Related papers: Using the Regular Chains Library to build cylindri…
Automatic methods for reconstructing buildings from airborne LiDAR point clouds focus on producing accurate 3D models in a fast and scalable manner, but they overlook the problem of delivering simple and regularized models to practitioners.…
Convex polyhedral abstractions of logic programs have been found very useful in deriving numeric relationships between program arguments in order to prove program properties and in other areas such as termination and complexity analysis. We…
Object recognition has seen significant progress in the image domain, with focus primarily on 2D perception. We propose to leverage existing large-scale datasets of 3D models to understand the underlying 3D structure of objects seen in an…
A new predictor-corrector type incremental algorithm is proposed for the exact construction of weighted straight skeletons of 2D general planar polygons of arbitrary complexity based on the notion of deforming polygon. In the proposed…
We introduce a new method to reconstruct 3D objects using a set of volumetric primitives, i.e., superquadrics. The method hierarchically decomposes a target 3D object into pairs of superquadrics recovering finer and finer details. While…
A critical step in developing circuits for quantum simulation is to synthesize a desired unitary operator using the circuit building blocks. Studying unitaries and their generators from the Lie algebraic perspective has given rise to…
3D Computer-Aided Design (CAD) users need to overcome several obstacles to benefit from the flexibility of programmatic interface tools. Besides the barriers of any programming language, users face challenges inherent to 3D spatial…
Matrix decompositions are fundamental tools in the area of applied mathematics, statistical computing, and machine learning. In particular, low-rank matrix decompositions are vital, and widely used for data analysis, dimensionality…
We consider a subclass of tilings, the tilings obtained by cut and projection. Under somewhat standard assumptions, we show that the natural complexity function has polynomial growth. We compute its exponent \alpha in terms of the ranks of…
In this paper we develop the formalism of rational complex Bezier curves. This framework is a simple extension of the CAD paradigm, since it describes arc of curves in terms of control polygons and weights, which are extended to complex…
Computer-aided design (CAD) is crucial in prototyping 3D objects through geometric instructions (i.e., CAD programs). In practical design workflows, designers often engage in time-consuming reviews and refinements of these prototypes by…
The design of decoding algorithms is a significant technological component in the development of fault-tolerant quantum computers. Often design of quantum decoders is inspired by classical decoding algorithms, but there are no general…
One of the most fundamental ingredients in mixed-integer nonlinear programming solvers is the well-known McCormick relaxation for a product of two variables x and y over a box-constrained domain. The starting point of this paper is the fact…
Effectively parsing the facade is essential to 3D building reconstruction, which is an important computer vision problem with a large amount of applications in high precision map for navigation, computer aided design, and city generation…
Computer-Aided Design (CAD) delivers rapid, editable modeling for engineering and manufacturing. Recent AI progress now makes full automation feasible for various CAD tasks. However, progress is bottlenecked by data: public corpora mostly…
We present an algorithm for computation of cell adjacencies for well-based cylindrical algebraic decomposition. Cell adjacency information can be used to compute topological operations e.g. closure, boundary, connected components, and…
Constructing complex computation from simpler building blocks is a defining problem of computer science. In algebraic automata theory, we represent computing devices as semigroups. Accordingly, we use mathematical tools like products and…
Constructive-deductive method for plane Euclidean geometry is proposed and formalized within Coq Proof Assistant. This method includes both postulates that describe elementary constructions by idealized geometric tools (pencil, straightedge…
A tutorial of the Mathematica package CGAlgebra, for conformal geometric algebra calculations is presented. Using rule-based programming, the 5-dimensional conformal geometric algebra is implemented and defined functions simplify the…
Statistics and Optimization are foundational to modern Machine Learning. Here, we propose an alternative foundation based on Abstract Algebra, with mathematics that facilitates the analysis of learning. In this approach, the goal of the…