Bernstein polynomials are a classical tool in Computer Aided Design to create smooth maps with a high degree of local control. They are used for the construction of Bézier surfaces, free-form deformations, and many other applications. However, classical Bernstein polynomials are only defined for simplices and parallelepipeds. These can in general not directly capture the shape of arbitrary obje...

Generalizations of barycentric coordinates in two and higher dimensions have been shown to have a number of applications in recent years, including finite element analysis, the definition of Spatches (n-sided generalizations of Bézier surfaces), free-form deformations, mesh parametrization, and interpolation. In this paper we present a new form of d dimensional generalized barycentric coordinat...

Bézier surfaces are an important design tool in Computer Aided Design. They are parameterized surfaces where the parameterization can be represented as a homogeneous polynomial in barycentric coordinates. Usually, Wachspress coordinates are used to obtain tensor product Bézier surfaces over rectangular domains. Recently, Floater introduced mean value coordinates as an alternative to Wachspress ...

We present a method to handle cubic trimmed triangular Bézier patches. This scheme makes use of levels of detail and surface subdivision to achieve a fast and flexible hierarchical data structure that is specially useful to compute surface intersections in a robust and efficient way. The accuracy of the results can be adjusted by adding or subtracting elements to the levels of detail hierarchy,...

We present a tension-controlled 2-point Hermite interpolatory subdivision scheme that is capable of reproducing circles starting from a sequence of sample points with any arbitrary spacing and appropriately chosen first and second derivatives. Whenever the tension parameter is set equal to 1, the limit curve coincides with the rational quintic Hermite interpolant to the given data and has guara...

We examine the problem of determining, when possible, the exact topological adjacency structure of the planar subdivision induced on a rectangle by a set of curves given in implicit form. This means finding the number of points of intersection of the curves and the way curve segments are linked to determine regions. We use a recursive method based on estimates given by interval arithmetic, toge...

In this work, we explore epidemiological dynamics by the example of tuberculosis in Russian Federation. It has been shown that the epidemiological dynamics correlates linearly with the virulence of Mycobacterium tuberculosis during the period 1987-2012. To construct an appropriate model, we have analysed (using LogLet decomposition method) epidemiological World Health Organization (WHO) data (p...

In this paper we present a new multiresolution framework that takes into consideration reducing the coarse points’ energy during decomposition. We start from initial biorthogonal filters to include energy minimization in multiresolution. Decomposition and reconstruction are main operations for any multiresolution representation. We formulate decomposition as smooth reverse subdivision, based on...

This article presents a new and direct approach for fitting a subdivision surface from an irregular and dense triangle mesh of arbitrary topological type. All feature edges and feature vertices of the original mesh model are first identified. A topologyand feature-preserving mesh simplification algorithm is developed to further simplify the dense triangle mesh into a coarse mesh. A subdivision ...

This article focuses on algorithms for fast computation of the Euclidean distance between a query point and a subdivision surface. The analyzed algorithms include uniform tessellation approaches, an adaptive evalution technique, and an algorithm using Bézier conversions. These methods are combined with a grid hashing structure for space partitioning to speed up their runtime. The results show t...