Evolution-based least-squares fitting using Pythagorean hodograph spline curves

Computer Aided Geometric Design

Volumn 24, Issue 6, 2007, Pages 310-322

  Aigner, Martin ^a   Šír, Zbynek ^a   Jüttler, Bert ^a  

^a JOHANNES KEPLER UNIVERSITY LINZ   (Austria)

Author keywords

Least squares fitting; PH curves

Indexed keywords

CURVE FITTING; DIFFERENTIAL EQUATIONS; EULER EQUATIONS; NEWTON-RAPHSON METHOD; NUMERICAL METHODS; SPLINES;

GAUSS-NEWTON ITERATIONS; NON-LINEAR CURVE FITTING PROBLEM; PYTHAGOREAN HODOGRAPH; STATIONARY POINT;

LEAST SQUARES APPROXIMATIONS;

EID: 34347351975     PISSN: 01678396     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cagd.2007.04.001     Document Type: Article

References (22)

1. Aigner M., and Jüttler B. Hybrid curve fitting. Computing 79 (2007) 237-247
2. Aigner M., and Jüttler B. Approximation flows in shape manifolds. In: Chenin P., Lyche T., and Schumaker L.L. (Eds). Curve and Surface Design. Avignon 2006 (2007), Nashboro Press 1-10
3. Alhanaty M., and Bercovier M. Curve and surface fitting and design by optimal control methods. Comp. Aided Design 33 (2001) 167-182
4. Farouki R.T. Pythagorean-hodograph curves. Handbook of Computer Aided Geometric Design (2002), North-Holland, Amsterdam 405-427
5. 2 PH quintic splines. Numer. Algorithms 27 1 (2001) 35-60
6. Farouki R.T., Manjunathaiah J., and Jee S. Design of rational cam profiles with Pythagorean-hodograph curves. Mech. Mach. Theory 33 6 (1998) 669-682
7. Farouki R.T., Saitou K., and Tsai Y.-F. Least-squares tool path approximation with Pythagorean-hodograph curves for high-speed CNC machining. The Mathematics of Surfaces, VIII. Birmingham, 1998 (1998), Info. Geom., Winchester 245-264
8. Hoff K.E., Keyser J., Lin M., Manocha D., and Culver T. Fast computation of generalized Voronoi diagrams using graphics hardware. SIGGRAPH '99 (1999), ACM Press/Addison-Wesley, New York 277-286
9. Hoschek J., and Lasser D. Fundamentals of Computer Aided Geometric Design (1993), A K Peters, Wellesley, MA
10. Jüttler B. Hermite interpolation by Pythagorean hodograph curves of degree seven. Math. Comp. 70 235 (2001) 1089-1111
11. Kass M., Witkin A., and Terzopoulos D. Snakes: active contour models. Int. J. Comp. Vision 1 (1987) 321-331
12. Kubota K. Pythagorean triplets in unique factorization domains. Amer. Math. Monthly 79 (1972) 503-505
13. Meek D.S., and Walton D.J. Geometric Hermite interpolation with Tschirnhausen cubics. J. Comput. Appl. Math. 81 2 (1997) 299-309
14. Moon H.P., Farouki R.T., and Choi H.I. Construction and shape analysis of PH quintic Hermite interpolants. Comp. Aided Geom. Design 18 (2001) 93-115
15. Pottmann H., and Leopoldseder S. A concept for parametric surface fitting which avoids the parametrization problem. Comp. Aided Geom. Design 20 (2003) 343-362
16. Pottmann H., Leopoldseder S., and Hofer M. Approximation with active B-spline curves and surfaces. Proc. Pacific Graphics (2002), IEEE Press 8-25
17. Pottmann H., Leopoldseder S., Hofer M., Steiner T., and Wang W. Industrial geometry: recent advances and appl. in CAD. Comp. Aided Design 37 (2005) 751-766
18. Rogers D., and Fog N. Constrained B-spline curve and surface fitting. Comp. Aided Design 21 (1989) 641-648
19. Šír Z., Feichtinger R., and Jüttler B. Approximating curves and their offsets using biarcs and Pythagorean hodograph quintics. Comp. Aided Design 38 (2006) 608-618
20. Šír Z., and Jüttler B. Constructing acceleration continuous tool paths using Pythagorean hodograph curves. Mech. Mach. Theory 40 11 (2005) 1258-1272
21. Speer T., Kuppe M., and Hoschek J. Global reparametrization for curve approximation. Comput. Aided Geom. Design 15 (1998) 869-877
22. Wang W., Pottmann H., and Liu Y. Fitting B-spline curves to point clouds by squared distance minimization. ACM Trans. Graph. 25 2 (2006)