In the last decades, cloth animation has been the focus of much research, because of demands from the entertainment industry and from e-commerce. That type of animation is usually produced by means of physics simulations that are computationally expensive. Cloth folding during oscillations or due to contact with rigid objects often requires a very dense mesh when high curvatures are present. In those situations, the dynamics simulation will involve huge matrices and vectors. So, in the attempt to reduce costs, adaptive remeshing is frequently proposed. In this work, we investigate a remeshing approach during dynamics simulation of cloth. Mesh refinement is applied only to regions that need a fine level of detail. Our remeshing strategy refines the mesh in regions of high curvature and simplifies the mesh in regions of low curvature. No matter how regular and coarse the initial mesh is, our remeshing strategy produces meshes that are well adapted to the irregularities of the solid objects at every time step of the draping simulation. The fabric model consists of a triangular mesh and uses a springmass-damper system to compute the forces between particles, which are located at the mesh's vertices. Collision detection depends on the arrangement of the cloth model and the objects in the scene. Although the tests show that, for comparable mesh sizes, the adaptive method does not always outperforms nonadaptive methods, the quality of the draping is much better when adaptive methods are used. Thus, adaptive methods can deliver comparable draping quality with fewer elements and less cost.