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Interactive Editing of C1-Continuous 2D Spline Deformations Using ECLES Method

We describe 2DSD, a general algorithm for interactive editing of smooth deformations of the plane defined by polynomial splines of degree 5 on an triangular mesh. 2DSD is based on ECLES, a flexible and general exact method for interactive editing of numeric parameters subject to linear or affine constraints. Each editing action is abstracted as setting a set of anchor points to new positions, and recomputing some derived points so as to satisfy the constraints. When there are multiple solutions, ECLES uses least squares to choose the closest solution to a suggested hint. The advantages of 2DSD include immunity to rounding errors, automatic selection of the derived points for each editing action, and a representation of the deformation whose complexity does not grow with as editing progresses. To validate our algorithm, we re-implemented an editor of space deformations designed to assist the matching of 3D models of flexible microorganisms to microscope images of the same.