A criterion is given for the convergence of numerical solutions of the Navier-Stokes equations in two dimensions under steady conditions. The criterion applies to all cases, of steady viscous flow in two dimensions and shows that if the local ' mesh Reynolds number ', based on the size of the mesh used in the solution, exceeds a certain fixed value, the numerical solution will not converge.

On the Navier-Stokes equations

Computational geometry

Computer systems commonly cache the values of variables to gain efficiency. In applications where the goal is to track attributes of a continuously moving or deforming physical system over time, caching relations between variables works better than caching individual values. The reason is that, as the system evolves, such relationships are more stable than the values of individual variables.Kinetic data structures (KDSs) are a novel formal framework for designing and analyzing sets of assertions to cache about the environment, so that these assertion sets are at once relatively stable and tailored to facilitate or trivialize the computation of the attribute of interest. Formally, a KDS is a mathematical proof animated through time, proving the validity of a certain computation for the attribute of interest. KDSs have rigorous associated measures of performance and their design shares many qualities with that of classical data structures.The KDS framework has led to many new and promising algorithms in applications where the efficient modeling of motion is essential. Among these are collision detection for moving rigid and deformable bodies, connectivity maintenace in ad-hoc networks, local environment tracking for mobile agents, and visibility/occlusion maintenance. This talk will survey the general ideas behind KDSs and illustrate their application to simple geometric problems that arise in virtual and physical environments.

Data structures for mobile data (invited talk) (abstract only)

Path planning still remains one of the core problems in modern robotic applications, such as the design of autonomous vehicles and perceptive systems. The basic path-planning problem is concerned with finding a good-quality path from a source point to a destination point that does not result in collision with any obstacles. In this article, we chose the roadmap approach and utilized the Voronoi diagram to obtain a path that is a close approximation of the shortest path satisfying the required clearance value set by the user. The advantage of the proposed technique versus alternative path-planning methods is in its simplicity, versatility, and efficiency.

Roadmap-Based Path Planning - Using the Voronoi Diagram for a Clearance-Based Shortest Path

Computer-Aided Geometric Design

: The characterisation of geometric shapes produces their concise description and is, therefore, important for subsequent analyses, for example in Computer Vision, Machine Learning

/pdf/geometric-shape-characterisation-based-on-a-multi-sweeping-1ueqdxqz.pdf

Geometric Shape Characterisation Based on a Multi-Sweeping Paradigm

The paper surveys main features of computational geometry and presents the argument that a course oriented to applied computational geometry should be a part of the computer graphics curriculum, as it teaches effective algorithmic methods and helps to develop abstract thinking. Possible contents of the course and forms suitable and interesting for computer graphics students are discussed. The students' feedback on such a course has been mostly positive.

Computational Geometry Education for Computer Graphics Students.

Subdivision surfaces are becoming an important tool in Computer Graphics. They can be found in modern software as well as implemented in GPUs. However, their description is complex, and simple relations, as the inherently parallel manner of rewriting, are obfuscated by the indexing scheme.We propose using L-systems for tensor product surfaces subdivision description. The parallel rewriting helps us to merge the parallel manner of a surface subdivision. We demonstrate their functionality on Bezier bicubic and rational Bezier bicubic surfaces. We show that the power of L-systems can be easily applied to this scheme which is intuitive and easy to control. Parametric L-systems allow us to manage the level of subdivision and Open L-systems help to generate adaptive surfaces where the level of subdivision is controlled by an external condition. The e-rule helps to generate surfaces with holes and in this way we can emboss classical fractals to 3D surfaces.

http://hpcg.purdue.edu/bbenes/papers/Kolingerova06SCCG.pdf

Tensor product surfaces as rewriting process

https://doi.org/10.1016/j.dib.2022.107806

Ivana Kolingerová

Papers

Geometric Shape Characterisation Based on a Multi-Sweeping Paradigm

Computational Geometry Education for Computer Graphics Students.

Tensor product surfaces as rewriting process

Data on annotated approximate bilaterally symmetric leaf-off trees based on particle flow simulation and predefined tree crown shape

Local Reflectional Symmetry Detection in Point Clouds Using a Simple PCA-Based Shape Descriptor