%A WANG Jun, DAI Ze-jian
%T Construction of Offset Surface Pencils Preserving Common Characteristic Curves
%0 Journal Article
%D 2023
%J Journal of Chaohu University
%R 10.12152/j.issn.1672-2868.2023.03.007
%P 56-61
%V 25
%N 3
%U {http://xb.chu.edu.cn/CN/abstract/article_732.shtml}
%8 2023-05-25
%X Offset surfaces are widely used in industrial fields, such as tool path geometry generation and robot path
planning in NC machining, surface plate representation in solid modeling, etc. Geodesic, line of curvature and asymptotic curve are three kinds of important characteristic curves which play a decisive role in the properties and shapes
of surfaces. The construction of offset surface pencils preserving common characteristic curves is studied, that is,
when constructing a surface pencil *P*（*s*，*t*） with a given curve *r*（*s*） as a common characteristic curve, the corresponding curve *r*（*s*） on the offset surface pencil *P*（*s*，*t*） is the same type of characteristic curve. Firstly, *P*（*s*，*t*）is expressed
as the linear combination of the Frenet frame of *r*（*s*）, and the coefficients of the linear combination are called the
scale functions. Then, *P*（*s*，*t*） is taken as the base surface to construct its offset surface pencil *P*（*s*，*t*）. According to
the properties of the characteristic curves, whether *r*（*s*） can be guaranteed to be the same type of characteristic curve
as *r*（*s*） on *P*（*s*，*t*） completely depends on the given curve and has nothing to do with the scale functions. Finally, the
cylindrical helix and circle are taken as examples to verify the correctness of the above conclusions.