Figure 1: Using LBC for 3D cage-based manipulation allows for local, smooth, and shape-aware deformations. Only parts near the manipulated control points are deformed, as indicated by the logarithmic color-coding of the displacement magnitude. Barycentric coordinates yield a powerful and yet simple paradigm to interpolate data values on polyhedral domains. They represent interior points of the domain as an affine combination of a set of control points, defining an interpolation scheme for any function defined on a set of control points. Numerous barycentric coordinate schemes have been proposed satisfying a large variety of properties. However, they typically define interpolation as a combination of all control points. Thus a local change in the value at a single control point will create a global change by propagation into the whole domain. In this context, we present a family of local barycentric coordinates (LBC), which select for each interior point a small set of control points and satisfy common requirements on barycentric coordinates, such as linearity, non-negativity, and smoothness. LBC are achieved through a convex optimization based on total variation, and provide a compact representation that reduces memory footprint and allows for fast deformations. Our experiments show that LBC provide more local and finer control on shape deformation than previous approaches, and lead to more intuitive deformation results.
To reach compactness, Zhang et al. REF prefer to define a family of local barycentric coordinates using a small set of control points.
Local barycentric coordinates
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Computer Science