suggested method two experimental examples are conducted. The results show the
validity and effectiveness of the method from the accuracy and computation time point
of view.