References in raw/Page_74.html

• Robust approximation of offsets, bisectors, and medial axes of plane curves
  JB Oliveira, LH De Figueiredo - Reliable computing, 2003 - Springer
  ... Affine arithmetic [3] is one of these tools, and its use in interval methods has resulted in faster ... A natural next step is to use affine arithmetic instead of interval arithmetic in the global ...
  

• Real-time ray tracing of implicit surfaces on the GPU
  JM Singh, PJ Narayanan - IEEE transactions on visualization ..., 2009 - ieeexplore.ieee.org
  ... algebraic surfaces up to order 4 using analytical roots on the GPU [5] and selected algebraic surfaces and some nonalgebraic surfaces using interval analysis and affine arithmetic on ...
  

• A Knowledge-based Approach for Configuring Automobile Design and Development
  F Wawrzik, C Grimm - researchgate.net
  ... We intend to build a constraint solver with Affine Arithmetic, which is able to handle multiplications and divisions and other functions of symbolic variables with boundaries, and thus ...
  

• A probability box representation method for power flow analysis considering both interval and probabilistic uncertainties
  Q Li, N Zhao - International Journal of Electrical Power & Energy ..., 2022 - Elsevier
  ... In the affine arithmetic method, the interval variables are represented as affine combinations ... considering correlated interval variables in the affine arithmetic method. Besides, Levin et al...
  

• Uncertainty in Geometric Computations
  J Winkler, M Niranjan - 2002 - books.google.com
  Computer simulations and modelling are used frequently in science and engineering, in applications ranging from the understanding of natural and artificial phenomena to the design, ...
  

• DH quaternion transformation method for kinematics analysis of serial mechanisms
  Z Zhong-hai, LI Duan-ling - Journal of Beijing university of Posts ..., 2015 - journal.bupt.edu.cn
  ... Finite鄄precision error modeling using affine arithmetic[C]椅Acoustics, Speech and Signal ... by a modified affine arithmetic [ J]. Computers and Chemical Engineering, 2013(48): 48鄄57. ...
  

• 3.9 Integration of Interval Contractors in Hierarchical Space Decomposition Structures
  S Kiel - Uncertainty modeling and analysis with intervals ... - dagstuhl.sunsite.rwth-aachen.de
  ... arithmetics like affine arithmetic or Taylor models to reduce the overestimation. Another way to tighten enclosures is to use contractors which identify parts of the decomposition disjoint ...
  

• DC power flow analysis incorporating interval input data and network parameters through the optimizing-scenarios method
  C Zhang, H Chen, M Guo, X Wang, Y Liu... - International Journal of ..., 2018 - Elsevier
  ... the Krawczyk-Moore method in conjunction with affine arithmetic [18] to obtain the ranges of bus ... To overcome the limitations of affine arithmetic (AA) -based methods, the OSM has been ...
  

• An efficient solution to systems of multivariate polynomial using expression trees
  G Elber, T Grandine - IEEE Transactions on Visualization and ..., 2009 - ieeexplore.ieee.org
  ... techniques such as affine arithmetic have been developed in recent years. Affine arithmetic [8] ... Affine arithmetic excels in the common case when different terms in the expression are ...
  

• A Novel Belief Function Based Framework for UOPF With Multiprobability-Characterized and Knowledge Deficient Power Sources
  B Liu, Q Huang, J Zhao, W Hu - IEEE Transactions on Industrial ..., 2020 - ieeexplore.ieee.org
  ... According to Vaccaro and Cañizares [28], we can perform the affine arithmetic based UOPF for ... Note that the affine arithmetic based UOPF transfers the affine form based OPF into two ...