Example: Cylindrical Spline Surface Data Format
The cylindrical spline surface is a nonuniform bicubic spline surface that passes through a grid with tangent vectors given at each point. The grid is curvilinear in uv space.
The following illustration shows a cylindrical spline surface.
1. Cone surface S1
2. Cylindrical surface, S0 Spline
Data format:
 e1[3] x' vector of the local coordinate system e2[3] y' vector of the local coordinate system e3[3] z' vector of the local coordinate system, which corresponds to the axis of revolution of the surface origin[3] Origin of the local coordinate system splsrf Spline surface data structure
The spline surface data structure contains the following fields:
 u_par_arr[] Point parameters, in the u direction, of size Nu v_par_arr[] Point parameters, in the v direction, of size Nv point_arr[][3] Array of points, in cylindrical coordinates, of size, Nu & Nv. The array components are as follows:point_arr[i][0]—Radiuspoint_arr[i][1]—Thetapoint_arr[i][2]—Z u_tan_arr[][3] Array of u tangent vectors in cylindrical coordinates, of size Nu & Nv v_tan_arr[][3] Array of v tangent vectors in cylindrical coordinates, of size Nu & Nv uvder_arr[][3] Array of mixed derivatives in cylindrical coordinates, of size Nu & Nv
Engineering Notes
If the surface is represented in cylindrical coordinates (r, theta, z), the local coordinate system values (x', y', z') are interpreted as follows:
x' = r cos (theta)
y' = r sin (theta)
z' = z
You can obtain a cylindrical spline surface, for example, by creating a smooth rotational blend (shown in the figure on the previous page). In some cases, you can replace a cylindrical spline surface with a surface such as a plane, cylinder, or cone. The illustration shows the cylindrical spline surface S1 replaced with a cone (r1=r2, r3=r4, and r1r3). If you cannot replace it (such as for the surface S0 in the illustration Cylindrical Spline Surface (ra≠rb or rc≠rd), leave it as a cylindrical spline surface representation.