In this paper, we introduce a new approach to mesh an animated implicit surface for rendering purposes. This approach is based on a double triangulation of the surface. In the first triangulation, the vertices are the nodes of a finite element model. The aim of this model is to uniformly and dynamically sample the surface. It is robust, efficient and prevents the inversion of triangles. The second triangulation is dynamically created from the first one at each frame and provides details in regions of high curvature. Lastly, we present a mechanism to deal with both the topological merging and splitting of surfaces. As shown in our results, our approach provides robust, quality, interactive rendering of animated implicit surfaces, including those with certain kinds of topology changes.