Grundlagen Kurven- und Flächen—Orientierter Modellierung

1. Ball, A.A.: Consurf I-III, Computer-aided Design 6 (1974),243–249, 7 (1975), 237–242, 9 (1977), 9–12

   Google Scholar 

2. Barnhill, R.E.; Riesenfeld, R,F.(eds.): Computer Aided Geometric Design, Academic Press (1974)

   MATH  Google Scholar 

3. Barnhill, R.E.: Representation and Approximation of Surfaces, in Mathematical Software I II, J.R. Rice ed., Academic Press (1977)

   Google Scholar 

4. Barnhill, R.E.: Computer Aided Surface Representation and Design, in 1Bar82b1

   Google Scholar 

5. Barnhill, R.E,; Böhm, W. (eds.): Surfaces in CAGD, North-Holland (1982)

   Google Scholar 

6. Bézier, P.: Essai de Définition Numérique des Courbes et de Surfaces Expérimentales, Diss. Paris (1977)

   Google Scholar 

7. Böhm, W.; Gose, G.: Einführung in die Methoden der Numerischen Mathematik, Vieweg (1977)

   MATH  Google Scholar 

8. Böhm, W.: Cubic B-Spline Curves and Surfaces in CAGD, Computing 19 (1977), 29–34

   Article  MathSciNet  MATH  Google Scholar 

9. Böhm, W.: Inserting new Knots into B-Spline Curves, Computer-aided Design 12 (1980), 199–201

   Article  Google Scholar 

10. Böhm, W.: Generating the Bézier Points of B-Spline Curves and Surfaces, Computer-aided Design 13 (1981), 365–366

    Article  Google Scholar 

11. Böhm, W.: Mathematische Grundlagen der Geometrischen Datenverarbeitung, Vorlesung TU Braunschweig (1981)

    Google Scholar 

12. Böhm, W.: On Cubics, A Survey, Computer Graphics and Image Processing 19 (1982), 201–226

    Article  MATH  Google Scholar 

13. Böhm, W.: Generating the Bézier Points of, Triangular Splines, in 1Bar82bI

    Google Scholar 

14. de Boor, C.: On Calculating with B-Splines, J. Approximation Theory 6 (1972), 50–62

    Article  MathSciNet  MATH  Google Scholar 

15. de Boor, C.: A Practical Guide to Splines, Springer (1978)

    Book  MATH  Google Scholar 

16. Breden, D.: Die Verwendung von bikubischen Splineflächen zur Darstellung von Tragflügeln und Propellern, Diss. TU Braunschweig (1982)

    Google Scholar 

17. Brown, J.H.: Conforming and Nonconforming Finite Element Models for Curved Regions, Diss. Dundee (1976)

    Google Scholar 

18. Bruckner, I.: Construction of Bézier Points of Quadrilaterals from Those of Triangles, Computer-aided Design 12 (1980), 21–24

    Article  Google Scholar 

19. de Casteljau, F.: Courbes et Surfaces a Poles, Andre Citroën Automobiles SA, Paris (1959)

    Google Scholar 

20. Catmull, E.E., Clark, J.H.: Recursively Generated B-Spline Surfaces on Arbitrary Topological Meshes, Computer-aided Design 10 (1978), 350–355

    Article  Google Scholar 

21. Chaikin, G.M.: An Algorithm for High Speed Curve Algorithm, Computer Graphics and Image Processing 3 (1974), 346–349

    Article  Google Scholar 

22. Cohen, E.; Lyche, T.; Riesenfeld, R.F.: Discrete B-Splines and Subdivision Techniques in Computer Aided Geometric Design and Computer Graphics, Computer Graphics and Image Processing 14 (1980), 87–111

    Article  Google Scholar 

23. Coons, S.A.: Surfaces for Computer Aided Design of Space Forms, MIT Project MAC-TR-41 (1967)

    Google Scholar 

24. Doo, D.; Sabin, M.A.: Behavior of Recursive Division Surfaces near Extraordinary Points, Computer-aided Design 6 (1978), 356–360

    Article  Google Scholar 

25. Doo, D.W.H.:A Subdivision Algorithm for Smoothing Down Irregular Shaped Polyhedrons, Eurographics ’78, Bologna (1978)

    Google Scholar 

26. Farin, G.E.: Konstruktion und Eigenschaften von Bézier-Kurven und Bézier-Flächen, Diplom-Arbeit TU Braunschweig (1977)

    Google Scholar 

27. Farin, G.E.: Subsplines über Dreiecken, Diss.TU Braunschweig (1979)

    Google Scholar 

28. Farin, G.E.: Designing C1 Surfaces consisting of Triangular Cubic Patches, Computer-aided Design 14 (1982), 253–256

    Article  Google Scholar 

29. Farin, G.E.: Visually C2 Cubic Splines, Computer-aided Design 14 (1982), 137–139

    Article  Google Scholar 

30. Farin, G.E.: Smooth Interpolation to Scattered 3D Data, in 1Bar82bI

    Google Scholar 

31. Faux, I. D.; Pratt, M. J.: Computational Geometry for Design and Manufacture, Ellis Horwood (1979)

    MATH  Google Scholar 

32. Forrest, A.R.: The Twisted Cubic Curve: A Computer Aided Geometric Design Approach, Computer-aided Design 12 (1980), 165–172

