R-function is a widely used tool when considering objects obtained through the Boolean operations start from simple base primitives.However,there is square root operation in the representation.Considering that the use...R-function is a widely used tool when considering objects obtained through the Boolean operations start from simple base primitives.However,there is square root operation in the representation.Considering that the use of splines will facilitate the calculations within the CAD system,in this paper,we propose a system of R-functions represented in spline form called Spline R-function(SR).After trans-forming the function ranges of two base primitives to a new coordinate system,a series of sign constraints following a specific Boolean operation are derived and the spline R-function can be formulated as a piecewise function.Representation of SR in both B´ezier form and B-spline form have been given.Among which the B´ezier ordinates are determined with the help of the B-net method through setting up a series of relations according to the sign constraints and properties of R-functions.The construction processes for both Boolean intersection and union operations with different smoothness are discussed in detail.Numerical experiments are conducted to show the potential of the proposed spline R-function.展开更多
基金We would like to thank the anonymous reviewers and our labo-ratory group for helpful discussions and comments.The work is supported by the NSF of China(No.11771420).
文摘R-function is a widely used tool when considering objects obtained through the Boolean operations start from simple base primitives.However,there is square root operation in the representation.Considering that the use of splines will facilitate the calculations within the CAD system,in this paper,we propose a system of R-functions represented in spline form called Spline R-function(SR).After trans-forming the function ranges of two base primitives to a new coordinate system,a series of sign constraints following a specific Boolean operation are derived and the spline R-function can be formulated as a piecewise function.Representation of SR in both B´ezier form and B-spline form have been given.Among which the B´ezier ordinates are determined with the help of the B-net method through setting up a series of relations according to the sign constraints and properties of R-functions.The construction processes for both Boolean intersection and union operations with different smoothness are discussed in detail.Numerical experiments are conducted to show the potential of the proposed spline R-function.
