An Approach to Polynomial Curve Comparison in Geometric Object Database
In image processing and visualization, comparing two
bitmapped images needs to be compared from their pixels by matching
pixel-by-pixel. Consequently, it takes a lot of computational time
while the comparison of two vector-based images is significantly
faster. Sometimes these raster graphics images can be approximately
converted into the vector-based images by various techniques. After
conversion, the problem of comparing two raster graphics images
can be reduced to the problem of comparing vector graphics images.
Hence, the problem of comparing pixel-by-pixel can be reduced to
the problem of polynomial comparisons. In computer aided geometric
design (CAGD), the vector graphics images are the composition of
curves and surfaces. Curves are defined by a sequence of control
points and their polynomials. In this paper, the control points will be
considerably used to compare curves. The same curves after relocated
or rotated are treated to be equivalent while two curves after different
scaled are considered to be similar curves. This paper proposed an
algorithm for comparing the polynomial curves by using the control
points for equivalence and similarity. In addition, the geometric
object-oriented database used to keep the curve information has also
been defined in XML format for further used in curve comparisons.
[1] Ball A. A.,1974, CONSURF, Part one: Introduction to conic lifting title.
Computer-Aided Design 6, pp. 243-249.
[2] Ball A. A.,1975, CONSURF, Part two: Description of the algorithms.
Computer-Aided Design 7, pp. 237-242.
[3] Ball A. A.,1977, CONSURF, Part three: How the program is used.
Computer-Aided Design 9,pp. 912.
[4] Delgado, J. and Pen˜a, J.M.,2003,A Shape Preserving Representation with
an evaluation algorithm of linear complexity, Computer Aided Geometric
Design, pp. 1-10.
[5] Farin, G. ,1990, Curves and Surfaces for Computer Aided Geometric
Design , A Practical Guide, 5nd Edition, Academic Press Inc., London.
[6] Hu, S.M., Wang, G.Z. and Jin, T.G., 1996, Properties of Two Types of
Generalized Ball Curves, Computer-Aided Design, Vol. 28, No. 2, pp.
125-133.
[7] Itsariyawanich,K. ,2007,DP curve and its properties, Master Thesis, King
Mongkut-s University of Technology Thonburi, Thailand.
[8] Jiang, S.R. and Wang, G.J.,2005,Conversion and Evaluation for Two
Types of Parametric Surface Constructed by NTP Bases,Computers and
Mathematics with Applications, Vol. 49, No. 2, pp. 321-329.
[9] Said, H.B., 1989, A Generalized Ball Curve and Its Recursive Algorithm,
ACM Transactions on Graphics, Vol. 8, No. 4, pp. 360-371.
[10] Tien, H.L. ,1997,Further Developments on Ball Curves and Surfaces,
Ph.D Dissertation, Asian Institute of Technology School of Advanced
Technologies, Bangkok, Thailand.
[11] Wang, G.Z., 1987, Ball Curve of High Degree and Its Geometric
Propertied, Appl. Math: A journal of Chinese Universities, Vol. 2, No.
1, pp. 126-140.
[1] Ball A. A.,1974, CONSURF, Part one: Introduction to conic lifting title.
Computer-Aided Design 6, pp. 243-249.
[2] Ball A. A.,1975, CONSURF, Part two: Description of the algorithms.
Computer-Aided Design 7, pp. 237-242.
[3] Ball A. A.,1977, CONSURF, Part three: How the program is used.
Computer-Aided Design 9,pp. 912.
[4] Delgado, J. and Pen˜a, J.M.,2003,A Shape Preserving Representation with
an evaluation algorithm of linear complexity, Computer Aided Geometric
Design, pp. 1-10.
[5] Farin, G. ,1990, Curves and Surfaces for Computer Aided Geometric
Design , A Practical Guide, 5nd Edition, Academic Press Inc., London.
[6] Hu, S.M., Wang, G.Z. and Jin, T.G., 1996, Properties of Two Types of
Generalized Ball Curves, Computer-Aided Design, Vol. 28, No. 2, pp.
125-133.
[7] Itsariyawanich,K. ,2007,DP curve and its properties, Master Thesis, King
Mongkut-s University of Technology Thonburi, Thailand.
[8] Jiang, S.R. and Wang, G.J.,2005,Conversion and Evaluation for Two
Types of Parametric Surface Constructed by NTP Bases,Computers and
Mathematics with Applications, Vol. 49, No. 2, pp. 321-329.
[9] Said, H.B., 1989, A Generalized Ball Curve and Its Recursive Algorithm,
ACM Transactions on Graphics, Vol. 8, No. 4, pp. 360-371.
[10] Tien, H.L. ,1997,Further Developments on Ball Curves and Surfaces,
Ph.D Dissertation, Asian Institute of Technology School of Advanced
Technologies, Bangkok, Thailand.
[11] Wang, G.Z., 1987, Ball Curve of High Degree and Its Geometric
Propertied, Appl. Math: A journal of Chinese Universities, Vol. 2, No.
1, pp. 126-140.
@article{"International Journal of Engineering, Mathematical and Physical Sciences:53917", author = "Chanon Aphirukmatakun and Natasha Dejdumrong", title = "An Approach to Polynomial Curve Comparison in Geometric Object Database", abstract = "In image processing and visualization, comparing two
bitmapped images needs to be compared from their pixels by matching
pixel-by-pixel. Consequently, it takes a lot of computational time
while the comparison of two vector-based images is significantly
faster. Sometimes these raster graphics images can be approximately
converted into the vector-based images by various techniques. After
conversion, the problem of comparing two raster graphics images
can be reduced to the problem of comparing vector graphics images.
Hence, the problem of comparing pixel-by-pixel can be reduced to
the problem of polynomial comparisons. In computer aided geometric
design (CAGD), the vector graphics images are the composition of
curves and surfaces. Curves are defined by a sequence of control
points and their polynomials. In this paper, the control points will be
considerably used to compare curves. The same curves after relocated
or rotated are treated to be equivalent while two curves after different
scaled are considered to be similar curves. This paper proposed an
algorithm for comparing the polynomial curves by using the control
points for equivalence and similarity. In addition, the geometric
object-oriented database used to keep the curve information has also
been defined in XML format for further used in curve comparisons.", keywords = "Bezier curve, Said-Ball curve, Wang-Ball curve, DP curve, CAGD, comparison, geometric object database.", volume = "1", number = "8", pages = "352-7", }