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Regular algebraic curve segments (I)—Definitions and characteristics

✍ Scribed by Guoliang Xu; Chandrajit L. Bajaj; Weimin Xue

Book ID
104304828
Publisher
Elsevier Science
Year
2000
Tongue
English
Weight
257 KB
Volume
17
Category
Article
ISSN
0167-8396

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✦ Synopsis

In this paper (part one of a trilogy), we introduce the concept of a discriminating family of regular algebraic curves (real, nonsingular and connected). Several discriminating families are obtained which yield different characterizations of the Bernstein-Bézier (BB) bivariate polynomials over the plane triangle and the quadrilateral domain such that their zero contours are smooth and connected. These regular curve segments in BB basis can be smoothly joined together to form algebraic curve splines or A-splines. Algorithms for the efficient graphics display of these new A-spline families are also provided.

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Regular algebraic curve segments (III)—a
Regular algebraic curve segments (III)—applications in interactive design and data fitting
✍ Chandrajit L. Bajaj; Guoliang Xu 📂 Article 📅 2001 🏛 Elsevier Science 🌐 English ⚖ 941 KB

In this paper (part three of the trilogy) we use low degree G 1 and G 2 continuous regular algebraic spline curves defined within parallelograms, to interpolate an ordered set of data points in the plane. We explicitly characterize curve families whose members have the required interpolating propert