TY - JOUR
T1 - Regular algebraic curve segments (I)—Definitions and characteristics
AU - Xu, Guoliang
AU - Bajaj, Chandrajit L.
AU - Xue, Weimin
N1 - Funding Information:
Chandrajit L. Bajaj supported in part by NSF grants CCR.
Guoliang Xu Project 19671081 supported by NSFC.
Weimin Xue supported by FRG of Hong Kong Baptist University.
Publisher copyright:
© 2000 Elsevier Science B.V. All rights reserved.
PY - 2000/7
Y1 - 2000/7
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=0034230867&partnerID=8YFLogxK
U2 - 10.1016/S0167-8396(00)00012-1
DO - 10.1016/S0167-8396(00)00012-1
M3 - Journal article
AN - SCOPUS:0034230867
SN - 0167-8396
VL - 17
SP - 485
EP - 501
JO - Computer Aided Geometric Design
JF - Computer Aided Geometric Design
IS - 6
ER -