The Skip Quadtree: A Simple Dynamic Data Structure for Multidimensional Data

We present a new multi-dimensional data structure, which we call the skip quadtree (for point data in R^2) or the skip octree (for point data in R^d, with constant d>2). Our data structure combines the best features of two well-known data structures, in that it has the well-defined "box"-shaped regions of region quadtrees and the logarithmic-height search and update hierarchical structure of skip lists. Indeed, the bottom level of our structure is exactly a region quadtree (or octree for higher dimensional data). We describe efficient algorithms for inserting and deleting points in a skip quadtree, as well as fast methods for performing point location and approximate range queries.Comment: 12 pages, 3 figures. A preliminary version of this paper appeared in the 21st ACM Symp. Comp. Geom., Pisa, 2005, pp. 296-30

Indirect test of M-S circuits using multiple specification band guarding

Testing analog and mixed-signal circuits is a costly task due to the required test time targets and high end technical resources. Indirect testing methods partially address these issues providing an efficient solution using easy to measure CUT information that correlates with circuit performances. In this work, a multiple specification band guarding technique is proposed as a method to achieve a test target of misclassified circuits. The acceptance/rejection test regions are encoded using octrees in the measurement space, where the band guarding factors precisely tune the test decision boundary according to the required test yield targets. The generated octree data structure serves to cluster the forthcoming circuits in the production testing phase by solely relying on indirect measurements. The combined use of octree based encoding and multiple specification band guarding makes the testing procedure fast, efficient and highly tunable. The proposed band guarding methodology has been applied to test a band-pass Butterworth filter under parametric variations. Promising simulation results are reported showing remarkable improvements when the multiple specification band guarding criterion is used.Peer ReviewedPostprint (author's final draft

Geometric transformations in octrees using shears

Existent algorithms to perform geometric transformations on octrees can be classified in two families: inverse transformation and address computation ones. Those in the inverse transformation family essentially resample the target octree from the source one, and are able to cope with all the affine transformations. Those in the address computation family only deal with translations, but are commonly accepted as faster than the former ones for they do no intersection tests, but directly calculate the transformed address of each black node in the source tree. This work introduces a new translation algorithm that shows to perform better than previous one when very small displacements are involved. This property is particularly useful in applications such as simulation, robotics or computer animation.Postprint (published version

Linkless octree using multi-level perfect hashing

The standard C/C++ implementation of a spatial partitioning data structure, such as octree and quadtree, is often inefficient in terms of storage requirements particularly when the memory overhead for maintaining parent-to-child pointers is significant with respect to the amount of actual data in each tree node. In this work, we present a novel data structure that implements uniform spatial partitioning without storing explicit parent-to-child pointer links. Our linkless tree encodes the storage locations of subdivided nodes using perfect hashing while retaining important properties of uniform spatial partitioning trees, such as coarse-to-fine hierarchical representation, efficient storage usage, and efficient random accessibility. We demonstrate the performance of our linkless trees using image compression and path planning examples.postprin

Estructuras geométricas jerárquicas para la modelización de escenas 3D

This work surveys on the principal hierarchical geometric structures used to represent 3D scenes. We also present the basic algorithms to work with them, an overview on some recent works and a comparative discussion. This work has been the outcomes of the graduate coursePostprint (published version

Sweep encoding: Serializing space subdivision schemes for optimal slicing

Slicing a model (computing thin slices of a geometric or volumetric model with a sweeping plane) is necessary for several applications ranging from 3D printing to medical imaging. This paper introduces a technique designed to compute these slices efficiently, even for huge and complex models. We voxelize the volume of the model at a required resolution and show how to encode this voxelization in an out-of-core octree using a novel Sweep Encoding linearization. This approach allows for efficient slicing with bounded cost per slice. We discuss specific applications, including 3D printing, and compare these octrees’ performance against the standard representations in the literature.This work has been partially funded by the Spanish Ministry of Science and Innovation (MCIN / AEI / 10.13039/501100011033) and FEDER (‘‘A way to make Europe’’) under grant TIN2017- 88515-C2-1-R.Peer ReviewedPostprint (published version