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We present simple models of trajectories in space, both in 2D and in 3D. The first examples, which model bicircular moves in the same direction, are classical curves (epicycloids, etc.). Then, we explore bicircular moves in reverse…

This paper is devoted to an interaction of 2 objects: the 1st of them is octonions, the classical structure of pure mathematics, the 2nd one is Mobilevision, the recently developped technique of computer graphics. Namely, it is shown that…

We give a new application of the theory of holomorphic motions to the study the distortion of level lines of harmonic functions and stream lines of ideal planar fluid flow. In various settings, we show they are in fact quasilines - the…

A transformation based on mean curvature is introduced which morphs triangulated surfaces into round spheres.

We make several new contributions to the study of proper holomorphic mappings between balls. Our results include a degree estimate for rational proper maps, a new gap phenomenon for convex families of arbitrary proper maps, and an…

Learning image transformations is essential to the idea of mental simulation as a method of cognitive inference. We take a connectionist modeling approach, using planar neural networks to learn fundamental imagery transformations, like…

We consider partial matchings, which are finite graphs consisting of edges and vertices of degree zero or one. We consider transformations between two states of partial matchings. We introduce a method of presenting a transformation between…

We give a new proof and extend a result of J. Kwapisz: whenever a set C is realized as the rotation set of some torus homeomorphism, the image of C under certain projective transformations is also realized as a rotations set.

We present a general theory of fractal transformations and show how it leads to a new type of method for filtering and transforming digital images. This work substantially generalizes earlier work on fractal tops. The approach involves…

Linear fractional transformations on the extended complex plane are classified up to topological conjugacy. Recall that two transformations f and g are called topologically conjugate if there exists a homeomorphism h such that hg=fh.

An ellipsoid is the image of a ball under an affine transformation. If this affine transformation is over the complex numbers, we refer to it as a complex ellipsoid. Characterizations of real ellipsoids have received much attention over the…

We survey recent developments in the theory and applications of the broken ray transforms. Furthermore, we discuss some open problems.

We analyse the deformations of a cylindrical elastic body resulting from displacements in a varying gravitational field.

Metamorphism is a recently introduced integral transform, which is useful in solving partial differential equations. Basic properties of metamorphism can be verified by direct calculations. In this paper we present metamorphism as a sort of…

We study equivariant geometry and rationality of moduli spaces of points on the projective line, for twists associated with permutations of the points.

Image processing is one of the most immerging and widely growing techniques making it a lively research field. Image processing is converting an image to a digital format and then doing different operations on it, such as improving the…

We explore boundedness properties in the context of metric measure spaces, of some natural operators of convolution type whose study is suggested by certain transformations used in computer vision.

The quaternion spaces can be used to describe the property of electromagnetic field and gravitational field. In the quaternion space, some coordinate transformations can be deduced from the feature of quaternions, including Lorentz…

In the article, we exhibit a series of new examples of rigid plane curves, that is, curves, whose collection of singularities determines them almost uniquely up to a projective transformation of the plane.

We study local convexity properties of the triangular ratio metric balls in proper subdomains of the real coordinate space. We also study inclusion properties of the visual angle metric balls and related hyperbolic type metric balls in the…