Vitaly Surazhsky

Explicit surface remeshing

We present a new remeshing scheme based on the idea of improving mesh quality by a series of local modifications of the mesh geometry and connectivity. Our contribution to the family of local modification techniques is an area-based smoothing technique. Area-based smoothing allows the control of both triangle quality and vertex sampling over the mesh, as a function of some criteria, e.g. the mesh curvature. To perform local modifications of arbitrary genus meshes we use dynamic patch-wise parameterization. The parameterization is constructed and updated on-the-fly as the algorithm progresses with local updates. As a post-processing stage, we introduce a new algorithm to improve the regularity of the mesh connectivity. The algorithm is able to create an unstructured mesh with a very small number of irregular vertices. Our remeshing scheme is robust, runs at interactive speeds and can be applied to arbitrary complex meshes.

Guaranteed intersection-free polygon morphing

Abstract We present a method for naturally and continuously morphing two simple planar polygons with corresponding vertices in a manner that guarantees that the intermediate polygons are also simple. This contrasts with all existing polygon morphing schemes who cannot guarantee the non-self-intersection property on a global scale, due to the heuristics they employ. Our method achieves this property by reducing the polygon morphing problem to the problem of morphing compatible planar triangulations of corresponding point sets, which is performed by interpolating vertex barycentric coordinates instead of vertex locations. The reduction involves compatibly triangulating simple polygons and polygons with a single hole. We show how to achieve this using only a small number of extra (Steiner) vertices.

Controllable morphing of compatible planar triangulations

Two planar triangulations with a correspondence between the pair of vertex sets are compatible (isomorphic) if they are topologically equivalent. This work describes methods for morphing compatible planar triangulations with identical convex boundaries in a manner that guarantees compatibility throughout the morph. These methods are based on a fundamental representation of a planar triangulation as a matrix that unambiguously describes the triangulation. Morphing the triangulations corresponds to interpolations between these matrices.We show that this basic approach can be extended to obtain better control over the morph, resulting in valid morphs with various natural properties. Two schemes, which generate the linear trajectory morph if it is valid, or a morph with trajectories close to linear otherwise, are presented. An efficient method for verification of validity of the linear trajectory morph between two triangulations is proposed. We also demonstrate how to obtain a morph with a natural evolution of triangle areas and how to find a smooth morph through a given intermediate triangulation.

Texture Mapping with Hard Constraints

We show how to continuously map a texture onto a 3D triangle mesh when some of the mesh vertices are constrained to have given (u, v) coordinates. This problem arises frequently in interactive texture mapping applications and, to the best of our knowledge, a complete and efficient solution is not available. Our techniques always guarantee a solution by introducing extra (Steiner) vertices in the triangulation if needed. We show how to apply our methods to texture mapping in multi‐resolution scenarios and image warping and morphing.

INTRINSIC MORPHING OF COMPATIBLE TRIANGULATIONS

Two planar triangulations with a correspondence between two vertex sets are compatible (isomorphic) if they are topologically equivalent. This work presents a simple and robust method for morphing two compatible planar triangulations with identical convex boundaries that locally preserves the intrinsic geometric properties of triangles throughout the morph. The method is based on the barycentric coordinates representation of planar triangulations, and thus, guarantees compatibility of all intermediate triangulations. The intrinsic properties are preserved by interpolating angles and edge lengths components of mean value barycentric coordinates, rather than interpolating the barycentric coordinates themselves. As a result, the method generates a natural-looking and guaranteed intersection-free morphing sequence.

High quality compatible triangulations

Compatible meshes are isomorphic meshings of the interiors of two polygons having a correspondence between their vertices. Compatible meshing may be used for constructing sweeps, suitable for finite element analysis, between two base polygons. They may also be used for meshing a given sequence of polygons forming a sweep. We present a method to compute compatible triangulations of planar polygons, sometimes requiring extra (Steiner) vertices. Experimental results show that for typical real-life inputs, the number of Steiner vertices introduced is very small. However, having a small number of Steiner vertices, these compatible triangulations are usually not of high quality, i.e. they do not have well-shaped triangles. We show how to increase the quality of these triangulations by adding Steiner vertices in a compatible manner, using remeshing and mesh smoothing techniques. The total scheme results in high-quality compatible meshes with a small number of triangles. These meshes may then be morphed to obtain the intermediate triangulated sections of a sweep, if needed.

Blending polygonal shapes with different topologies

Abstract In this paper, we propose a new method for morphing between two polygonal, possibly non-simply connected, shapes in the plane. The method is based on reconstructing an xy -monotone surface whose extreme cross-sections coincide with the given shapes. The surface generated by our algorithm does not contain any self-intersections, does not change the topologies of the input slices, does not contain any horizontal triangles, and guarantees that all the topology changes occur at a mid-height which is a degenerate form of both input topologies. All these properties are highly desirable for blending shapes of different topologies.

Type-safe covariance in C++

We present a programming technique for implementing type safe covariance in C++. In a sense, we implement most of Bruces matching approach to the covariance dilemma in C++. The appeal in our approach is that it relies on existing mechanisms, specifically templates, and does not require any modification to the existing language. The practical value of the technique was demonstrated in its successful incorporation in a large software body. We identify the ingredients of a programming language required for applying the technique, and discuss extensions to other languages.