The results given show the problems of self-intersection and leakage and the quality of mesh that can be achieved by including the relaxation stage. Figure 4 illustrates the mesh deforming at different stages using mesh relaxation and is the result of applying our deformable surface to the knee data. Nodes are gradually added to the mesh when needed using a coarse to fine strategy, that is we refine only the longest of face edges until the longest edge is less than the `minimum value' in this case 15 units. Several nodes in the earlier meshes exhibit a very non-smooth appearance, this is permitted in order to allow the mesh to deform up the stem of the femur. This movement would not be possible if the mesh was over-constrained and is exaggerated by initialising the mesh far from the feature boundary.
Figure 5 shows meshes exhibiting surface self-intersection because the relaxation phase of the deformation process is omitted. It can be seen that the surface is far less smooth than the equivalent iteration meshes in figure 4 . Self-intersection can be seen at the condyles where the mesh becomes tangled and irregular.
Figure 6 shows the result of only using the first phase in the relaxation process to prevent self-intersection and omitting the second phase that controls leakage. If the meshes produced are compared with the mesh grown using relaxation in figure 4 , it can be seen that one of the condyles is abnormally large. This problem is caused by a node being placed outside the femur during refinement and because of a high energy wall at the object boundary it is unable to contract back into the mesh and subsequently deforms into a gross malformation.
N Hill
