A Fractal model equipped with detail concept like the one used in wavelet transforms is introduced and used to represent objects in a more efficient way . This new representation can be used to deform object (locally and globally) and to manipulate the geometric texture of these objects. This fractal model based on Projected IFS attractors allows the definition of free form fractal shapes controlled by a set of points. The projected IFS is a type of IFS (Iterated Function System) which mixes free forms models with IFS models. The details concept idea taken from wavelet theory represents the geometric texture of the object. This concept is introduced by wavelet transform. The wavelet transform represents a signal in hierarchic manner. The signal is divided in two parts: one representing the signal in different scales, and the other representing the details of this signal. We proposed a model based on projected IFS and used the idea of details introduced by wavelet theory. An approximation step is first done to fit the model to the object, this step is formulated as a non-linear fitting problem and resolved using a modified Levenberg-Marquardt minimization method. Our goal is to change the representation of objects from an ordered set of data(points, pixels,..) to a set of control data and a vector of details such that this new representation facilitate the manipulation of objects. In this work, we focus on 2D curves.