Harmonic Guidance for Surface Deformation

We present an interactive method for applying deformations to a surface mesh while preserving its global shape and local properties. Two surface editing scenarios are discussed, which conceptually differ in the specification of deformations: Either interpolation constraints are imposed explicitly, e.g., by dragging a subset of vertices, or, deformation of a reference surface is mimicked. The contribution of this paper is a novel approach for interpolation of local deformations over the manifold and for efficiently establishing correspondence to a reference surface from only few pairs of markers. As a general tool for both scenarios, a harmonic field is constructed to guide the interpolation of constraints and to find correspondence required for deformation transfer. We show that our approach fits nicely in a unified mathematical framework, where the same type of linear operator is applied in all phases, and how this approach can be used to create an intuitive and interactive editing tool. Figure 1: A simple edit: The visualized harmonic field is used as guidance for bending the cactus (left). Here, the field is defined by one source (red) at the tip of the left arm and one sink (blue) below the middle of the trunk. The result is shown in the center image. Notice the different propagation of the rotation compared to the edit on the right, where three sources on all arms were chosen (without picture). 1.