This paper presents an automatic method for creating surface models at multiple levels of detail from a given polygonal description. The primary contributions include a robust method for connecting new vertices over a surface, using curvature estimates to distribute more vertices in regions of higher curvature, and smoothly interpolating between models at different levels of detail. The key concept is the creation of an intermediate model called the *mutual tessellation*, which combines original vertices with new points to form a re-tiling of the surface. The new model is then created by locally re-triangulating the surface, ensuring that the topology matches the original. This technique has been successfully applied to various models, including iso-surfaces, molecular models, and minimal surfaces. The paper also discusses the benefits of having multiple representations of an object, such as improving rendering rates and feature recognition. The re-tiling method is particularly useful for curved surfaces but may not be suitable for models with sharp edges. The paper concludes with a discussion on future research directions, including improving curvature estimation and feature elimination at low levels of detail.This paper presents an automatic method for creating surface models at multiple levels of detail from a given polygonal description. The primary contributions include a robust method for connecting new vertices over a surface, using curvature estimates to distribute more vertices in regions of higher curvature, and smoothly interpolating between models at different levels of detail. The key concept is the creation of an intermediate model called the *mutual tessellation*, which combines original vertices with new points to form a re-tiling of the surface. The new model is then created by locally re-triangulating the surface, ensuring that the topology matches the original. This technique has been successfully applied to various models, including iso-surfaces, molecular models, and minimal surfaces. The paper also discusses the benefits of having multiple representations of an object, such as improving rendering rates and feature recognition. The re-tiling method is particularly useful for curved surfaces but may not be suitable for models with sharp edges. The paper concludes with a discussion on future research directions, including improving curvature estimation and feature elimination at low levels of detail.