5,771 research outputs found
Finite Boolean Algebras for Solid Geometry using Julia's Sparse Arrays
The goal of this paper is to introduce a new method in computer-aided
geometry of solid modeling. We put forth a novel algebraic technique to
evaluate any variadic expression between polyhedral d-solids (d = 2, 3) with
regularized operators of union, intersection, and difference, i.e., any CSG
tree. The result is obtained in three steps: first, by computing an independent
set of generators for the d-space partition induced by the input; then, by
reducing the solid expression to an equivalent logical formula between Boolean
terms made by zeros and ones; and, finally, by evaluating this expression using
bitwise operators. This method is implemented in Julia using sparse arrays. The
computational evaluation of every possible solid expression, usually denoted as
CSG (Constructive Solid Geometry), is reduced to an equivalent logical
expression of a finite set algebra over the cells of a space partition, and
solved by native bitwise operators.Comment: revised version submitted to Computer-Aided Geometric Desig
Data Cube Approximation and Mining using Probabilistic Modeling
On-line Analytical Processing (OLAP) techniques commonly used in data warehouses allow the exploration of data cubes according to different analysis axes (dimensions) and under different abstraction levels in a dimension hierarchy. However, such techniques are not aimed at mining multidimensional data.
Since data cubes are nothing but multi-way tables, we propose to analyze the potential of two probabilistic modeling techniques, namely non-negative multi-way array factorization and log-linear modeling, with the ultimate objective of compressing and mining aggregate and multidimensional values. With the first technique, we compute the set of components that best fit the initial data set and whose superposition coincides with the original data; with the second technique we identify a parsimonious model (i.e., one with a reduced set of parameters), highlight strong associations among dimensions and discover possible outliers in data cells. A real life example will be
used to (i) discuss the potential benefits of the modeling output on cube exploration and mining, (ii) show how OLAP queries can be answered in an approximate way, and (iii) illustrate the strengths and limitations of these modeling approaches
A Framework for Developing Real-Time OLAP algorithm using Multi-core processing and GPU: Heterogeneous Computing
The overwhelmingly increasing amount of stored data has spurred researchers
seeking different methods in order to optimally take advantage of it which
mostly have faced a response time problem as a result of this enormous size of
data. Most of solutions have suggested materialization as a favourite solution.
However, such a solution cannot attain Real- Time answers anyhow. In this paper
we propose a framework illustrating the barriers and suggested solutions in the
way of achieving Real-Time OLAP answers that are significantly used in decision
support systems and data warehouses
Diamond Dicing
In OLAP, analysts often select an interesting sample of the data. For
example, an analyst might focus on products bringing revenues of at least 100
000 dollars, or on shops having sales greater than 400 000 dollars. However,
current systems do not allow the application of both of these thresholds
simultaneously, selecting products and shops satisfying both thresholds. For
such purposes, we introduce the diamond cube operator, filling a gap among
existing data warehouse operations.
Because of the interaction between dimensions the computation of diamond
cubes is challenging. We compare and test various algorithms on large data sets
of more than 100 million facts. We find that while it is possible to implement
diamonds in SQL, it is inefficient. Indeed, our custom implementation can be a
hundred times faster than popular database engines (including a row-store and a
column-store).Comment: 29 page
Shape Animation with Combined Captured and Simulated Dynamics
We present a novel volumetric animation generation framework to create new
types of animations from raw 3D surface or point cloud sequence of captured
real performances. The framework considers as input time incoherent 3D
observations of a moving shape, and is thus particularly suitable for the
output of performance capture platforms. In our system, a suitable virtual
representation of the actor is built from real captures that allows seamless
combination and simulation with virtual external forces and objects, in which
the original captured actor can be reshaped, disassembled or reassembled from
user-specified virtual physics. Instead of using the dominant surface-based
geometric representation of the capture, which is less suitable for volumetric
effects, our pipeline exploits Centroidal Voronoi tessellation decompositions
as unified volumetric representation of the real captured actor, which we show
can be used seamlessly as a building block for all processing stages, from
capture and tracking to virtual physic simulation. The representation makes no
human specific assumption and can be used to capture and re-simulate the actor
with props or other moving scenery elements. We demonstrate the potential of
this pipeline for virtual reanimation of a real captured event with various
unprecedented volumetric visual effects, such as volumetric distortion,
erosion, morphing, gravity pull, or collisions
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