Space-filling Curve Generation: A Table-based Approach
نویسندگان
چکیده
We introduce a table-based specification for spacefilling curves. This specification consists of a primitive curve representation and a movement specification table. We present an algorithm that uses these tables to enumerate points on a space-filling curve and discuss how to generate such tables automatically. Experimental results on three modern microprocessor based platforms show that our algorithm is up to 63% faster than the latest recursive algorithm for generating 2D curves and up to a factor of 66 faster than a previous byte-oriented, non-recursive implementation.
منابع مشابه
Parallelizing an Unstructured Grid Generator with a Space-Filling Curve Approach
A new parallel load distribution algorithm for unstructured parallel grid generation is presented. This new approach is based on a space-filling curve. The space-filling curve’s indices are calculated recursively and in parallel, thus leading to a very efficient, and fast load distribution. The partitions resulting from this distribution are simply connected and the processor boundaries are suf...
متن کاملMemory efficient adaptive mesh generation and implementation of multigrid algorithms using Sierpinski curves
We will present an approach to numerical simulation on recursively structured adaptive discretisation grids. The respective grid generation process is based on recursive bisection of triangles along marked edges. The resulting refinement tree is sequentialised according to a Sierpinski space-filling curve, which leads to both minimal memory requirements and inherently cache-efficient processing...
متن کاملAlgebraic Formulation and Program Generation of Three-Dimensional Hilbert Space-Filling Curves
We use a tensor product based multi-linear algebra theory to formulate three-dimensional Hilbert space-filling curves. A 3-D Hilbert space-filling curve is specified as a permutation which rearranges threedimensional n n n data elements stored in the row major order as in C language or the column major order as in FORTRAN language to the order of traversing a 3-D Hilbert space-filling curve. Th...
متن کاملUsing Space-filling Curves for Computation Reordering
Space-filling curves have been widely used in mathematics and to transform multi-dimensional problems into one-dimensional forms. For scientific applications, ordering data or computation along spacefilling curves can be useful for exploiting locality when partitioning onto parallel systems or when restructuring to exploit memory hierarchy. In this paper, we present an efficient approach for en...
متن کاملOptimization of Numerically Controlled Five Axis Machining Using Curvilinear Space Filling Curves
The paper presents optimization and visualization methods for tool path planning of 5 axis milling machines. The first method is based on the grid generation techniques whereas the second method exploits the space filling curve technologies. Combination of the two techniques is superior with regard to the conventional methods and with regard to the case when the two methods are applied independ...
متن کامل