Explicit Control of Vector Field Based Shape Deformations

Vector field based shape deformations (VFSD) have been introduced as an efficient method to deform shapes in a volume-preserving foldover-free manner. However, mainly simple implicitly defined shapes like spheres or cylinders have been explored as deformation tools by now. In contrast, boundary constraint modeling approaches enable the user to exactly define the support of the deformation on the surface. We present an approach to explicitly control VFSD: a scalar function together with two thresholds is placed directly on the shape to mark regions of full, zero, and blended deformation. The resulting deformation is volume-preserving and free of local self-intersections. In addition, the full deformation is steered by a 3D parametric curve and a parametric twisting function. This way our deformations appear to be a generalization of the boundary constraint modeling metaphor. We apply our approach in different scenarios. A parallelization of the computation on the GPU allows for editing high-resolution meshes at interactive speed.