Related papers: Repulsive Curves
Understanding turbulence is the key to our comprehension of many natural and technological flow processes. At the heart of this phenomenon lies its intricate multi-scale nature, describing the coupling between different-sized eddies in…
In this paper, we proposed an interior point method for constrained optimization, which is characterized by the using of quasi-tangential subproblem. This algorithm follows the main ideas of primal dual interior point methods and…
Simulations of physical phenomena are essential to the expedient design of precision components in aerospace and other high-tech industries. These phenomena are often described by mathematical models involving partial differential equations…
We introduce novel finite element schemes for curve diffusion and elastic flow in arbitrary codimension. The schemes are based on a variational form of a system that includes a specifically chosen tangential motion. We derive optimal $L^2$-…
It seems that in the current age, computers, computation, and data have an increasingly important role to play in scientific research and discovery. This is reflected in part by the rise of machine learning and artificial intelligence,…
This paper develops a novel mathematical framework for collaborative learning by means of geometrically inspired kernel machines which includes statements on the bounds of generalisation and approximation errors, and sample complexity. For…
We present an efficient, trivially parallelizable algorithm to compute offset surfaces of shapes discretized using a dexel data structure. Our algorithm is based on a two-stage sweeping procedure that is simple to implement and efficient,…
The need to compute the intersections between a line and a high-order curve or surface arises in a large number of finite element applications. Such intersection problems are easy to formulate but hard to solve robustly. We introduce a…
We apply contact homology to obtain new results in the problem of distinguishing immersed plane curves without dangerous self-tangencies.
Ruled surface is widely used in engineering design such as parting surface design of injection mold and checking surface design of checking fixture, which are usually generated by offsetting 3D curves. However, in 3D curve offset, there…
We provide theoretical foundations and computational tools for the systematic design of optimization-based control laws with constraints that have different priorities. By introducing the concept of prioritized intersections, we extend and…
We propose a family of nonconvex optimization algorithms that are able to save gradient and negative curvature computations to a large extent, and are guaranteed to find an approximate local minimum with improved runtime complexity. At the…
This paper pushes the performance of cloth simulation, making the simulation interactive even for high-resolution garment models while keeping every triangle untangled. The penetration-free guarantee is inspired by the interior point…
We present some algorithms that provide useful topological information about curves in surfaces. One of the main algorithms computes the geometric intersection number of two properly embedded 1-manifolds $C_1$ and $C_2$ in a compact…
We present a new method for visualizing implicit real algebraic curves inside a bounding box in the $2$-D or $3$-D ambient space based on numerical continuation and critical point methods. The underlying techniques work also for tracing…
Designing physical artifacts that serve a purpose - such as tools and other functional structures - is central to engineering as well as everyday human behavior. Though automating design has tremendous promise, general-purpose methods do…
High-fidelity entangling gates are essential for quantum computation. Currently, most approaches to designing such gates are based either on simple, analytical pulse waveforms or on ones obtained from numerical optimization techniques. In…
Geodesic models are known as an efficient tool for solving various image segmentation problems. Most of existing approaches only exploit local pointwise image features to track geodesic paths for delineating the objective boundaries.…
Optimizing deformation energies over a mesh, in two or three dimensions, is a common and critical problem in physical simulation and geometry processing. We present three new improvements to the state of the art: a barrier-aware line-search…
Addressing irregular cutting and packing (C&P) optimization problems poses two distinct challenges: the geometric challenge of determining whether or not an item can be placed feasibly at a certain position, and the optimization challenge…