On a remarkable class of rational surfaces in 4-space generalizing surfaces with linear normal vector fields
نویسندگان
چکیده
In the present paper we investigate a special class of two-dimensional rational surfaces Φ in R whose tangent planes satisfy the following property: For any threespace E in R there exists a unique tangent plane T (u, v) of Φ which is parallel to E. For all possible varieties of tangent planes T (u, v) the corresponding families of surfaces in R are constructed explicitly. Quadratic triangular Bézier surfaces in R occur as special cases. This construction generalizes the concept of LN-surfaces in R 3 to two-dimensional surfaces in R.
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