Spline Surface
The parametric 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. Use this for bicubic blending between corner points.
Data Format:
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 interpolant points, of
size Nu x Nv
u_tan_arr[][3] Array of u tangent vectors
at interpolant points, of size
Nu x Nv
v_tan_arr[][3] Array of v tangent vectors at
interpolant points, of size
Nu x Nv
uvder_arr[][3] Array of mixed derivatives at
interpolant points, of size
Nu x Nv
direction, of size Nu
v_par_arr[] Point parameters, in the v
direction, of size Nv
point_arr[][3] Array of interpolant points, of
size Nu x Nv
u_tan_arr[][3] Array of u tangent vectors
at interpolant points, of size
Nu x Nv
v_tan_arr[][3] Array of v tangent vectors at
interpolant points, of size
Nu x Nv
uvder_arr[][3] Array of mixed derivatives at
interpolant points, of size
Nu x Nv
Engineering Notes:
• Allows for a unique 3x3 polynomial around every patch.
• There is second order continuity across patch boundaries.
• The point and tangent vectors represent the ordering of an array of [i][j], where u varies with i, and v varies with j. In walking through the point_arr[][3], you will find that the innermost variable representing v(j) varies first.