Related papers: Visualizing Squircular Implicit Surfaces
We investigate a type of distance between triangulations on finite type surfaces where one moves between triangulations by performing simultaneous flips. We consider triangulations up to homeomorphism and our main results are upper bounds…
We study the systems of ordinary differential equations which are implicit with respect to the higher derivatives, appearing in the linear form, and their solutions near the singular points. The invertibility of the higher derivatives…
This paper is devoted to presenting a new approach to determine the intersection of two quadrics based on the detailed analysis of its projection in the plane (the so called cutcurve) allowing to perform the corresponding lifting correctly.…
In this study, we give the relation of being general helix and slant helix of two curves by using the equation between them. Also we find some results and express the characterizations of these curves.
A new field of discrete differential geometry is presently emerging on the border between differential and discrete geometry. Whereas classical differential geometry investigates smooth geometric shapes (such as surfaces), and discrete…
We study analytic surfaces in 3-dimensional Euclidean space containing two circular arcs through each point. The problem of finding such surfaces traces back to the works of Darboux from XIXth century. We reduce finding all such surfaces to…
We study the set of lines that meet a fixed line and are tangent to two spheres and classify the configurations consisting of a single line and three spheres for which there are infinitely many lines tangent to the three spheres that also…
Quadratic surfaces gain more and more attention among the Geometric Algebra community and some frameworks were proposed in order to represent, transform, and intersect these quadratic surfaces. As far as the authors know, none of these…
There exist cubical transition systems containing cubes having an arbitrarily large number of faces. A regular transition system is a cubical transition system such that each cube has the good number of faces. The categorical and…
We investigate the crossover between weak and strong self-avoidance in a simulation of random surfaces with extrinsic curvature. We consider both dynamically triangulated and rigid surfaces with the two possible discretizations of the…
We consider the two-dimensional (2D) flow in a flat free-slip surface that bounds a three-dimensional (3D) volume in which the flow is turbulent. The equations of motion for the two-dimensional flow in the surface are neither compressible…
We consider spherical quadrangulations -- spherical embeddings of multigraphs, possibly with loops, so that every face has boundary walk of length 4 -- in which all vertices have degree 3 or 4. Interpreting each degree 4 vertex as a…
Using a notation of corner between edges when graph has a fixed rotation, i.e. cyclical order of edges around vertices, we define combinatorial objects - combinatorial maps as pairs of permutations, one for vertices and one for faces.…
We define and study analogs of curve graphs for infinite type surfaces. Our definitions use the geometry of a fixed surface and vertices of our graphs are infinite multicurves which are bounded in both a geometric and a topological sense.…
A wormhole is a hypothetical tunnel through space. We employ the techniques taught in a standard calculus course to generate the images (embedding diagrams) of the Schwarzschild Wormhole and the Thorne-Morris Wormhole.
We study the surface of Gauss double points associated to a very general quartic surface and the natural morphisms associated to it.
Mathematically representing the shape of an object is a key ingredient for solving inverse rendering problems. Explicit representations like meshes are efficient to render in a differentiable fashion but have difficulties handling topology…
In this paper we construct a new class of algebraic surfaces in three-dimensional Euclidean space generated by a cyclic-harmonic curve and a congruence of circles. We study their properties and visualize them with the program Mathematica.
Optical surfaces represented by second-degree polynomials (quadratic or conics) are ubiquitous in optics. We revisit the equations of the conic shapes in the context of grazing incidence optics, gathering together the curves commonly used…
Let X be a scroll over a rational surface. We construct a linear system of surfaces in P^3 yielding a birational map from P^3 to X. We apply this construction to the scrolls of Bordiga and Palatini.