Skip to main content
Erschienen in: Engineering with Computers 2/2008

01.06.2008 | Original Article

Fitting NURBS spherical patches to measured data

verfasst von: L. A. Piegl, W. Tiller

Erschienen in: Engineering with Computers | Ausgabe 2/2008

Einloggen

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config
loading …

Abstract

Algorithms and empirical studies for fitting spherical and planar NURBS patches to random data are presented. Algebraic as well as geometric methods are discussed leading to efficient techniques for surface as well as patch fitting. An automatic fitter is also presented that determines whether a plane or a sphere fit is optimal, computes the appropriate entities, and clips the geometry to obtain a NURBS sphere or plane fit. It is argued that patch fitting is necessary in order to avoid numerical problems due to pole and seam problems.

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

Literatur
1.
Zurück zum Zitat Ahn SJ, Rauh W, Warnecke HJ (2001) Least squares orthogonal distances fitting of circle, sphere, ellipse, hyperbola, and parabola. Pattern Recognit 34:2283–2303MATHCrossRef Ahn SJ, Rauh W, Warnecke HJ (2001) Least squares orthogonal distances fitting of circle, sphere, ellipse, hyperbola, and parabola. Pattern Recognit 34:2283–2303MATHCrossRef
2.
Zurück zum Zitat Albano A (1974) Representation of digitized contours in terms of conic arcs and straight-line segments. Comput Graph Image Process 3:23–33CrossRef Albano A (1974) Representation of digitized contours in terms of conic arcs and straight-line segments. Comput Graph Image Process 3:23–33CrossRef
3.
Zurück zum Zitat Biggerstaff RH (1972) Three variations in dental arch form estimated by a quadratic equation. J Dent Res 51:1509–1523 Biggerstaff RH (1972) Three variations in dental arch form estimated by a quadratic equation. J Dent Res 51:1509–1523
4.
Zurück zum Zitat Bookstein FL (1979) Fitting conic sections to scattered data. Comput Graph Image Process 9:56–71CrossRef Bookstein FL (1979) Fitting conic sections to scattered data. Comput Graph Image Process 9:56–71CrossRef
5.
Zurück zum Zitat Brent RP (1973) Algorithms for Minimization without Derivatives. Prentice Hall, Englewood CliffsMATH Brent RP (1973) Algorithms for Minimization without Derivatives. Prentice Hall, Englewood CliffsMATH
6.
Zurück zum Zitat Cooper DB, Yalabic N (1976) On the computational cost of approximating and recognizing noise-perturbed straight lines and quadratic arcs in the plane. IEEE Trans Comput C-25:1020–1032CrossRef Cooper DB, Yalabic N (1976) On the computational cost of approximating and recognizing noise-perturbed straight lines and quadratic arcs in the plane. IEEE Trans Comput C-25:1020–1032CrossRef
7.
Zurück zum Zitat Coxeter HSM (1980) Introduction to Geometry, 2nd Edn, Wiley, New York Coxeter HSM (1980) Introduction to Geometry, 2nd Edn, Wiley, New York
8.
Zurück zum Zitat Fitzgibbon AW, Fisher RB (1995) A buyer’s guide to conic fitting. British machine vision conference, Birmingam, pp 265–271 Fitzgibbon AW, Fisher RB (1995) A buyer’s guide to conic fitting. British machine vision conference, Birmingam, pp 265–271
9.
Zurück zum Zitat Fitzgibbon AW, Pilu M, Fisher RB (1996) Direct least squares fitting of ellipses. Proceedings of 13th international conference on pattern recognition, Vienna, pp 253–257 Fitzgibbon AW, Pilu M, Fisher RB (1996) Direct least squares fitting of ellipses. Proceedings of 13th international conference on pattern recognition, Vienna, pp 253–257
10.
Zurück zum Zitat Fletcher R (1987) Practical methods of optimization. Wiley, New YorkMATH Fletcher R (1987) Practical methods of optimization. Wiley, New YorkMATH
11.
Zurück zum Zitat Freeman H, Shapira R (1975) Determining the minimum-area encasing rectangle for an arbitrary closed curve. CACM 18:409–413MATHMathSciNet Freeman H, Shapira R (1975) Determining the minimum-area encasing rectangle for an arbitrary closed curve. CACM 18:409–413MATHMathSciNet
12.
13.
Zurück zum Zitat Halir R, Flusser J (1998) Numerically stable direct least squares fitting of ellipses, Proceedings of 6th international conference in central Europe on computer graphics and visualization. Pilzen 1, pp 125–132 Halir R, Flusser J (1998) Numerically stable direct least squares fitting of ellipses, Proceedings of 6th international conference in central Europe on computer graphics and visualization. Pilzen 1, pp 125–132
14.
Zurück zum Zitat Haralick RM, Shapiro LG (1992) Computer and Robot Vision. Vol 1, Addison-Wesley, Reading Haralick RM, Shapiro LG (1992) Computer and Robot Vision. Vol 1, Addison-Wesley, Reading
15.
Zurück zum Zitat Kanatani K (1994) Statistical bias of conic fitting and renormalization. IEEE T-PAMI 16:320–326MATH Kanatani K (1994) Statistical bias of conic fitting and renormalization. IEEE T-PAMI 16:320–326MATH
16.
Zurück zum Zitat Keren D, Cooper D, Subrahmonia J (1994) Describing complicated objects by implicit polynomials. IEEE T-PAMI 16:38–53 Keren D, Cooper D, Subrahmonia J (1994) Describing complicated objects by implicit polynomials. IEEE T-PAMI 16:38–53
