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A theoretical approach to construct free form surfaces is presented. We develop the concepts that arise when a free form surface is generated by tracing a mesh, using differentiable manifold theory, and generalizing the B-spline scheme. This approach allows to define a family of practical schemes. Four different applications of the generic approach are also presented in this paper.doi:10.1145/566282.566291 dblp:conf/sma/Cotrina-NavauPV02 fatcat:3hf6vdxiwfgkzbzim4ypqrotha