Traditional approaches for surface reconstruction from range data require that the input data be either range images or unorganized sets of points. Since a large number of range sensors provide data along curvilinear patterns such as profiles, this paper presents an approach for reconstructing a surface from a set of unorganized curves. A strategy for updating the reconstructed surface during data acquisition is described as well. Curves are accumulated in a volumetric structure in which a vector field is built and updated. The information that is needed for efficient curve registration is also directly available in this vector field. This leads to a unified modeling approach combining surface reconstruction and curve registration. The algorithm implementing the approach is of linear complexity with respect to the number of input curves and makes it suitable for interactive modeling. Simulated data based on a set of six curvilinear patterns as well as data acquired with a range sensor are used to illustrate the various steps of the algorithm.