Designing NURBS surfaces by manipulating control points directly requires too much trial and error for immersive VR applications. A more natural interface is provided by deforming a NURBS surface so that it passes through a given target point; and by repeating such deformations we can make the surface follow one or more target curves. These deformations can be achieved by modifying the pseudo-inverse matrix of the basis functions, but this matrix is often ill-conditioned. However, the application of a modified FE approach to the weights and control points provides controllable deformations, which are demonstrated across a range of example shapes.

A surface extraction algorithm with NURBS has been developed for the mesh generation from the scattered data after a cell-based simulation. The triangulation of a surface is initiated with a step of describing the geometry along the polygonal boundary with multiple points. In this work, an NURBS surface can be generated with scattered data for each polygonal surface by employing a multilevel B-spline surface approximation. The NURBS mesh in accordance with our algorithm excellently represents the surface evolution of the topography on the wafer. A dynamically allocated topography model, so-called cell advancing model, is proposed to resolve an extensive memory requirement for the numerical simulation of a complicated structure on the wafer. A concave cylindrical DRAM cell capacitor was chosen to test the capability of our model. A set of capacitance present in the cell capacitor and interconnects was calculated with three-dimensional tetrahedral meshes generated from the NURBS surface on CRAY T3E supercomputer. A total of 5,475,600 (130 156 270) cells was employed for the simulation of semiconductor regions comprising four DRAM cell capacitors with a dimension of 1.3 µm 1.56 µm 2.7 µm . The size of the required memory is about 22 Mbytes and the simulation time is 64,082 seconds. The number of nodes for the FEM calculation was 70,078 with 395,064 tetrahedrons.