Patent ID: 6917361

Claim:
A computerized method for computing a transversal derivative field along a curve on a surface comprising: receiving data defining the surface, the surface represented in terms of parameters u and v as S(u,v); receiving data defining the curve, the curve represented in terms of a parameter t as c(t); receiving a number equal to N constraint conditions for the derivative field, wherein N is a positive integer; determining a scalar function w(u,v) according to the constraint formula L ⁡ ( t i ) = ∂ S ⁡ ( u ⁡ ( t i ) , v ⁡ ( t i ) ) ∂ w , wherein 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 determining by a computer the transversal derivative L(t) field according to the formula ∂ S ⁡ ( u ⁡ ( t ) , v ⁡ ( t ) ) ∂ w = L ⁡ ( t ) . wherein: u,v, and t are real numbers: S(u,v), w(u,v), c(t), and L(t) are real value functions; and u(t) and v(t) are real value functions of the curve parameter t that relate the parameterization of the curve t and the parameterization of the surface S(u,v).