Patent ID: 8284193

Claim:
A method for preserving design intent of a Non-Uniform Rational B-spline (NURBS) surface without representation of a parent surface, comprising: representing an output surface having control points that are independent from a refinement of said output surface, the output surface c defined by c ⁡ ( u , v ) = ∑ i = 0 I - 1 ⁢ ⁢ ∑ j = 0 J - 1 ⁢ ⁢ c i , j ⁢ N m , i , u ⁡ ( u ) ⁢ N n , j , v ⁡ ( v ) ; interpolating a base surface from said output surface, the base surface b defined by b ⁡ ( u , v ) = ∑ k = 0 K - 1 ⁢ ⁢ ∑ l = 0 L - 1 ⁢ ⁢ b k , l ⁢ N r , k , p ⁡ ( u ) ⁢ N s , t , q ⁡ ( v ) ; calculating a delta vector that is a difference between said output surface and said base surface; and transforming said delta vector based upon a local coordinate system of a normal vector and a tangent plane of said base surface to form a delta surface, wherein r>1, s>1, m>1, and n>1 are orders, p={p k } k=0 K+r−1 and q={q l } l=0 L+s−1 are knot sequences of b in a u-direction and a v-direction, respectively, N r,k,p denotes the k th normalized B-spline of order r with respect to a knot sequence p, N s,l,q denotes the k1 th normalized B-spline of order s with respect to a knot sequence q, b k,l ε 3 denotes a (k,l) th control point, u={u i } i=0 l+m−1 and v={v j } j=0 j+s−1 are knot sequences of b in a u-direction and a v-direction, respectively.