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## Filters

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Formally certified floating-point filters for homogeneous geometric predicates

2007
*
RAIRO - Theoretical Informatics and Applications
*

Floating-point arithmetic provides a fast but inexact way of

doi:10.1051/ita:2007005
fatcat:o5qjaez4kzbkdh5kukkfrm2zuq
*computing**geometric*predicates. ... In order for these predicates to be*exact*, it is important to rule out all the numerical situations where floating-point*computations*could lead to wrong results. ...*And*we conclude*with*a comparison to other existing*methods*. ORIENTATION-2 PREDICATE This predicate is*one*of the most often encountered*geometric*predicates. ...##
###
Indirect Predicates for Geometric Constructions

2020
*
Computer-Aided Design
*

*Geometric*predicates are a basic ingredient to implement a vast range of algorithms in

*computational*geometry. ... outperforms state-of-the-art solutions based

*on*lazy

*exact*intermediate representations. ... In our implementation we consider three

*computation*models: floating point arithmetic (

*with*semi-static filter),

*interval*arithmetic (

*with*dynamic filter), expansion arithmetic (

*exact*). ...

##
###
The Design of Core 2: A Library for Exact Numeric Computation in Geometry and Algebra
[chapter]

2010
*
Lecture Notes in Computer Science
*

This paper is concerned

doi:10.1007/978-3-642-15582-6_24
fatcat:cbtmtmiapbclxlchcfuzpwxwya
*with**one*such approach called*Exact*Numeric*Computation*(ENC). ... The ENC approach to algebraic number*computation*is based*on*iterative verified approximations, combined*with*constructive*zero*bounds. ... Also known as*Exact**Geometric**Computation*(EGC) in the context of*geometric*applications. ...##
###
A geometric construction of iterative functions of order three to solve nonlinear equations

2007
*
Computers and Mathematics with Applications
*

Some examples are given of deriving several third-order iteration

doi:10.1016/j.camwa.2007.01.007
fatcat:t5cwssbkkzeuzcuqmysajy23ra
*methods*,*and*several numerical results follow to illustrate the performance of the derived*methods*. ... In this paper we consider a*geometric*construction of iteration functions of order three to develop cubically convergent iterative*methods*for solving nonlinear equations. ... Acknowledgements The author would like to thank the referees for their useful comments*and*constructive suggestions which substantially improved the quality of this paper. ...##
###
Geometric classification tests using interval arithmetic in b-rep solid modeling

2003
*
Journal of the Brazilian Society of Mechanical Sciences and Engineering
*

It is necessary to control the growth of the

doi:10.1590/s1678-58782003000400012
fatcat:you5u5bdgzaefntm5iuq36cc7q
*intervals*based*on*the geometry*and*topology. This work will introduce the application of*interval*arithmetic to a B-Rep solid modeler. ... Another important step in the Boolean operation is the determination of intersection points where the use of*interval*arithmetic can have side effects as*intervals**with*large dimensions,*and*may cause ... Acknowledgement This work was partially supported by FAPESP*and*CNPq under grant 300.224/96. ...##
###
Algebraic methods and arithmetic filtering for exact predicates on circle arcs

2002
*
Computational geometry
*

The purpose of this paper is to present a new

doi:10.1016/s0925-7721(01)00050-5
fatcat:kib7tzagnjctvnb6egr2dmib74
*method*to design*exact**geometric*predicates in algorithms dealing*with*curved objects such as circular arcs. ... This*method*allows the use of efficient arithmetic*and*filtering techniques leading to fast implementation as shown by the experimental results. ... Acknowledgements The authors would like to thank Sylvain Pion for helpful discussions*on*arithmetic filters. ...##
###
Analytic Root Clustering: A Complete Algorithm Using Soft Zero Tests
[chapter]

2013
*
Lecture Notes in Computer Science
*

This is formalized as the root clustering problem,

doi:10.1007/978-3-642-39053-1_51
fatcat:zxgpk2iqw5f5xeocnd6w5eb4pm
*and*we provide a complete (δ, ǫ)-*exact*algorithm based*on*soft*zero*tests. ⋆ This paper was presented at an invited Special Session*on*"*Computational*...*Zero*tests are expensive*and*may be uncomputable. So we seek*geometric*algorithms based*on*a weak form of such tests, called soft*zero*tests. ... From the perspective of*Exact**Geometric**Computation*(EGC), current models of continua*computing*are lacking [22] . The touchstone is the*Zero*Problem, deciding if a real constant is*zero*. ...##
###
Controlled perturbation for arrangements of circles

2003
*
Proceedings of the nineteenth conference on Computational geometry - SCG '03
*

that the predicates involved in the construction can be safely

doi:10.1145/777792.777832
dblp:conf/compgeom/HalperinL03
fatcat:23bh3zvkkzbbzkyir6bslsyani
*computed**with*the given (limited) precision arithmetic. ... We implemented the perturbation scheme*and*the construction of the arrangement*and*we report*on*experimental results. ... To evaluate the bound*on*the error of an expression E, we*compute*an*interval*, which contains the*exact*value of E,*and*its length will be the bound*on*the error. ...##
###
Controlled perturbation for arrangements of circles

