Automatic curve fairing system using visual languages

Generally, in the field of industrial design, the measurement data of a clay model are faired, and a 3D model is made in CAD. However, it is a problem that this fairing work takes a long time and requires a great deal of labor. We propose an automatic curve fairing system for the application to reverse engineering technology. The system is constructed by the following five steps. (1) Key-line data are extracted from a clay model by a 3D digitizer. (2) The extracted key-line data are approximated by a spline with a genetic algorithm. (3) The spline curve (key-line) is divided into curves of monotone curvature. (4) The "characteristic" of the curve is analyzed for each monotone-curvature curve. (5) Each monotone-curvature curve is substituted by a visual language based on the result of the analysis mentioned above, and each key-line is reconstructed by the visual language. By using this system, we can easily obtain an aesthetic curve, as intended by a designer, in a short time.

[1]  Rida T. Farouki,et al.  Pythagorean-hodograph quintic transition curves of monotone curvature , 1997, Comput. Aided Des..

[2]  MUHAMMAD SARFRAZ,et al.  A C2 rational cubic spline alternative to the nurbs , 1992, Comput. Graph..

[3]  Muhammad Sarfraz,et al.  Curve Fitting for Large Data Using Rational Cubic Splines , 2003, International Journal of Computers and Their Applications.

[4]  Lalit M. Patnaik,et al.  Adaptive probabilities of crossover and mutation in genetic algorithms , 1994, IEEE Trans. Syst. Man Cybern..

[5]  Paul Dierckx,et al.  Curve and surface fitting with splines , 1994, Monographs on numerical analysis.

[6]  Muhammad Sarfraz Optimal Curve Fitting to Digital Data , 2003, WSCG.

[7]  Muhammad Sarfraz,et al.  Cubic spline curves with shape control , 1994, Comput. Graph..

[8]  Muhammad Sarfraz,et al.  Designing of curves and surfaces using rational cubics , 1993, Comput. Graph..

[9]  David E. Goldberg,et al.  Genetic Algorithms in Search Optimization and Machine Learning , 1988 .

[10]  T. K. Pal,et al.  Two-dimensional curve synthesis using linear curvature elements , 1977 .

[11]  Muhammad Sarfraz,et al.  A Web based system to capture outlines of Arabic fonts , 2003, Inf. Sci..

[12]  Toshinobu Harada,et al.  Automatic knot placement by a genetic algorithm for data fitting with a spline , 1999, Proceedings Shape Modeling International '99. International Conference on Shape Modeling and Applications.

[13]  G. Schwarz Estimating the Dimension of a Model , 1978 .

[14]  Toshinobu Harada,et al.  An aesthetic curve in the field of Industrial design , 1999, Proceedings 1999 IEEE Symposium on Visual Languages.

[15]  Carl de Boor,et al.  A Practical Guide to Splines , 1978, Applied Mathematical Sciences.

[16]  Muhammad Sarfraz Interpolatory rational cubic spline with biased, point and interval tension , 1992, Comput. Graph..

[17]  Muhammad Sarfraz,et al.  An algorithm for automatic capturing of the font outlines , 2002, Comput. Graph..