Related papers: Aspect Ratio Universal Rectangular Layouts
In this article a relation between curvature functionals for surfaces in the Euclidean space and area functionals in relative differential geometry will be given. Relative differential geometry can be described as the geometry of surfaces…
A rectangle blanket is a set of non-overlapping axis-aligned rectangles, used to approximately represent the two dimensional image of a shape approximately. The use of a rectangle blanket is a widely considered strategy for speeding-up the…
Geometric algebra is an optimal frame work for calculating with vectors. The geometric algebra of a space includes elements that represent all the its subspaces (lines, planes, volumes, ...). Conformal geometric algebra expands this…
This research provides algorithms and numerical methods to geometrically control the magnitude of the internal and external forces in the reciprocal diagrams of 3D/Polyhedral Graphic statics (3DGS). In 3DGS, the form of the structure and…
Graph embeddings, wherein the nodes of the graph are represented by points in a continuous space, are used in a broad range of Graph ML applications. The quality of such embeddings crucially depends on whether the geometry of the space…
This paper addresses the challenge of object-centric layout generation under spatial constraints, seen in multiple domains including floorplan design process. The design process typically involves specifying a set of spatial constraints…
A linear layout of a graph typically consists of a total vertex order, and a partition of the edges into sets of either non-crossing edges, called stacks, or non-nested edges, called queues. The stack (queue) number of a graph is the…
Twisted diagrams are "diagrams" with components in different categories. Structure maps are defined using auxiliary data which consists of functors relating the various categories to each other. Prime examples of the construction are…
The basic idea of quantum complexity geometry is to endow the space of unitary matrices with a metric, engineered to make complex operators far from the origin, and simple operators near. By restricting our attention to a finite subgroup of…
We introduce the notion of one-sided mapping cones of positive linear maps between matrix algebras. These are convex cones of maps that are invariant under compositions by completely positive maps from either the left or right side. The…
A finite-dimensional unital and associative algebra over $\mathbb{R}$, or what we shall call simply "an algebra" in this paper for short, generalities the construction by which we derive the complex numbers by "adjoining an element $i$" to…
Subsurface projection has become indispensable in studying the geometry of the mapping class group and the curve complex of a surface. When the subsurface is an annulus, this projection is sometimes called relative twisting. We give two…
The domains of mesh functions are strict subsets of the underlying space of continuous independent variables. Spaces of partial maps between topological spaces admit topologies which do not depend on any metric. Such topologies…
In this article, we briefly describe various tools and approaches that algebraic geometry has to offer to straighten bent objects. Throughout this article we will consider a specific example of a bent or curved piece of paper which in our…
This paper addresses the following basic question: given two layouts of the same graph, which one is more aesthetically pleasing? We propose a neural network-based discriminator model trained on a labeled dataset that decides which of two…
Let $L$ be a slim, planar, semimodular lattice (slim means that it does not contain ${\mathsf M}_3$-sublattices). We call the interval $I = [o, i]$ of $L$ \emph{rectangular}, if there are $u_l, u_r \in [o, i] - \{o,i\}$ such that $i = u_l…
The variation of pose, illumination and expression makes face recognition still a challenging problem. As a pre-processing in holistic approaches, faces are usually aligned by eyes. The proposed method tries to perform a pixel alignment…
Representing a polygon using a set of simple shapes has numerous applications in different use-case scenarios. We consider the problem of covering the interior of a rectilinear polygon with holes by a set of area-weighted, axis-aligned…
Embedding diagrams have been used extensively to visualize the properties of curved space in Relativity. We introduce a new kind of embedding diagram based on the {\it extrinsic} curvature (instead of the intrinsic curvature). Such an…
This paper presents a new axis-based shape representation scheme along with a matching framework to address the problem of generic shape recognition. The main idea is to define the relative spatial arrangement of local symmetry axes and…