TY - JOUR
T1 - Analysis and applications of pipe surfaces
AU - Maekawa, Takashi
AU - Patrikalakis, Nicholas M.
AU - Sakkalis, Takis
AU - Yu, Guoxin
N1 - Funding Information:
Funding for this work was obtained, in part, from the Office of Naval Research under grant number N000|4-96-1-0857. The authors would like to thank Mr. S.L. Abrams for his assistance, Prof. T.J. Peters for his comments and the referees for their suggestions which improved the paper.
PY - 1998/5
Y1 - 1998/5
N2 - A pipe (or tubular) surface is the envelope of a one-parameter family of spheres with constant radii r and centers C(t). In this paper we investigate necessary and sufficient conditions for the nonsingularity of pipe surfaces. In addition, when C(t) is a rational function, we develop an algorithmic method for the rational parametrization of such a surface. The latter is based on finding two rational functions α(t) and β(t) such that |C′(t)|2 = α2(t) + β2(t) (Lü and Pottmann, 1996).
AB - A pipe (or tubular) surface is the envelope of a one-parameter family of spheres with constant radii r and centers C(t). In this paper we investigate necessary and sufficient conditions for the nonsingularity of pipe surfaces. In addition, when C(t) is a rational function, we develop an algorithmic method for the rational parametrization of such a surface. The latter is based on finding two rational functions α(t) and β(t) such that |C′(t)|2 = α2(t) + β2(t) (Lü and Pottmann, 1996).
KW - Global self-intersection
KW - Local self-intersection
KW - Pipe surface
KW - Rational parametrization
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U2 - 10.1016/S0167-8396(97)00042-3
DO - 10.1016/S0167-8396(97)00042-3
M3 - Article
AN - SCOPUS:0032074009
SN - 0167-8396
VL - 15
SP - 437
EP - 458
JO - Computer Aided Geometric Design
JF - Computer Aided Geometric Design
IS - 5
ER -