Journal of Chaohu University ›› 2023, Vol. 25 ›› Issue (3): 56-61.doi: 10.12152/j.issn.1672-2868.2023.03.007

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Construction of Offset Surface Pencils Preserving Common Characteristic Curves

WANG Jun,DAI Ze-jian:School of Mathematics and Big Data, Chaohu University   

  1. School of Mathematics and Big Data, Chaohu University, Chaohu Anhui 238024
  • Received:2022-09-29 Online:2023-05-25 Published:2023-10-24

Abstract: 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 Pst with a given curve rs as a common characteristic curve, the corresponding curve rs on the offset surface pencil Pst is the same type of characteristic curve. Firstly, Pstis expressed as the linear combination of the Frenet frame of rs, and the coefficients of the linear combination are called the scale functions. Then, Pst is taken as the base surface to construct its offset surface pencil Pst. According to the properties of the characteristic curves, whether rs can be guaranteed to be the same type of characteristic curve as rs on Pst 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.

Key words: offset surface, geodesic, asymptotic curve, line of curvature, Bertrand curve

CLC Number: 

  • TP391.72