    Article  Google Scholar 

33. Gordon, W.: Distributive Lattices and the Approximation of Multivariate Functions, in Approx. with Special Emphasis on Spline Functions ( Schoenberg ed. ), Academic Press (1969)

    Google Scholar 

34. Gordon, W.: Blending-Function Methods of Bivariate and Multivariate Interpolation and Approximation, SIAM J. Numerical Analysis 8 (1971), 158–177

    Article  MATH  Google Scholar 

35. Gordon, W.; Riesenfeld, R.E.: B-Spline Curves and Surfaces, in IBar741

    Google Scholar 

36. Gregory, J.A.: A CI Triangular Interpolation Patch for Computer Aided Geometric Design, Computer Graphics and Image Processing 13 (1980), 80–87

    Article  Google Scholar 

37. Gregory, 3.A.: C¹ Rectangular and Non-Rectangular Surface Patches, in IBar820

    Google Scholar 

38. Greville, T.N.E.: On the Normalisation of the B-Splines and the Locationof the Nodes for the Case of Unequally Spaced Knots, in Inequalities (O.Shisha ed.),Academic Press (1967)

    Google Scholar 

39. Hosaka, M.; Kimura, F.: Synthesis Methods of Curves and Surfaces in Interactive CAD, Eurographics ’78, Bologna (1978)

    Google Scholar 

40. Kahmann, J.: Krümmungsübergänge zusammengesetzter Kurven und Flächen, Diss. TU Braunschweig (1982)

    Google Scholar 

41. Kestner, W.; Saniter, J.et al.: Einführung in Computer Graphics, TU Berlin (1974)

    Google Scholar 

42. Lane, J.M.; Riesenfeld, R.F.: A Theoretical Development for the Computer Generation of Piecewise Polynomial Surfaces, IEEE Transactions on Pattern Analysis and Machine Intelligence PAMI 2, (1980), 35–46

    Article  MATH  Google Scholar 

43. Lee, E.: A Simplified B-Spline Computation Routine, ersch.demn.

    Google Scholar 

44. Little, F.F.: Convex Combination Surfaces, in IBar82bI

    Google Scholar 

45. Nielson, G.M.: Some Piecewise Polynomial Alternatives to Splines under Tension, in IBar741

    Google Scholar 

46. Poeppelmeier, C.C.: A Boolean Sum Interpolation Scheme to Random Data for Computer Aided Geometric Design, Master’s Thesis, U Salt Lake City (1975)

    Google Scholar 

47. Sabin, M.A.: The Use of Piecewise Forms for the Numerical Representation of Shape, Diss., MTA Budapest (1977)

    Google Scholar 

48. Schmidt, R.M.: Fitting Scattered Surface Data with Large Gaps, in 1Bar82b1

    Google Scholar 

49. Schoenberg, I.: On Variation Diminishing Approximation Methods, in On Numerical Approximation (R. Langer ed.),Madison-Wisc. (1959)

    Google Scholar 

50. Schoenberg, I.: On Spline Functions, in Inequalities (O. Shisha ed.),Academic Press (1967)

    Google Scholar 

51. Shepard, D.: A Two Dimensional Interpolation Function for IrregularlySpaced Data, Proc. ACM Nat. Conf. (1965), 517–524

    Google Scholar 

52. Stärk, E.: Mehrfach differenzierbare Bézier-Kurven und BézierFlächen, Diss TU Braunschweig (1976)

    Google Scholar 

Ergänzende Literatur

• Barnhill,R.E.; Brown,J.H.; Klusewicz,I.M.: A New Twist in CAGD, Computer Graphics and Image Processing 8 (1978), 78–91

  Article  Google Scholar 

• Barnhill,R.E.; Jirkhoff,G.; Gordon,W.J.:Smooth Interpolation in Triangles, J. Approx. Theory 8 (1973), 114–128

  Article  MATH  Google Scholar 

• Barsky,B.A.: The Beta-Spline: A local representation based on shape parameter and fundamental geometric measures, Diss.,U Salt Lake City (1981)

  Google Scholar 

• Ferguson,J.C.:Multivariable Curve Interpolation, J.ACM II/2 (1964), 221–228

  Article  MathSciNet  Google Scholar 

• Greene,P.J.; Sibson,R.: Computing Dirichlet Tesselations in the Plane, The Computer Journal 21 (1977), 168–173

  Google Scholar 

• Forrest,A.R.: Interactive Interpolation and Approximation by Bézier Polynomials, The Computer Journal 15 (1972), 71–79

  MathSciNet  MATH  Google Scholar 

• Goldmann,R.N.:Using Degenerated Bézier Triangles and Tetrahedra to subdivide Bézier Curves, Computer-aided Design 14 (1982), 307–311

  Article  Google Scholar 

• Lawson,C.L.:Software for C’Surface Interpolation, Mathematical Software III, Rice (ed),Academic Press (1977),161–194

  Google Scholar 

• Riesenfeld,R.R.:On Chaikin’s Algorithm, Computer Graphics and Image Processing 4 (1975),304–310

  Article  Google Scholar 

• Schumaker,L.L.:Spline Functions:Basic Theory, Wiley & Sons (1981)

  Google Scholar 

• Strang,G.; Fix,G.:An Analysis of the Finite Element Method, Prentice-Hall (1973)

  Google Scholar 

• Barsky,B.A.:Computer-Aided Geometric Design, A Bibliography with Keywords and Classified Index, IEEE Computer Graphics and Applications 1 (1981),67–109

  Article  Google Scholar 

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