Estimation of differential quantities using Hermite RBF interpolation
M. Prant, L. Váša
This article has been published in The Visual Computer - link
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
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