ECLES: A general method for local editing of parameters with linear constraints

We describe ECLES (Editing by Constrained LEast Squares), a general method for interactive local editing of objects that are defined by a list of parameters subject to a set of linear or affine constraints. The method is intended for situations where each edit action affects only a small set of the parameters; some of which (the "anchors") are to be set to new given values, whereas the rest (the "derived" ones) are to be modified so as to preserve the constraints. We use exact integer arithmetic in order to reliably determine solvability, to detect and eliminate redundancies in the set of constraints, and to ensure that the solution exactly satisfies the constraints. We also use constrained least squares to choose a suitable solution when the constraints allow multiple solutions. Unlike the usual finite element approach, the method allows editing of any set of anchors with any sufficiently large set of derived parameters. As an example of application, we show how the method can be used to edit smooth (C1) deformations of geometric mesh models.