Method and system for computing a transverse derivative field along a curve on a surface

摘要

According to one embodiment of the invention, a computerized method for computing a transversal derivative field along a curve on a surface includes receiving data defining the surface, the surface represented in terms of parameters u and v as S(u,v), and receiving data defining the curve, the curve represented in terms of a parameter t as c(t). The method also includes receiving a number equal to N constraint conditions for the derivative field, wherein N is a positive integer and determining the transversal derivative L(t) field according to the formula $L\left(t\right)=\frac{\partial S\left(u\left(t\right),v\left(t\right)\right)}{\partial w},$ where i is an index identifying a particular one of N numbers of constraint conditions and L(t_i) is the value of the transversal derivative field at the ith constraint condition and w is a scalar function of u and v that satisfies $\frac{\partial S\left(u\left(t_i\right),v\left(t_i\right)\right)}{\partial w}=L\left(t_i\right).$