Numerical Geometry Grid Generation and Scientific Computing : Proceedings of the 10th International Conference NUMGRID 2020 Delaunay 130 Celebrating the 130th Anniversary of Boris Delaunay Moscow Russia November 2020 Part I Delaunay Voronoi Theory and Applications Local Groups in Delone Sets Manifolds of Triangulations Braid Groups of Manifolds and the Groups Γ k n A Proof of the Invariant Based Formula for the Linking Number and its Asymptotic Behaviour The Singularity Set of Optimal Transportation Maps Polygonal and Polyhedral Delaunay Meshing On Decomposition of Embedded Prismatoids in R3 without Additional Points Out of core Constrained Delaunay Tetrahedralizations for Large Scenes Part II Adaptive Meshing Size Gradation Control for Anisotropic Hybrid Meshes Adjoint Computation on Anisotropic Meshes in High fidelity RANS Simulations Moving Deforming Mesh Generation Based on the Quasi isometric Functional Adaptive Grids for Non monotone Waves and Instabilities in a Non equilibrium PDE Model RBF VerBSS Hybrid Method for Mesh Deformation A Uniform Convergence Analysis for a Bakhvalov type Mesh with an Explicitly Defined Transition Point On a Comprehensive Grid for Solving Problems Having Exponential or Power–of–First–Type Layers Preserved Structure Constants for Red Refinements of Product Elements Part III Meshing and CAD Global Parametrization Based on Ginzburg Landau Functional Parametrization of Plane Irregular Regions: A Semi automatic Approach I A Hybrid Approach to Fast Indirect Quadrilateral Mesh Generation Hexahedral Mesh Generation Using Voxel Field Recovery Generation of Boundary Layer Meshes by the Enhanced Jump and Walk Method with a Fast Collision Detecting Algorithm Part IV Numerical Geometry and Applications An Improved Algorithm for Scattered Data Interpolation using Quartic Triangular Bézier Surfaces On Integral based (Transfinite) Laplace Coordinates Part V Numerical Methods Fully implicit Collocated Finite Volume Method for the Unsteady Incompressible Navier–Stokes Problem Efficient Steady Flow Computations with Exponential Multigrid Methods Exponential Time Integrators for Unsteady Advection–diffusion Problems on Refined Meshes. The focus of these conference proceedings is on research development and applications in the fields of numerical geometry scientific computing and numerical simulation particularly in mesh generation and related problems. In addition this year’s special focus is on Delaunay triangulations and their applications celebrating the 130th birthday of Boris Delaunay. In terms of content the book strikes a balance between engineering algorithms and mathematical foundations. It presents an overview of recent advances in numerical geometry grid generation and adaptation in terms of mathematical foundations algorithm and software development and applications. The specific topics covered include: quasi conformal and quasi isometric mappings hyperelastic deformations multidimensional generalisations of the equidistribution principle discrete differential geometry spatial and metric encodings Voronoi Delaunay theory for tilings and partitions duality in mathematical programming and numerical geometry mesh based optimisation and optimal control methods. Further aspects examined include iterative solvers for variational problems and algorithm and software development. The applications of the methods discussed are multidisciplinary and include problems from mathematics physics biology chemistry material science and engineering.