Manifold Learning Methods assume that a high-dimensional data set has a low-dimensional representation. These methods can be employed in order to simplify data, and to obtain a better understanding of the structure of which the data belong. In this thesis, a tensor voting approach is employed as a technique of manifold learning, to obtain information about the intrinsic dimensionality of the data and reliable estimates of the orientation of normal and tangent vectors at each data point in the manifold. Next, a constructive method is proposed to approximate an implicit manifold and perform a regression. The method is called Constructive Regression on Implicit Manifold (RCVI). With the obtained results, search is made in order to obtain a manifold approximation, which consists in a domain partition, error-controlled, based on 2n-trees (n means the number of features of the input data set) and binary partition trees with smooth transition functions. The construction implies in partition the data set into several subsets in order to approximate each subset with a simple implicit function. In this work, it is used multivariate polynomial functions. The global shape can be obtained by combining these simple structures. Each input data set is associated with an output data, then, from a good manifold approximation using those input data set, it is hoped that occurs a good estimate of the output data. Therefore, the stop criteria of the domain subdivision include a precision, deffined by the user, on the manifold approximation, as well as a criterion that involves the output dispersion on each subdomain. To evaluate the performance of the proposed method, a regression on real data is computed, and compared with some supervised learning algorithms and also an application on well data is performed.