Geodesic
Interpolating B\'ezier spline curves with local control
Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 2 (2014), pp. 18-28.

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The paper presents a technique for construction of interpolating spline curves in linear spaces by means of blending parametric curves. A class of polynomials which satisfy special boundary conditions is used for blending. Properties of the polynomials are stated. An application of the technique to construction of interpolating Bézier spline curves with local control is considered. The presented interpolating Bézier spline curves can be used in on-line geometric applications or for fast sketching and prototyping of spline curves in geometric design. 
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     author = {A. P. Pobegailo},
     title = {Interpolating {B\'ezier} spline curves with local control},
     journal = {Buletinul Academiei de \c{S}tiin\c{t}e a Republicii Moldova. Matematica},
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     number = {2},
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}
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A. P. Pobegailo. Interpolating B\'ezier spline curves with local control. Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 2 (2014), pp. 18-28. https://geodesic-test.mathdoc.fr/item/BASM_2014_2_a2/

[1] Chuan Sun, Huanxi Zhao, “Generating fair, $C^2$ continuous splines by blending conics”, Computers Graphics, 33:2 (2009), 173–180 | DOI

[2] Hartmann E., “Parametric $G^n$ blending of curves and surfaces”, The Visual Computer, 17:1 (2001), 1–13 | DOI | Zbl

[3] Jakubiak J., Leite F. T., Rodrigues R. C., “A two-step algorithm of smooth spline generation on Riemannian manifolds”, Journal of Computational and Applied Mathematics, 194:2 (2006), 177–191 | DOI | MR | Zbl

[4] Liska R., Shashkov M., Swartz B., Smoothly blending successive circular interpolants in two and three dimensions, Tech. Rep. LA-UR 98-4969, LANL, 1998

[5] Meek D. S., Walton D. J., “Blending two parametric curves”, Computer-Aided Design, 41:6 (2009), 423–431 | DOI

[6] Overhauser A. W., Analytic Definition of Curves and Surfaces by Parabolic Blending, Tech. Rep. SL68-40, Ford Motor Company Scientific Laboratory, 1968

[7] Pobegailo A. P., “Local interpolation with weight functions for variable-smoothness curve design”, Computer-Aided Design, 23:8 (1991), 579–582 | DOI | Zbl

[8] Pobegailo A. P., “Geometric modeling of curves using weighted linear and circular segments”, The Visual Computer, 8:4 (1992), 241–245 | DOI

[9] Pobegailo A. P., “$C^n$ interpolation on smooth manifolds with one-parameter transformations”, Computer-Aided Design, 28:12 (1996), 973–979 | DOI

[10] Rogers D. F., Adams J. A., Mathematical elements for computer graphics, McGraw-Hill, 1989; The Visual Computer, 8:4 (1992), 241–245 | DOI

[11] Séquin C. H., Kiha Lee, Jane Yen, “Fair, $G^2$- and $C^2$-continuous circle splines for the interpolation of sparse data points”, Computer-Aided Design, 37:2 (2005), 201–211 | DOI

[12] Szilvási-Nagy M., Vendel T. P., “Generating curves and swept surfaces by blended circles”, Computer Aided Geometric Design, 17:2 (2000), 197–206 | DOI | MR

[13] Wenz H.-J., “Interpolation of curve data by blended generalized circles”, Computer Aided Geometric Design, 13:8 (1996), 673–680 | DOI | MR | Zbl

[14] Wiltsche A., “Blending curves”, Journal for Geometry and Graphics, 9:1 (2005), 67–75 | MR | Zbl

[15] Zavjalov Y. S., Leus V. A., Skorospelov V. A., Splines in Engineering Geometry, Maschinostroenie, Moscow, 1985