This paper presents a new technique based on dual Kriging interpolation for modeling curves and surfaces in the presence of uncertainties in data points. Uncertainties result from measurement errors; therefore, a direct application of this method is found in curve/surface modeling using discrete sets of digitized points. It focuses on a common problem in geometric modeling, the trade-off between curve/surface smoothness and the approximation errors. The Kriging model filters the noise in the data while controlling the deviation locally at each point. However, the classical least-squares technique minimizes the average deviation, hence allowing only a global control of the model. The presented method generates smoother and more accurate representation of the actual curve or surface. It has potential applications in reverse engineering, NC machining, computer-aided inspection and tolerance analysis and verification. Examples of a computer mouse and a portion of the hood of a scaled-down car are presented for illustration.

Issue Section:
Research Papers
Topics:
Modeling, Uncertainty, Errors, Approximation, Computer-aided engineering, Computers, Filters, Geometric modeling, Inspection, Interpolation, Machining, Noise (Sound), Reverse engineering, Tolerance analysis, Tradeoffs
1.
Cheng
F.
, and
Barsky
B. A.
,
1991
, “
Interproximation; Interpolation and Approximation Using Cubic Spline Curves
,”
Computer-Aided Design
, Vol.
23
, No.
10
, pp.
700
–
706
.
2.
Davis, P. J., 1975, Interpolation and Approximation, Dover Publication Inc., New York.
3.
de Boor, C., 1978, A Practical Guide to Splines, Springer-Verlag, New York, USA.
4.
Dowd, P. A., 1985, “A Review of Geostatistical Techniques for Contouring,” in Ernshaw, R. A. (Ed.) Fundamental Algorithms for Computer Graphics, Springer-Verlag, Germany, pp. 483–529.
5.
Feng
L.
, and
Gossard
D. C.
,
1995
, “
Multidimensional Curve Fitting to Unorganized Data Points by Non Nonlinear Minimization
,”
Computer Aided Design
, Vol.
27
, No.
1
, pp.
48
–
58
.
6.
Goshtasby
A.
, and
O’Neill
W. M.
,
1993
, “
Surface Fitting to Scattered Data by a Sum of Gaussians
,”
Computer Aided Geometric Design
, Vol.
10
, pp.
143
–
156
.
7.
Lee
E. T. Y.
,
1989
, “
Choosing Nodes in Parametric Curve Interpolation
,”
Computer Aided Design
, Vol.
21
, No.
6
, pp.
363
–
370
.
8.
Limaiem, A., and ElMaraghy, H. A., 1995, “Analytical Solid Modeling Using Dual Kriging,” Proc. 21st ASME Design Automation Conference, Boston, MA, pp. 123–128.
9.
Menq
C. H.
,
Yau
H. T.
, and
Wong
C. L.
,
1992
, “
An Intelligent Planning Environment for Automated Dimensional Inspection Using Coordinate Measuring Machines
,”
Journal of Engineering far Industry
, Vol.
114
, pp.
222
–
229
.
10.
Mortenson, M., 1985, Geometric Modeling, John Wiley & Sons, New York.
11.
Nassef, A., Limaiem, A., and ElMaraghy, H. A., 1997, “On the Accurate Evaluation of Geometric Deviations from CMM Data,” 5th CIRP Seminar on Computer-Aided Tolerancing, April 27–30, Toronto, Ontario, Canada.
12.
Phillips, S. D., Borchardt, B., and Gadrey, G., 1993, “Measurement Uncertainty Consideration for Coordinate Measuring Machines,” NISTIR 5170, US Department of Commerce, Technology Administration, National Institute of Standards and Technology.
13.
Piegl, L., 1991, “On NURBS: Survey,” IEEE Computer Graphics & Applications, pp. 51–71.
14.
Poirier
C.
, and
Tinawi
R.
,
1991
, “
Finite Element Stress Tensor Field Interpolation and Manipulation Using 3D Dual Kriging
,”
Computer & Structure
, Vol.
4
, No.
2
, pp.
211
–
225
.
15.
Rogers
F. F.
, and
Fog
N. G.
,
1989
, “
Constrained B-spline Curve and Surface Fitting
,”
Computer-Aided Design
, Vol.
21
, No.
10
, pp.
641
–
648
.
16.
Stytz
M. R.
, and
Parrott
R. W.
,
1993
, “
Using Kriging for 3D Medical Imaging
,”
Computerized Medical Imaging and Graphics
, Vol.
17
, No.
6
, pp.
421
–
442
.
17.
Trochu
F.
,
1993
, “
A Contouring Program Based on Dual Kriging Interpolation
,”
Engineering with Computers
, Vol.
9
, pp.
160
–
177
.
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