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23 2011

NURBS : 30

B- ( NURBS . Non-Uniform Rational B-Spline) . 1981 . Boeing NURBS IGES. , : NURBS , SDRC Computervision. , 30 , NURBS . ? NURBS ? , , NURBS.

, CAD ( ), CAM ( ). 1950- . ( ) MIT ( , ) , . , .

Citroen DS

. 1. Citron DS

Citron DS ( 1955-1975), . , (Paul de Casteljau), Citron. , . 1974 ., 1959 ., , (Pierre Bézier). , , .

( , ) , ? , (bilinear patch):

. 2.

(ruled surface), , :

. 3.

(Steven Coons), MIT, , (Coons patch):

. 4.

1967 . Surfaces for Computer-Aided Design in Space Form [Coons 1967] . . . , (Ivan Sutherland), Sketchpad, .

, . , 1960- . UNISURF Renault.

. 5.

, , ( XIX .), , . (Hermite curve) : . , :

. 6.

, , , , ( , , ). ( ), , , . (Bézier curve) , , , , . :

. 7.

1962 ., Citron , , . , .

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. , . . , , . . . , , .

. 8.

, , , , , . , (, ). , .

, , . , ظ [Schoenberg 1946]. ( ) , . On calculating with B-Splines, (1972) The numerical evaluation of B-Splines .

B- : , B- .

B- , , , . B- (knots), .

NURBS

NURBS (Ken Versprille), - [Versprille 1975].

 ,  NURBS

. 9. , NURBS

-, , . , NURBS . Computervision CADDS 3. ( ) , , , NURBS ( ) .

Computervision, NURBS. , , , : - - 0 1 ! , NURBS, . !

2005 CAD Society, , NURBS. COFES, .

Boeing

1979 . Boeing CAD/CAM TIGER [Solid Modeling 2011]. , , 11 , B-. (Eugene Lee) , ( ) , . . ( , , .)

[Lee 1981]. B-. , NURBS. , TIGER .

Boeing NURBS IGES, . , SDRC.

SDRC

1967 . () SDRC (Structural Dynamics Research Corporation). , SDRC . CAE ( ) CAD (), I-DEAS, , - . I-DEAS GEOMOD.

GEOMOD , . Boeing NURBS, SDRC NURBS GEOMOD. (Wayne Tiller), "The NURBS Book" [Piegl 1997].

 ,  GeomWare,

. 10. , GeomWare, " NURBS"

I-DEAS , 2001 . EDS SDRC, NLib (. ).

GeomWare, IntegrityWare Solid Modeling Solutions

IntegrityWare 1996 . . 1998 . Solid Modeling Solutions SMLib, .

SMLib , . NLib (NURBS Library), GeomWare. NLib NURBS. NLib [Piegl 1997], GeomWare. NLib 85 , .

NLib - GSNlib (General Surface NURBS Library), , , NURBS. IntegrityWare GSLib Robert McNeel & Associates ( Rhino 3D) Ford Motor Company.

(subdivision surfaces) () , (base mesh), . , . - (Chaikin), . , , . , . (corner cutting) 1:2:1 . , .

. 11.

, , B-.

, . (Doo) (Sabin) B- ( ) [Doo 1978]. , 3, 4, 5 ( ) B-. , . , . , , , . . , , , :

 -

. 12. -

(Catmull) (Clark) B- ( - B- - ) [Catmull 1978]. , , ( B-). . :

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. 13. -

. , . ( , .)

.

NURBS?

NURBS ? , , . NURBS . NURBS . NURBS , , . NURBS (// , , ), . NURBS , , , , [Piegl 1991].

NURBS . , : , NURBS- , 38 (, , ). , NURBS. ( ) . , ( ) NURBS.

, NURBS . ...

T-

T- - , B- (NURBS). T- NURBS , NURBS- , T- T- ( , ).

T-

. 14. -

T- NURBS ( G2- ).

T- (Thomas Sederberg) [Sederberg 2003]. T-NURCCs, - - NURBS, - . 2004 . T-Splines, Inc. (), - .

NURBS? .

, , T-Splines Autodesk. -. Autodesk, . - STEP?

Catmull, E., and Clark, J., 1978, Recursively generated B-spline surfaces on arbitrary topological meshes, Computer-Aided Design 10(6):350-355.

Coons S. ., 1967, Surfaces for Computer Aided Design of Space Form, MIT Project MAC, AUC-TR-41. http://publications.csail.mit.edu/lcs/pubs/pdf/MIT-LCS-TR-041.pdf

Cox, M. G., 1972, The Numerical Evaluation of B-Splines, J. Inst. Mathematics and Applications, Vol. 10, pp. 134-149.

De Boor, C., 1972, On Calculation with B-Splines, J. Approximation Theory, Vol. 6, No. 1, pp. 50-62.

Doo, D., 1978, A subdivision algorithm for smoothing down irregularly shaped polyhedrons, Proceedings on Interactive Techniques in Computer Aided Design, pp. 157-165.

Lee, E. T. Y., 1981, A Treatment of Conics in Parametric Rational Bezier Form, Boeing document, Boeing, Seattle, Wash.

Piegl, L., 1991, On NURBS: A Survey, IEEE CG&A, Vol. 11, No. 1, pp. 55-71. http://www.ece.uvic.ca/~bctill/papers/mocap/Piegl_1991.pdf

Piegl, L. A., and Tiller, W., 1997, The NURBS Book, Springer.

Schoenberg, I. J., 1946, Contributions to the problem of approximation of equidistant data by analytic functions, Part A: On the problem of smoothing or graduation, a first class of analytic approximation formulas, Quart. Appl. Math. 4, 4599.

Sederberg, T.-W., Zheng, J., Bakenov, A., and Nasri, A., 2003, T-Splines and T-NURCCs, ACM Transactions on. Graphics, 22(3), 477-484, http://cagd.cs.byu.edu/~tspline/innovation/papers/tspline.pdf

Solid Modeling Solutions, 2011, NURBS at Boeing. http://www.smlib.com/white%20papers/nurbsatboeing.htm

Versprille, K. J., 1975, Computer-Aided Design Applications of the Rational B-Splines Approxamation Form, doctoral dissertation, Syracuse Univ., Syracuse, N.Y.

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id 2672     29 2011, 16:19
 
a_schelyaev

- (1868-1908) (1890-1980) ( .. ) .

   

id 2676     3 2012, 14:01
 

a_schelyaev, id 2656:

.



, http://www.cadhistory.net/
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id 2680     4 2012, 2:55
 
,   , , . . 1986- CAD-, ? "cadhistory" . , , .

   

id 2681     4 2012, 9:43
 
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id 2690     10 2012, 12:49
 
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id 2694     11 2012, 12:35
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a_schelyaev, id 2671:
CAD, VAX ... ...



Bravo .
, , . , , . . 1987. "" "-" 1420, !
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,
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