4 Results

To illustrate the behaviour of the deformable surface we consider a simple example. The potential energy is given by . The surface that minimises this potential is an octahedron as shown in figure 1 (a). We seed the deformable surface with a valid mesh (96 faces) as shown in figure 1 (b). The control points converge to the positions shown in figure 1 (c). In figure (d) we show a flat shaded rendering of high and low smoothness fits.

   
Figure 1: (a) octahedron surface (b) the seed, (c) the control mesh, (d) high fit, (e) low fit.

In figure 2 we increase the density of the control mesh to 1944 faces and obtain a more faithful fit to the octahedron.

   
Figure 2: (a) the seed, (c) the fit to an octahedron.

In the next example we show a fit to a sphere with 2 different seeds. The seeds are shown in figures 3 (a) and 3 (d) and the converged control mesh is shown in 3 (b) and 3 (e). In figure 3 (c) we show a rendered view of the surface.

   
Figure 3: Fit to sphere (a) Control mesh for first seed (b) Control mesh for first fit (c) Rendered surface for first fit (d) Control mesh for second seed (e) control mesh for second fit

The next example shows how a deformable surface fit may be used to create a more compact representation of a high polygon count mesh. This is an alternative to mesh decimation. The volumetric potential is simply the square of the distance to the nearest point on the surface computed using a voxel based structure as reported in [ 7 ]. Figure 4 (a) shows the seed, and 4 (b) shows the converged control mesh with a vertex count of 618. Figure 4 (c) shows a flat-shaded rendering of the surface, compared with the original mesh in figure 4 (d) with a vertex count of 3091.

   
Figure 4: Surface fit to telephone data (a) Control mesh for seed (b) Control mesh for fit (c) Rendered result (d) Data

Finally we show some results with a new seeding strategy. A high polygon count bunny model was decimated with the algorithm developed by [ 1 ] to obtain the 370 vertex model shown in figure 5 (a). Each triangular face was split into 3 4-sided faces as shown in the 1763 vertex seed, figure 5 (b). This was fitted to the original data and the result is shown in 5 (c).

   
Figure 5: Surface fit to bunny (a) Decimated bunny (b) Control mesh for seed (c) Final result

A disadvantage of this method over the alternative seeding method is that it produces patches with up to 11 sides in this example, in contrast with the cube type seeds that have a maximum of 6-sided patches. At present we make an arbitrary decision not to render patches with more than 8 sides, which has caused the hole between the bunny's ears.