The flattening of triangulated surfaces incorporating darts and gussets

The problem of deriving patterns from 3D surfaces is described. An algorithm is presented for the flattening of 3D surfaces described in terms of a list of triangles. The algorithm incorporates an energy model in terms of the strain energy required to deform the edges of the triangular mesh. Also considered is the problem of arbitrarily siting darts or gussets to assist in the fitting process. The operation of the algorithm is demonstrated by fitting patterns to a classical geometric shape. The sensitivity of the final pattern to the algorithm's parameters is examined. Results are presented which quantify the strain energy reductions as a result of inserting darts or gussets in the pattern.