The use of tangential vector fields and thus the need for designing them has steadily been increasing over the years. In this master thesis, a method is proposed and implemented that defines localized tangential vector fields on a mesh surface, which allows for the designing of vector fields on the triangulated surfaces of these meshes. Similarly, as with 2D radial basis functions for function values, it is possible to accurately approximate, compress and design vector fields using the localized tangential vector fields with an applied radial basis function scalar. The proposed system constructs multiple localized tangential vector fields on the surface and creates a basis from them that covers the entire surface. Other works have already suggested methods for the designing of tangential vector fields but most did not allow for both soft and hard constraints to be used when designing fields in real-time. One approach was able to design fields in real-time but had the bottleneck that it required a lot of precomputation time as it was using spectral processing techniques and a spectral transform to work in the spectral representation. Using the proposed localized tangential vector fields basis in this work also allows for the real-time modeling of tangential vector fields without to much precomputation time. However, it should be noted to fully optimize the proposed system several improvements on the current techniques used in this work have to be made to compete with the spectral representation. The proposed system is the first to our knowledge that uses localized tangential vector fields on meshes for the designing of tangential vector fields.