2003
*
Proceedings of the nineteenth conference on Computational geometry - SCG '03
*

that the predicates involved in the construction can be safely

doi:10.1145/777829.777832
fatcat:a3tdmyixw5ewfksrmill63jedm
*computed**with*the given (limited) precision arithmetic. ... We implemented the perturbation scheme*and*the construction of the arrangement*and*we report*on*experimental results. ... To evaluate the bound*on*the error of an expression E, we*compute*an*interval*, which contains the*exact*value of E,*and*its length will be the bound*on*the error. ...##
###
Fast magnetic field manipulations and nonadiabatic geometric phases of nitrogen-vacancy center spin in diamond

2017
*
Journal of Physics D: Applied Physics
*

Here, we construct

doi:10.1088/1361-6463/aa7f1a
fatcat:vdvqtq3qwfclbi2sbzd7kcmavm
*exact*evolution operator of the nitrogen-vacancy-center (NV) spin in diamond under external magnetic fields*and*investigate the nonadiabatic*geometric*phases, both cyclic*and*non-cyclic ... It is believed that the nonadiabatic*geometric*phases can be measured in future experiments*and*these fast quantum manipulations can be useful in designing spin-based quantum applications. ... However, we notice that*with*Barnes's*method*[14] , it is difficult to obtain physically reasonable pulse which is*zero*in amplitude at initial*and*ending times. ...##
###
Numerical integration over implicitly defined domains with topological guarantee
[article]

2019
*
arXiv
*
pre-print

Numerical experiments are presented to demonstrate the accuracy

arXiv:1901.03498v1
fatcat:rxo6mnmat5euvmhf53znffzuoi
*and*the potential of the proposed*method*. ... Furthermore, a geometry-based local error estimate is explored to guide the hierarchical subdivision*and*save the*computation*cost. ... Acknowledgment We would like to thank the anonymous reviewers*and*our laboratory group for helpful discussions*and*comments. ...##
###
Assisted verification of elementary functions using Gappa

2006
*
Proceedings of the 2006 ACM symposium on Applied computing - SAC '06
*

The proof requires a tight bound

doi:10.1145/1141277.1141584
dblp:conf/sac/DinechinLM06
fatcat:524qrelltfe7zh7mkcnusggxbm
*on*the overall error of the implementation*with*respect to the mathematical function. ... Gappa has two main advantages over previous approaches: Its input format is very close to the actual C code to validate,*and*it automates error evaluation*and*propagation using*interval*arithmetic. ... This way of*computing**intervals*was then fine for writing robust floating-point*geometric*predicates, but still not good enough for certify-1 http://lipforge.ens-lyon.fr/www/crlibm/ 2 http://lipforge.ens-lyon.fr ...##
###
Analysis and algorithms for a regularized cauchy problem arising from a non-linear elliptic PDE for seismic velocity estimation

2009
*
Journal of Computational Physics
*

(iv) the need to

doi:10.1016/j.jcp.2009.06.036
fatcat:27nwpkbewrccri3x7nrxjntwqy
*compute*the solution only for a short*interval*of time. ... The key features of this scheme is the Lax-Friedrichs averaging*and*the wide stencil in space. The second approach is a spectral Chebyshev*method**with*truncated series. ... Krasny*and*C. Morawetz for their attention, comments,*and*suggestions. ...##
###
Determination of fractal dimensions for geometrical multifractals

1989
*
Physica A: Statistical Mechanics and its Applications
*

Two independent approaches, the box counting

doi:10.1016/0378-4371(89)90563-3
fatcat:depdzuipdrfppkgalyjhsm43vu
*and*the sand box*methods*are used for the determinatiov of the generalized dimensions (Dq) associated*with*, the*geometrical*structure of growing deterministic ... Our study demonstrates that the above-mentioned two*methods*are equivalent only if the sand box*method*is applied*with*an averaging over randomly selected centres. ... In this "box counting"*method*the structure is covered by a grid*with*a mesh size equal to 1*and*a box or lattice unit is considered as occupied if its intersection*with*the fractal is larger than*zero*...##
###
The Vasicek Model
[chapter]

2004
*
Interest Rate Modelling
*

*And*using a numerical

*method*Euler Maruyama

*and*

*computer*simulation

*with*the Maple software, for simulated data, gained averages

*and*Standard deviations, confidence

*interval*

*and*their normal histogram ... Also, average of the solutions obtained from

*computer*simulations is compared

*with*real

*ones*,

*and*after analyzing

*and*reviewing the results, performance of the Vasicek model will be measured, in interest ... We doing this job

*with*the average of the solutions obtained

*on*the

*computer*simulations

*and*compare it

*with*real answers. ...

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