Print ISSN: 1681-6900

Online ISSN: 2412-0758

Keywords : Computer Graphics


Statistical and Visual Analysis of Error In Interpolating Sculptured Surfaces

Tahseen F. Abbas; Aqeel S. Baden; Muhamed A. Salih

Engineering and Technology Journal, 2011, Volume 29, Issue 12, Pages 2520-2538

This paper presents a general method for automatic surface interpolation from
range data and describes the implementation of high order 2D langrangian methods
for interpolating surfaces from 3rd to 8th order. It uses a modified 2D lagrangian
method to interpolating, reconstructing and modeling several surfaces, and due to this
interpolation there will be an error between interpolated surface and the original one,
this paper present an algorithm to detect, represent and analyze these interpolating
errors and statistical criteria to compare the error in representing the sculptured
surfaces that interpolated with different order basis functions. The comparison is
performed using a mathematically defined data as real data obtained from the
proposed models.
The system has been implemented for the design of several sculptured surfaces to
illustrate the system flexibility. Then the design results have been implemented for
manufacturing two of these surfaces using three axis vertical CNC milling machine
tool with ball end mill cutter. The method can be used in a variety of CAD/CAM
applications and it has proven to be effective as demonstrated by a number of
examples using real data from mathematical functions. By applying the proposed
surface interpolating models the percent error was found to be ranged between
0.00001% for some model to 3.5% for some other interpolated models with Lagrange
method.

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.