A nonlinear static approach for curve editing

This paper introduces a method for interactively editing planar curves subject to positional and rotational constraints. We regard editing as a static deformation problem but our treatment differs from standard finite element methods in the sense that the interpolation is based on the deformation modes rather than the classic shape functions. A careful choice of these modes allows capturing the deformation behavior of the individual curve segments, and devising the underlying mathematical model from simple and tractable physical considerations. In order to correctly handle arbitrary user input (e.g. dragging vertices in a fast and excessive manner), our approach operates in the nonlinear regime. The arising geometric nonlinearities are addressed effectively through the modal representation without requiring complicated fitting strategies. In this way, we circumvent commonly encountered locking and stability issues while conveying a natural sense of flexibility of the shape at hand. Experiments on various editing scenarios including closed and nonsmooth curves demonstrate the robustness of the proposed approach.

Graphical abstractFigure optionsDownload full-size imageDownload high-quality image (311 K)Download as PowerPoint slideHighlights► A Robust approach for interactive deformation and editing of planar curves. ► Applicability to various curve editing scenarios including closed and nonsmooth curves. ► Efficient treatment of large planar deformations. ► Wiggling and oscillation free interaction.