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- Yutaka Ohtake, Alexander G. Belyaev, Ilia A. Bogaevski
- Computer-Aided Design
- 2001

The paper presents a set of mesh smoothing tools developed to increase mesh regularity, reduce oversmoothing, and enhance crease lines. Mesh smoothing with simultaneous increasing mesh regularity and… (More)

- Yutaka Ohtake, Alexander G. Belyaev, Ilia A. Bogaevski
- Proceedings Geometric Modeling and Processing…
- 2000

A computer graphics object reconstructed from real-world data often contains undesirable noise and small-scale oscillations. An important problem is how to remove the noise and oscillations while… (More)

A viscosity solution of a Hamilton-Jacobi equation is the asymptotics of the solution with the same initial condition of the original Hamilton-Jacobi equation regularized by vanishing viscosity. Even… (More)

- Alexander G. Belyaev, Ilia A. Bogaevski, Tosiyasu L. Kunii
- Optics & Photonics
- 1997

On a smooth generic surface we define ridges to be the local positive maxima of the maximal principal curvature along its associated curvature line and ravines. We investigate relationships between… (More)

- Ilia A. Bogaevski, Alexander G. Belyaev, Tosiyasu L. Kunii
- Optics & Photonics
- 1997

We consider deformations of a silhouette while its boundary evolves according to a function of the curvature. The functions assumed to satisfy some general conditions of monotonicity and… (More)

The subject of the paper is the geometrical optics of short linear waves on plane. We describe perestroikas of momentary fronts and scattering of rays when the light hypersurface has generic conical… (More)

We describe singularities of the convex hull of a generic compact smooth hypersurface in four-dimensional affine space up to diffeomorphism. It turns out that the boundary of the convex hull is the… (More)

We investigate singularities of the convex hull of a generic compact smooth hypersurface in four-dimensional aane space up to diieomorphisms. It turns out there are only two new singularities (in… (More)

We propose fast algorithms for the detection of viewindependent ridges on surfaces given by graphs of functions. The ridges are dejined via exifrema of the principal curvatures along the associated… (More)