User interactive methods of determining vertex correspondence between boundaries or curves on objects to be merged is provided. One method relates to projecting a boundary of one object onto a second object to determine a merging curve, along which the two objects will be joined. Another method includes projecting a first object onto a plane to form a planar curve. The planar curve is then mapped to a second object to form a merging curve. Still another method includes interactively selecting corresponding key vertices on different objects to form a merging curve. A system presented that can use one or more of the methods of determining correspondence between boundaries. A merged object can be generated from the merging curve using a mesh solver, such as a Poisson or non-Poisson mesh solver.