  Isosurfaces are an important tool for analysis and visualization of
univariate scalar fields. Earlier works have demonstrated the presence of
interesting isosurfaces at isovalues close to critical values. This motivated
the development of efficient methods for computing individual components of
isosurfaces restricted to a region of interest. Generalization of isosurfaces
to fiber surfaces and critical points to Jacobi sets has resulted in new
approaches for analyzing bivariate scalar fields. Unlike isosurfaces, there
exists no output sensitive method for computing fiber surfaces. Existing
methods traverse through all the tetrahedra in the domain. In this paper, we
propose the use of the Jacobi set to identify fiber surface components of
interest and present an output sensitive approach for its computation. The
Jacobi edges are used to initiate the search towards seed tetrahedra that
contain the fiber surface, thereby reducing the search space. This approach
also leads to effective analysis of the bivariate field by supporting the
identification of relevant fiber surfaces near Jacobi edges.
