Dual Laplacian Editing for Meshes

Oscar Kin-Chung Au    Chiew-Lan Tai    Ligang Liu    Hongbo Fu

IEEE Transaction on Visualization and Computer Graphics (TVCG)

handle-aware isolines

A deformation example created with our system. (a) Input model. (c) Edited model. (b) and (d) The corresponding dual models. The mesh is edited in the dual domain, but the dual models are hidden from users. Users are only required to specify the handle positions and the local features are automatically rotated smoothly.

Recently, differential information as local intrinsic feature descriptors has been used for mesh editing. Given certain user input as constraints, a deformed mesh is reconstructed by minimizing the changes in the differential information. Since the differential information is encoded in a global coordinate system, it must somehow be transformed to fit the orientations of details in the deformed surface, otherwise distortion will appear. We observe that visually pleasing deformed meshes should preserve both local parameterization and geometry details. We propose to encode these two types of information in the dual mesh domain due to the simplicity of the neighborhood structure of dual mesh vertices. Both sets of information are nondirectional and nonlinearly dependent on the vertex positions. Thus, we present a novel editing framework that iteratively updates both the primal vertex positions and the dual Laplacian coordinates to progressively reduce distortion in parametrization and geometry. Unlike previous related work, our method can produce visually pleasing deformations with simple user interaction, requiring only the handle positions, not local frames at the handles.
mesh editing, local shape representation, click-and-drag interface, shape preserving, dual Laplacian

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An earlier version: Technical report, HKUST-CS05-10, July 2005

Poster presented at Symposium on Geometry Processing 2005
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    author = {Oscar K.-C. Au and Chiew-Lan Tai and Ligang Liu and Hongbo Fu},
    title = {Dual {L}aplacian editing for meshes},
    journal = {IEEE Transaction on Visualization and Computer Graphics},
    year = {2006},
    volume = {12},
    pages = {386--395},
    number = {3},