Direct Manipulation of B-Spline

Youssef Ali Alhendawi


This paper introduces a technique for the immediate controls of B-spline and non-uniform discerning B-splines (NURBS) bends utilizing geometric imperatives. A deformable model is produced to characterize the misshapening vitality utilitarian of B-spline and NURBS bends. The limited component strategy is utilized to limit the distortion vitality useful and explain for the disfigured state of bends subjected to imperatives. This approach brings about an arrangement of direct conditions for a B-spline bend and an arrangement of non-straight conditions for a NURBS bend. A point of view mapping is utilized to linearize the NURBS details. NURBS bends are first mapped from the 3D Cartesian arrange space to the 4D homogeneous organize space, and changed to 4D B-spline bends. After the control in the 4D homogeneous facilitate space, the changed NURBS bends are then mapped back to the 3D Cartesian arrange space. The approach is executed by a model program, which is composed in C, and keeps running under WINDOWS.

Full Text:



Piegl L. Changing the state of normal B-splines. Section 1: bends. PC helped outline 1989;21(8):509– 18.

Piegl L. Changing the state of normal B-splines. Section 2: surfaces. PC Aided Design 1989;21(9):538– 46.

Au CK, Yuen MMF. Brought together way to deal with NURBS bend shape alteration. PC Aided Design 1995;27(2):85– 93.

Forsey DR, Bartels RH. Various leveled B-spline refinement. PC Graphics 1988;22(4):205– 12.

Bartels R, Beatty J. A strategy for the immediate control of spline bends. Procedures of the Graphics Interface 89. Los Altos, CA: Morgan Kaufmann. 1989. p. 33– 9.

Fowler B, Bartels R. Imperative based bend control. PC Graphics and Applications 1993:43– 9.

Hsu WM, Hughes JF, Kaufmann H. Coordinate control of freestyle disfigurements. PC Graphics 1992;26(2):177– 84.

Rappoport A, Hel-Or Y, Werman M. Intuitive plan of smooth items with probabilistic point imperatives. ACM Transactions on Graphics 1994;13(2):156– 76.

Terzopoulos D, Platt J, Barr A, Fleischer K. Flexibly deformable models. PC Graphics 1987;21(4):205– 14.

Terzopoulos D, Fleischer K. Deformable models. Visual Computer 1988;4(6):306– 31.

Celniker G, Gossard D. Deformable bend surface limited components with the expectation of complimentary frame shape plan. PC Graphics 1991;25(4):257– 66.

Celniker G, Welch W. Straight limitations for deformable B-spline surfaces. Procedures of the Symposium on Interactive 3D Graphics. New York: ACM, 1992. p. 165– 70.

Terzopoulos D, Qin H. Dynamic NURBS with geometric requirements for intuitive chiseling. ACM Transactions on Graphics 1994;13(2):103– 36.

Faloutsos P, Van de Panne M, Terzopoulos D. Dynamic freestyle distortions for activity union. IEEE Transactions on Visualization and Computer Graphics 1997;3(3):201– 12.

De Boor C. On figuring with B-splines. Diary of Approximation Theory 1972;6:50– 62.


  • There are currently no refbacks.

Abava   MSU conference 2018

ISSN: 2307-8162