Estimation of differential quantities using Hermite RBF interpolation

M. Prant, L. Váša

Exact curvature Proposed curvature Rusinkiewicz Kalogerakis
Figure1: From left to right - Exact curvature, Proposed solution (phi=exp(-epsilon * r^3)), Rusinkiewicz, Kalogerakis


Curvature is an important geometric property in computer graphics that provides information about the character of object surfaces. The exact curvature can only be calculated for a limited set of surface descriptions. Most of the time, we deal with triangles, point sets or some other discrete representation of the surface. For those, curvature can only be estimated. However, surfaces can be fitted by some kind of interpolation function and from it, curvature can be calculated directly. This paper proposes a method for curvature estimation and normal vector re-estimation based on surface fitting using Hermite Radial Basis Function interpolation. Hermite variation uses not only control points, but normal vectors at those points as well. This leads to a better and more robust interpolation than if only control points are used. Once the interpolant is obtained, the curvature and other possible properties can be directly computed using known approaches. The proposed algorithm was tested on several explicit and implicit functions and it outperforms current state-of-the-art methods if exact normals are available. For normals calculated directly from a triangle mesh, the proposed algorithm works on par with existing state-of-the-art methods.

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Source code: comming soon

Martin Prantl 2017
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