Ellipsoids are important primitives used in visualization and modeling, where often a larger number of ellipsoids have to be displayed in real-time. The standard approach of tessellating each ellipsoid into a smooth polygonal mesh leads to unacceptable polygon counts that dramatically increase the rendering time. In this paper a method is proposed to splat ellipsoids perspectively correct. The ...

In this paper, we describe an exact method for detecting collision between two moving ellipsoids under pre-specified rational motions. Our method is based on an algebraic condition that determines the separation status of two static ellipsoids – the condition itself is described by the signs of roots of the characteristic equation of the two ellipsoids. To deal with moving ellipsoids, we derive...

Monte Carlo computer simulations are used to study transient cavities and the solvation of hard-spheroid solutes in dipolar hard-sphere solvents. The probability distribution of spheroidal cavities in the solvent is shown to be well described by a Gaussian function, and the variations of fit parameters with cavity elongation and solvent properties are analyzed. The excess chemical potentials of...

In this thesis a Mode Coupling Theory (MCT) equation is derived that calculates the shear modulus for multi-component colloidal mixtures in two-dimensional systems in linear approximation. With this equation, the plateau shear modulus G∞ is calculated for two two-dimensional systems at the glass transition: for a binary mixture of hard spheres and for a binary mixture of dipolar particles. The ...

The thermodynamic properties of ferrofluids in applied magnetic fields are examined using theory and computer simulation. The dipolar hard sphere model is used. The second and third virial coefficients (B(2) and B(3)) are evaluated as functions of the dipolar coupling constant λ, and the Langevin parameter α. The formula for B(3) for a system in an applied field is different from that in the ze...

Abstract We present recursive formulas that compute the recently defined “higher symplectic capacities” for all convex toric domains. In special case of four-dimensional ellipsoids, we apply homological perturbation theory to associated filtered $\mathcal{L}_\infty $ algebras and prove resulting structure coefficients count punctured pseudoholomorphic curves in cobordisms between ellipsoids. As...

In many applications to biophysics and environmental engineering, sedimentation of non-spherical particles for example: ellipsoids, is an important problem. In our work, we simulate the dynamics of oblate ellipsoids under gravity. We study the settling velocity and the average orientation of the ellipsoids as a function of volume fraction. We see that the settling velocity shows a local maximum...

A set of tri-axial ellipsoids, with given semi-axes, is to be packed into a rectangular box; its widths, lengths and height are subject to lower and upper bounds. We want to minimize the volume of this box and seek an overlap-free placement of the ellipsoids which can take any orientation. We present closed non-convex NLP formulations for this ellipsoid packing problem based on purely algebraic...