Deformable objects play an important role in many applications, such as animation and simulation. Effective computation with deformable surfaces can be achieved through the use of dynamic meshes. In this paper, we introduce a framework for constructing and maintaining a timevarying adapted mesh structure that conforms to the underlying deformable surface. The adaptation function employs error metrics based on stochastic sampling. Our scheme combines normal and tangential geometric correction with refinement and simplification resolution control. Furthermore, it applies to both parametric and implicit surface descriptions. As the result, we obtain a simple and efficient general scheme that can be used for a wide range of computations.