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Issue No.02 - March/April (1994 vol.14)
pp: 56-60
<p>B-splines are a new tool for modeling complex objects with nonrectangular topology. The scheme is based on blending functions and control points, and lets us model piecewise polynomial surfaces of degree n that are C/sup n-1/-continuous throughout. Triangular B-splines permit the construction of smooth surfaces with the lowest degree possible. Because they can represent any piecewise polynomial surface, they provide a unified data format. The new B-spline scheme for modeling complex irregular objects over arbitrary triangulations has many desirable features. Applications like filling polygonal holes or constructing smooth blends demonstrate its potential for dealing with concrete design problems. The method permits real-time editing and rendering. Currently, we are improving the editor to accept simpler user input, optimizing intersection computations and developing new applications.</p>
Gunther. Greiner, Hans-Peter Seidel, "Modeling with Triangular B-Splines", IEEE Computer Graphics and Applications, vol.14, no. 2, pp. 56-60, March/April 1994, doi:10.1109/38.267471
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2. H.-P. Seidel, "Polar Forms and Triangular B-Spline Surfaces," inBlossoming: The New Polar-Form Approach to Spline Curves and Surfaces, Siggraph 1991 course notes, no. 26, ACM, New York, 1991, pp. 8.1-8.52.
3. H.-P. Seidel, "Representing Piecewise Polynomials as Linear Combinations of Multivariate B-Splines," inCurves and Surfaces, T. Lyche and L.L. Schumaker, eds., Academic Press, New York, 1992, pp. 559-566.
4. P. Fang,Shape Control for B-Splines over Arbitrary Triangulations, master's thesis, Univ. of Waterloo, Waterloo, Canada, 1992.
5. P. Fong and H.-P. Seidel, "An Implementation of Triangular B-Spline Surfaces over Arbitrary Triangulations,"Computer-Aided Geometric Design, Vol. 10, 1993, pp. 267-275.
6. C.A. Micchelli, "On a Numerically Efficient Method for Computing with Multivariate B-Splines," inMultivariate Approximation Theory, W. Schempp and K. Zeller, eds., Birkhäuser, Basel, Switzerland, 1979, pp. 211-248.
7. P. de Casteljau,FormesàPôles, Hermes, Paris, 1985.
8. L. Ramshaw, "Blossoming: A Connect-the-Dots Approach to Splines," tech. report, Digital Systems Research Center, Palo Alto, Calif., 1987.
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