This paper presents a simple geometric algorithm to generate splines of arbitrary degree of smoothness in Euclidean spaces. Unlike other existing methods, this simple geometric algorithm does not require a recursive procedure and, consequently, introduces a significant reduction in calculation time. The algorithm is then extended to other complete Riemannian manifolds, namely to matrix Lie grou...

Abstract. A method of constructing n × n matrix solutions(with n matrix elements) of Temperley-Lieb algebra relation is presented in this paper. The single loop of these solutions are d = √ n. Especially, a 9×9−matrix solution with single loop d= √ 3 is discussed in detail. An unitary Yang-Baxter R̆(θ, q1, q2) matrix is obtained via the Yang-Baxterization process. The entanglement property and g...

Current geometric and solid modeling systems use semi-algebraic sets for deening the boundaries of solid objects, curves and surfaces, geometric constraints with mating relationship in a mechanical assembly, physical contacts between objects, collision detection. It turns out that performing many of the geometric operations on the solid boundaries or interacting with geometric constraints is re...

Stationary digital breast tomosynthesis (sDBT) with distributed X-ray sources based on carbon nanotube (CNT) field emission cathodes has been recently proposed as an approach that can prevent motion blur produced by traditional DBT systems. In this paper, we simulate a geometric calibration method based on a proposed multi-source CNT X-ray sDBT system. This method is a projection matrix-based a...

The recently developed geometric morphometrics methods represent an important contribution of statistics and geometry to the study of biological shapes. We propose simple protocols using shape distances that incorporate geometric techniques into linear quantitative genetic models that should provide insights into the contribution of genetics to shape variation in organisms. The geometric approa...

We study systems of three bivariate polynomials whose Newton polygons are scaled copies of a single polygon. Our main contribution is to construct square resultant matrices, which are submatrices of those introduced by Cattani et al. (1998), and whose determinants are nontrivial multiples of the sparse (or toric) resultant. The matrix is hybrid in that it contains a submatrix of Sylvester type ...

Traditional methods of time-frequency and multiscale analysis, such as wavelets and Gabor frames, have been successfully employed for representing most classes of pseudodifferential operators. However these methods are not equally effective in dealing with Fourier Integral Operators in general. In this paper, we show that the shearlets, recently introduced by the authors and their collaborators...

We introduce real Lösungen as an analogue of roots. For each mutation sequence arbitrary skew-symmetrizable matrix, we define a family reflections along with associated vectors which are and set curves on Riemann surface. The matrix consisting these is called L-matrix. explain how the L-matrix naturally arises in connection C-matrix. Then conjecture that depends (up to signs row vectors) only s...

Computing roots of a monic polynomial may be done by computing the eigenvalues of the corresponding companion matrix using for instance the well-known QR-algorithm. We know this algorithm to be backward stable since it computes exact eigenvalues of a slightly modified matrix. But it may yield very poor backward errors in the coefficients of the polynomial. In this paper we investigate what can ...

We consider the epipolar geometry between two omnidirectional images acquired from a single viewpoint catadioptric vision sensor with parabolic mirror. This work in particular deals with the estimation of the respective epipoles. We use conformal geometric algebra to show the existence of a 3×3 essential matrix, which describes the underlying epipolar geometry. The essential matrix is preferabl...