If you select a solid to be interpolated or smoothed and you want the boundary faces to be smoothed as well, then you should select each of the faces for the same interpolation or smoothing. Sometimes, by interpolating or smoothing the faces, there is no need to interpolate or smooth the interior.
There is a consistent way that TrueGrid® interpolates or smooths part of the mesh and it is based on the dimension of the selected region.
- CASE 1 - 1 Dimension
- When an interpolation is done along an edge of the mesh, the end nodes are fixed and serve as the boundary condition for the interpolation.
- CASE 2 - 2 Dimensions
- When a face is interpolated or smoothed, the edges of the face are fixed and serve as the boundary conditions for the interior.
- CASE 3 - 3 Dimensions
- When a solid is interpolated or smoothed, the faces of the solid are fixed and serve as the boundary conditions for the interior.
- CASE 4 - Neumann boundary
- Some smoothing algorithms will move the boundary nodes to produce a near orthogonal mesh near the boundary. This makes it possible to glue several blocks together and get a smooth mesh at their interface. The disadvantage is two fold. First, this limits the shape of the mesh at the interface, which may not be ideal. Second, most implementations cause the nodes to wonder off of the surface. In TrueGrid®, we have resisted this approach. A better solution is achieved by smoothing the two blocks together. Also, the Neumann boundary condition violates the nodal distribution conditions that TrueGrid® works hard at preserving.