17.
Zurück zum Zitat Liming RA (1979) Mathematics for Computer Graphics. Aero Publishers Inc., Fallbrook Liming RA (1979) Mathematics for Computer Graphics. Aero Publishers Inc., Fallbrook
18.
Zurück zum Zitat Lukacs G, Martin R, Marshall RD (1998) Faithful least-squares fitting of spheres, cylinders, cones and tori for reliable segmentation. in Proc Computer Vision—ECCV 98:671–686 Lukacs G, Martin R, Marshall RD (1998) Faithful least-squares fitting of spheres, cylinders, cones and tori for reliable segmentation. in Proc Computer Vision—ECCV 98:671–686
19.
Zurück zum Zitat Martin RR, Stephenson PC (1988) Putting objects into boxes. Comput Aided Des 20:506–514CrossRef Martin RR, Stephenson PC (1988) Putting objects into boxes. Comput Aided Des 20:506–514CrossRef
20.
Zurück zum Zitat Miller RD (1994) Computing the area of a spherical polygon. In: Heckbert PS (eds) Graphics gems IV. Academic, Boston, pp 132–137 Miller RD (1994) Computing the area of a spherical polygon. In: Heckbert PS (eds) Graphics gems IV. Academic, Boston, pp 132–137
21.
Zurück zum Zitat Nakagawa Y, Rosenfeld A (1979) A note on polygonal and elliptical approximation of mechanical parts. Pattern Recognit 11:133–142CrossRef Nakagawa Y, Rosenfeld A (1979) A note on polygonal and elliptical approximation of mechanical parts. Pattern Recognit 11:133–142CrossRef
23.
Zurück zum Zitat Paton KA (1970) Conic sections in chromosome analysis. Pattern Recognit 2:39–51CrossRef Paton KA (1970) Conic sections in chromosome analysis. Pattern Recognit 2:39–51CrossRef
24.
Zurück zum Zitat Paton KA (1970) Conic sections in automatic chromosome analysis. Mach Intell 5:411–434 Paton KA (1970) Conic sections in automatic chromosome analysis. Mach Intell 5:411–434
25.
Zurück zum Zitat Piegl L, Tiller W (1997) The NURBS book. Springer, New York Piegl L, Tiller W (1997) The NURBS book. Springer, New York
26.
Zurück zum Zitat Porrill J (1990) Fitting ellipses and predicting confidence envelopes using a bias corrected Kalman filter. Image Vis Comput 8:37–41CrossRef Porrill J (1990) Fitting ellipses and predicting confidence envelopes using a bias corrected Kalman filter. Image Vis Comput 8:37–41CrossRef
27.
Zurück zum Zitat Pratt V (1987) Direct least-squares fitting of algebraic surfaces. Comput Graph 21:145–152MathSciNet Pratt V (1987) Direct least-squares fitting of algebraic surfaces. Comput Graph 21:145–152MathSciNet
28.
Zurück zum Zitat Press W, Teukolsky S, Vetterling W, Flannery B (1992) Numerical recipes in C. Cambridge University Press, New YorkMATH Press W, Teukolsky S, Vetterling W, Flannery B (1992) Numerical recipes in C. Cambridge University Press, New YorkMATH
29.
Zurück zum Zitat Rosin P (1993) A note on the least-squares fitting of ellipses. Pattern Recognit Lett 14:799–808MATHCrossRef Rosin P (1993) A note on the least-squares fitting of ellipses. Pattern Recognit Lett 14:799–808MATHCrossRef
30.
Zurück zum Zitat Rosin P (1993) Ellipse fitting by accumulating five-point fits. Pattern Recognit Lett 14:661–669CrossRef Rosin P (1993) Ellipse fitting by accumulating five-point fits. Pattern Recognit Lett 14:661–669CrossRef
31.
Zurück zum Zitat Sampson PD (1982) Fitting conic sections to ‘very scattered’ data: an interactive refinement of the Bookstein algorithm. Comput Graph Image Process 18:97–108CrossRef Sampson PD (1982) Fitting conic sections to ‘very scattered’ data: an interactive refinement of the Bookstein algorithm. Comput Graph Image Process 18:97–108CrossRef
33.
Zurück zum Zitat Taubin G (1991) Estimation of planar curves, surfaces and non-planar space curves defined by implicit equations with applications to edge and range image segmentation. IEEE T-PAMI 13:1115–1138 Taubin G (1991) Estimation of planar curves, surfaces and non-planar space curves defined by implicit equations with applications to edge and range image segmentation. IEEE T-PAMI 13:1115–1138
34.
Zurück zum Zitat Toussaint GT (1983) Solving geometric problems with the rotating calipers. Proc IEEE MELECON’83, Athens, Greece Toussaint GT (1983) Solving geometric problems with the rotating calipers. Proc IEEE MELECON’83, Athens, Greece
35.
Zurück zum Zitat Varady T, Benko P, Kos G (1998) Reverse engineering regular objects: simple segmentation and surface fitting procedures. Int J Shape Model 4:127–142CrossRef Varady T, Benko P, Kos G (1998) Reverse engineering regular objects: simple segmentation and surface fitting procedures. Int J Shape Model 4:127–142CrossRef
Metadaten
Titel
Fitting NURBS spherical patches to measured data
verfasst von
L. A. Piegl
W. Tiller
Publikationsdatum
01.06.2008
Verlag
Springer-Verlag
Erschienen in
Engineering with Computers / Ausgabe 2/2008
Print ISSN: 0177-0667
Elektronische ISSN: 1435-5663
DOI
https://doi.org/10.1007/s00366-007-0076-8

Weitere Artikel der Ausgabe 2/2008

Engineering with Computers 2/2008 Zur Ausgabe

Neuer Inhalt