Related papers: Looping Animations Using the Modular Flow and Elli…

We construct doubly periodic Stokes flows in two dimensions using elliptic functions. This method has advantages when the doubly periodic lattice of obstacles has less than maximal symmetry. We find the mean flow through an arbitrary…

We define a modular function which is a generalization of the elliptic modular lambda function. We show this function and the modular invariant function generate the modular function field with respect to the principal congruence subgroup.…

Polymorphic circuits are a special kind of circuits which possess multiple build-in functions, and these functions are activated by environment parameters, like temperature, light and VDD. The behavior of a polymorphic circuit can be…

We provide analytic solutions of the nonlinear differential equation system describing the particle paths below small-amplitude periodic gravity waves travelling on a constant vorticity current. We show that these paths are not closed…

We extend the concept of optical flow with spatiotemporal regularisation to a dynamic non-Euclidean setting. Optical flow is traditionally computed from a sequence of flat images. The purpose of this paper is to introduce variational motion…

Flow fields are often represented by a set of static arrows to illustrate scientific vulgarization, documentary film, meteorology, etc. This simple schematic representation lets an observer intuitively interpret the main properties of a…

We use some fundamental ideas from complex analysis to create symmetric images and animations. Using a domain coloring algorithm, we generate mappings to the entire complex plane or the hyperbolic upper half-plane. The resulting designs can…

In this paper we examine the flow generated by coupled surface and internal small-amplitude water waves in a two-fluid layer model, where we take the upper layer to be rotational (constant vorticity) and the lower layer to be irrotational.…

A theoretical and experimental study of the spin-over mode induced by the elliptical instability of a flow contained in a slightly deformed rotating spherical shell is presented. This geometrical configuration mimics the liquid rotating…

Morphing is a long-standing problem in vision and computer graphics, requiring a time-dependent warping for feature alignment and a blending for smooth interpolation. Recently, multilayer perceptrons (MLPs) have been explored as implicit…

In this paper, we construct rotating frames for curves, including plane curves, space curves and curves on surfaces. Hence, the behaviour of an arbitrary moving point on a curve can be seen as the composite of linear motion and rotation.…

We study all the possibilities of producing rotating flow in an incompressible fluid by electric and magnetic fields. We start with a general theoretical basis and look for different configurations and set-ups which electric/magnetic field…

Modular forms are highly self-symmetric functions studied in number theory, with connections to several areas of mathematics. But they are rarely visualized. We discuss ongoing work to compute and visualize modular forms as 3D surfaces and…

Elliptical rotation is the motion of a point on an ellipse through some angle about a vector. The purpose of this paper is to examine the generation of elliptical rotations and to interpret the motion of a point on an elipsoid using…

It is shown that the elliptic flow can be successfully described in the color string picture with fusion and percolation provided anisotropy of particle emission from the fused string is taken into account. Two possible sources of this…

A fluid flow in a multiply connected domain generated by an arbitrary number of point vortices is considered. A stream function for this flow is constructed as a limit of a certain functional sequence using the method of images. The…

We propose a method to interactively control the animation of fluid elements in still images to generate cinemagraphs. Specifically, we focus on the animation of fluid elements like water, smoke, fire, which have the properties of repeating…

Paint marbling refers to techniques for creating intricate designs in colored paints floating on a liquid surface. If the marbling motions are executed slowly, then this layer of paints can be modeled as a two-dimensional incompressible…

In this paper, we demonstrate a fully automatic method for converting a still image into a realistic animated looping video. We target scenes with continuous fluid motion, such as flowing water and billowing smoke. Our method relies on the…

We extend the concept of optical flow to a dynamic non-Euclidean setting. Optical flow is traditionally computed from a sequence of flat images. It is the purpose of this paper to introduce variational motion estimation for images that are…