Related papers: Dual-Quaternion Interpolation
In this paper, we extend the structure-preserving interpolatory model reduction framework, originally developed for linear systems, to structured bilinear control systems. Specifically, we give explicit construction formulae for the model…
We generalize the formerly proposed relationship between a special complex geometry (originating from the structure of biquaternion algebra) and induced real geometry of (extended) space-time. The primordial dynamics in complex space allows…
One of the best things about geometry is that it's cool! Geometry enables us to create incredible designs and astounding patterns. This article shows how to use a simple technique (iteration) to create designs that are both cool and…
Rational agents acting as observers use ``knowables'' to construct a vision of the outside world. Thereby, they are bound by the information exchanged with what they consider to be objects. The cartesian cut or, in modern terminology, the…
Rotations on the 3-dimensional Euclidean vector-space can be represented by real quaternions, as was shown by Hamilton. Introducing complex quaternions allows us to extend the result to elliptic and hyperbolic rotations on the Minkowski…
Image warping is a necessary step in many multimedia applications such as texture mapping, image-based rendering, panorama stitching, image resizing and optical flow computation etc. Traditionally, color image warping interpolation is…
Coupling qubits together towards large-scale integration is a key point for realizing a quantum computer. We study the capacitively coupled superconducting phase qubits using two diagonalization methods, which are very efficient to obtain…
The Fractional Fourier Transform is a ubiquitous signal processing tool in basic and applied sciences. The Fractional Fourier Transform generalizes every property and application of the Fourier Transform. Despite the practical importance of…
We define a notion of general uniform interpolant, generalizing the notions of cover and of uniform interpolant and identify situations in which symbol elimination can be used for computing general uniform interpolants. We investigate the…
Quantum computing is rapidly emerging as a promising technology for solving complex optimization problems that arise in various engineering fields. Therefore, it holds significant promise to transform the computational foundations of power…
We are seeing a Cambrian explosion of 3D shape representations for use in machine learning. Some representations seek high expressive power in capturing high-resolution detail. Other approaches seek to represent shapes as compositions of…
We consider the quasiconformal dilatation of projective transformations of the real projective plane. For non-affine transformations, the contour lines of dilatation form a hyperbolic pencil of circles, and these are the only circles that…
This paper addresses the problem of interpolating visual textures. We formulate this problem by requiring (1) by-example controllability and (2) realistic and smooth interpolation among an arbitrary number of texture samples. To solve it we…
We explain the orthogonal planes split (OPS) of quaternions based on the arbitrary choice of one or two linearly independent pure unit quaternions $f,g$. Next we systematically generalize the quaternionic Fourier transform (QFT) applied to…
This paper is concerned with applications of the theory of approximation and interpolation based on compensated convex transforms developed in [K. Zhang, E. Crooks, A. Orlando, Compensated convexity methods for approximations and…
We introduce the concept of quantum supermap, describing the most general transformation that maps an input quantum operation into an output quantum operation. Since quantum operations include as special cases quantum states, effects, and…
This paper presents a method for enhancing the gray level images. This method takes part from the category of point transforms and it is based on interpolation functions. The latter have a graphic represented by polygonal lines. The…
I investigate the scattering properties of transformation devices as the traditional impedance matching criteria are altered. This is demonstrated using simple theory and augmented by numerical simulations that investigate the role of…
We develop a systematic method of obtaining duality symmetric actions in different dimensions. This technique is applied for the quantum mechanical harmonic oscillator, the scalar field theory in two dimensions and the Maxwell theory in…
The primary objectives of this paper are to present the construction of bivariate fractal interpolation functions over triangular interpolating domain using the concept of vertex coloring and to propose a double integration formula for the…