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Projective geometry provides the preferred framework for most implementations of Euclidean space in graphics applications. Translations and rotations are both linear transformations in projective geometry, which helps when it comes to…
Dynamical Systems theory generally deals with fixed point iterations of continuous functions. Computation by Turing machine although is a fixed point iteration but is not continuous. This specific category of fixed point iterations can only…
Latent representations are an important theme in modern machine learning. Any network training with the notion of locality introduces a latent geometry which we can analyze with the help of differential geometry, specifically information…
Geometric duality theory for multiple objective linear programming problems turned out to be very useful for the development of efficient algorithms to generate or approximate the whole set of nondominated points in the outcome space. This…
Computational imaging has been playing a vital role in the development of natural sciences. Advances in sensory, information, and computer technologies have further extended the scope of influence of imaging, making digital images an…
The area of geometry with its very strong and appealing visual contents and its also strong and appealing connection between the visual content and its formal specification, is an area where computational tools can enhance, in a significant…
The paper is an informal report on joint work with Stefan Haller on Dynamics in relation with Topology and Spectral Geometry. By dynamics one means a smooth vector field on a closed smooth manifold; the elements of dynamics of concern are…
Computational complexity is a new quantum information concept that may play an important role in holography and in understanding the physics of the black hole interior. We consider quantum computational complexity for $n$ qubits using…
Geometrization of physical theories have always played an important role in their analysis and development. In this contribution we discuss various aspects concerning the geometrization of physical theories: from classical mechanics to…
This is an introduction to geometric algebra, an alternative to traditional vector algebra that expands on it in two ways: 1. In addition to scalars and vectors, it defines new objects representing subspaces of any dimension. 2. It defines…
Despite encouraging recent progresses in ensemble approaches, classification methods seem to have reached a plateau in development. Further advances depend on a better understanding of geometrical and topological characteristics of point…
Solid modeling is a technique underlying CAD software as we see it today, and its theories and algorithms are among the most fundamental milestones in the historical development of CAD. Basically, it has answered the question of what…
Heterogeneous object design is an active research area in recent years. The conventional CAD modeling approaches only provide geometry and topology of the object, but do not contain any information with regard to the materials of the object…
We consider the problem of reconstructing the paths of a set of points over time, where, at each of a finite set of moments in time the current positions of points in space are only accessible through some small number of their X-rays. This…
A simple geometrical model is presented for the gravity-driven motion of a single particle on a rough inclined surface. Adopting a simple restitution law for the collisions between the particle and the surface, we arrive at a model in which…
Diagram semigroups are interesting algebraic and combinatorial objects, several types of them originating from questions in computer science and in physics. Here we describe diagram semigroups in a general framework and extend our…
Much prior work has been done on designing computational geometry algorithms that handle input degeneracies, data imprecision, and arithmetic round-off errors. We take a new approach, inspired by the noisy sorting literature, and study…
Smooth parametrization consists in a subdivision of the mathematical objects under consideration into simple pieces, and then parametric representation of each piece, while keeping control of high order derivatives. The main goal of the…
A compendium of thirty previously published open problems in computational geometry is presented.
Stochastic geometric mechanics (SGM) is known for its potential utility in quantifying uncertainty in global climate modelling of the Earth's ocean and atmosphere while also preserving the fundamental advective transport properties of ideal…