This paper presents an automatic method for creating surface models at multiple levels of detail from a polygonal description of an object. The method involves distributing new vertices over the surface and connecting them to form a re-tiling that preserves both geometry and topology. Key contributions include a robust method for connecting new vertices, using surface curvature to distribute vertices more densely in high-curvature regions, and a method for smoothly interpolating between models at different levels of detail. The re-tiling process involves creating an intermediate model called the mutual tessellation, which includes both original and new vertices. The original vertices are then removed, and the surface is locally re-triangulated to maintain the original topology. This technique has been applied to iso-surface models, molecular models, and minimal surfaces. The paper discusses previous work on levels of detail, including methods for simplifying polygonal models through vertex removal and local re-triangulation. It also covers the use of Voronoi regions and Delaunay triangulation in mesh generation. The re-tiling method begins by placing points uniformly over the surface using a relaxation procedure, then forming a mutual tessellation to incorporate both original and new vertices. The mutual tessellation is then used to remove original vertices and re-triangulate the surface, ensuring topological consistency. The method also includes checks to ensure that the new triangles do not fold the surface or connect regions that were not connected in the original model. Curvature is used to adjust the distribution of vertices, with more points placed in regions of higher curvature. The paper also describes how to interpolate between models at different levels of detail by flattening vertices and triangles from a high-detail model onto a low-detail model. This allows for smooth transitions between models. The method is applied to various models, including radiation dose surfaces, molecular models, and minimal surfaces. The paper concludes with future work, including the use of curvature direction to guide local re-triangulation and the exploration of feature elimination at low levels of detail.This paper presents an automatic method for creating surface models at multiple levels of detail from a polygonal description of an object. The method involves distributing new vertices over the surface and connecting them to form a re-tiling that preserves both geometry and topology. Key contributions include a robust method for connecting new vertices, using surface curvature to distribute vertices more densely in high-curvature regions, and a method for smoothly interpolating between models at different levels of detail. The re-tiling process involves creating an intermediate model called the mutual tessellation, which includes both original and new vertices. The original vertices are then removed, and the surface is locally re-triangulated to maintain the original topology. This technique has been applied to iso-surface models, molecular models, and minimal surfaces. The paper discusses previous work on levels of detail, including methods for simplifying polygonal models through vertex removal and local re-triangulation. It also covers the use of Voronoi regions and Delaunay triangulation in mesh generation. The re-tiling method begins by placing points uniformly over the surface using a relaxation procedure, then forming a mutual tessellation to incorporate both original and new vertices. The mutual tessellation is then used to remove original vertices and re-triangulate the surface, ensuring topological consistency. The method also includes checks to ensure that the new triangles do not fold the surface or connect regions that were not connected in the original model. Curvature is used to adjust the distribution of vertices, with more points placed in regions of higher curvature. The paper also describes how to interpolate between models at different levels of detail by flattening vertices and triangles from a high-detail model onto a low-detail model. This allows for smooth transitions between models. The method is applied to various models, including radiation dose surfaces, molecular models, and minimal surfaces. The paper concludes with future work, including the use of curvature direction to guide local re-triangulation and the exploration of feature elimination at low levels of detail.