Vector fields produced by experiments or simulations are usually extremely dense, which makes their manipulation and visualization cumbersome. Often, such fields can be simplified without much loss of information.

A simplification method for 3D vector fields defined over tetrahedral meshes is presented. The underlying tetrahedral mesh is progressively simplified by successive half-edge collapses. The order of collapses is determined by a compound metric which takes into account the field and domain error incurred as well as the quality of the resulting mesh. Special attention is given to the preservation of the mesh boundary and of critical points on the vector field.

A tool has been developed for the measurement of the difference between two vector fields over tetrahedral meshes, and it is used to quantify the simplification error.