1,109 research outputs found
Adaptive Planar Point Location
We present a self-adjusting point location structure for convex subdivisions. Let n be the number of vertices in a convex subdivision S. Our structure for S uses O(n) space and processes any online query sequence sigma in O(n + OPT) time, where OPT is the minimum time required by any linear decision tree for answering point location queries in S to process sigma. The O(n + OPT) time bound includes the preprocessing time. Our result is a two-dimensional analog of the static optimality property of splay trees. For connected subdivisions, we achieve a processing time of O(|sigma| log log n + n + OPT)
Dynamic Distribution-Sensitive Point Location
We propose a dynamic data structure for the distribution-sensitive point
location problem. Suppose that there is a fixed query distribution in
, and we are given an oracle that can return in time the
probability of a query point falling into a polygonal region of constant
complexity. We can maintain a convex subdivision with vertices
such that each query is answered in expected time, where OPT
is the minimum expected time of the best linear decision tree for point
location in . The space and construction time are . An
update of as a mixed sequence of edge insertions and deletions
takes amortized time. As a corollary, the randomized incremental
construction of the Voronoi diagram of sites can be performed in expected time so that, during the incremental construction, a nearest
neighbor query at any time can be answered optimally with respect to the
intermediate Voronoi diagram at that time.Comment: To appear in Proceedings of the International Symposium of
Computational Geometry, 202
Aspects of Unstructured Grids and Finite-Volume Solvers for the Euler and Navier-Stokes Equations
One of the major achievements in engineering science has been the development of computer algorithms for solving nonlinear differential equations such as the Navier-Stokes equations. In the past, limited computer resources have motivated the development of efficient numerical schemes in computational fluid dynamics (CFD) utilizing structured meshes. The use of structured meshes greatly simplifies the implementation of CFD algorithms on conventional computers. Unstructured grids on the other hand offer an alternative to modeling complex geometries. Unstructured meshes have irregular connectivity and usually contain combinations of triangles, quadrilaterals, tetrahedra, and hexahedra. The generation and use of unstructured grids poses new challenges in CFD. The purpose of this note is to present recent developments in the unstructured grid generation and flow solution technology
Convexity preserving interpolatory subdivision with conic precision
The paper is concerned with the problem of shape preserving interpolatory
subdivision. For arbitrarily spaced, planar input data an efficient non-linear
subdivision algorithm is presented that results in limit curves,
reproduces conic sections and respects the convexity properties of the initial
data. Significant numerical examples illustrate the effectiveness of the
proposed method
Kinetic Environments: Explorations into the Spatial Experience of Transformable Surfaces
This doctoral thesis explores kinetic environments through a narrative of historic definitions cross referenced with analysis of the spatial experiences of transformable surfaces. Research by Rudolph Arnheim and Thomas Thiis-Evensen along with project case studies gives foundation to an argument for investigating the relationship between human perception and kinetic environments. These relationships are understood further through a systematic cataloging and analysis of modeled transformable surfaces, computer generated simulation studies, and prototype proposals for the physical application and testing of kinetic principles. These explorations serve to show that existing definitions of spatial experience are not applicable when considering the potentialities of kinetic surfaces, and thus a refined framework is generated to begin to understand the spatial experience of kinetic environments
Multilevel Solvers for Unstructured Surface Meshes
Parameterization of unstructured surface meshes is of fundamental importance in many applications of digital geometry processing. Such parameterization approaches give rise to large and exceedingly ill-conditioned systems which are difficult or impossible to solve without the use of sophisticated multilevel preconditioning strategies. Since the underlying meshes are very fine to begin with, such multilevel preconditioners require mesh coarsening to build an appropriate hierarchy. In this paper we consider several strategies for the construction of hierarchies using ideas from mesh simplification algorithms used in the computer graphics literature. We introduce two novel hierarchy construction schemes and demonstrate their superior performance when used in conjunction with a multigrid preconditioner
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