BOOLE: A BOUNDARY EVALUATION SYSTEM FOR BOOLEAN COMBINATIONS OF SCULPTURED SOLIDS

2001 ◽  
Vol 11 (01) ◽  
pp. 105-144 ◽  
Author(s):  
S. KRISHNAN ◽  
D. MANOCHA ◽  
M. GOPI ◽  
T. CULVER ◽  
J. KEYSER
Keyword(s):  
Evaluation System ◽  
Numerical Algorithms ◽  
Numerical Linear Algebra ◽  
Intersection Curve ◽  
Topological Information ◽  
Boundary Evaluation ◽  
Intersection Algorithm ◽  
Shared Memory Multiprocessor ◽  
Boundary Representations ◽  
Bradley Fighting Vehicle

In this paper we describe a system, BOOLE, that generates the boundary representations (B-reps) of solids given as a CSG expression in the form of trimmed Bézier patches. The system makes use of techniques from computational geometry, numerical linear algebra and symbolic computation to generate the B-reps. Given two solids, the system first computes the intersection curve between the two solids using our surface intersection algorithm. Using the topological information of each solid, it computes various components within each solid generated by the intersection curve and their connectivity. The component classification step is performed by ray-shooting. Depending on the Boolean operation performed, appropriate components are put together to obtain the final solid. We also present techniques to parallelize this system on shared memory multiprocessor machines. The system has been successfully used to generate B-reps for a number of large industrial models including parts of a notional submarine storage and handling room (courtesy - Electric Boat Inc.) and Bradley fighting vehicle (courtesy - Army Research Labs). Each of these models is composed of over 8000 Boolean operations and is represented using over 50,000 trimmed Bézier patches. Our exact representation of the intersection curve and use of stable numerical algorithms facilitate an accurate boundary evaluation at every Boolean set operation and generation of topologically consistent solids.

A survey of numerical linear algebra methods utilizing mixed-precision arithmetic

2021 ◽  
pp. 109434202110033 ◽  
Author(s):  
Ahmad Abdelfattah ◽  
Hartwig Anzt ◽  
Erik G Boman ◽  
Erin Carson ◽  
Terry Cojean ◽  
...  
Keyword(s):  
Linear Algebra ◽  
Special Function ◽  
Numerical Algorithms ◽  
Theoretical Background ◽  
Numerical Linear Algebra ◽  
Efficient Utilization ◽  
Sparse Linear Algebra ◽  
Mixed Precision ◽  
Machine Learning Applications ◽  
Comprehensive Survey

The efficient utilization of mixed-precision numerical linear algebra algorithms can offer attractive acceleration to scientific computing applications. Especially with the hardware integration of low-precision special-function units designed for machine learning applications, the traditional numerical algorithms community urgently needs to reconsider the floating point formats used in the distinct operations to efficiently leverage the available compute power. In this work, we provide a comprehensive survey of mixed-precision numerical linear algebra routines, including the underlying concepts, theoretical background, and experimental results for both dense and sparse linear algebra problems.

scholarly journals Generation of test matrices with specified eigenvalues using floating-point arithmetic

2021 ◽  
Author(s):  
Katsuhisa Ozaki ◽  
Takeshi Ogita
Keyword(s):  
Eigenvalue Problems ◽  
Numerical Algorithms ◽  
Numerical Linear Algebra ◽  
Floating Point ◽  
Diagonal Form ◽  
Floating Point Arithmetic ◽  
Complex Eigenvalues ◽  
Test Matrices ◽  
Block Diagonal Form ◽  
Point Arithmetic

AbstractThis paper concerns test matrices for numerical linear algebra using an error-free transformation of floating-point arithmetic. For specified eigenvalues given by a user, we propose methods of generating a matrix whose eigenvalues are exactly known based on, for example, Schur or Jordan normal form and a block diagonal form. It is also possible to produce a real matrix with specified complex eigenvalues. Such test matrices with exactly known eigenvalues are useful for numerical algorithms in checking the accuracy of computed results. In particular, exact errors of eigenvalues can be monitored. To generate test matrices, we first propose an error-free transformation for the product of three matrices YSX. We approximate S by ${S^{\prime }}$ S ′ to compute ${YS^{\prime }X}$ Y S ′ X without a rounding error. Next, the error-free transformation is applied to the generation of test matrices with exactly known eigenvalues. Note that the exactly known eigenvalues of the constructed matrix may differ from the anticipated given eigenvalues. Finally, numerical examples are introduced in checking the accuracy of numerical computations for symmetric and unsymmetric eigenvalue problems.

Numerical Algorithms for Subspace State Space System Identification (N4SID)

1997 ◽  
Author(s):  
Peter Van Overschee ◽  
Bart De Moor ◽  
Wouter Favoreel
Keyword(s):  
State Space ◽  
State Space Model ◽  
Numerical Algorithms ◽  
Numerical Linear Algebra ◽  
Subspace Identification ◽  
Oblique Projection ◽  
Hankel Matrices ◽  
State Space System ◽  
Value Decomposition ◽  
The Given

Abstract We present the basic notions on subspace identification algorithms for linear systems. These methods estimate state sequences or extended observability matrices directly from the given data, through an orthogonal or oblique projection of the row spaces of certain block Hankel matrices into the row spaces of others. The extraction of the state space model is then achieved through the solution of a least squares problem. These algorithms can be elegantly implemented using well-known numerical linear algebra algorithms such as the LQ- and singular value decomposition. The paper aims at giving an overview of the methodologies used in time domain subspace identification. A short overview of frequency domain subspace identification results is also presented.

A SURFACE INTERSECTION ALGORITHM BASED ON LOOP DETECTION

1991 ◽  
Vol 01 (04) ◽  
pp. 473-490 ◽  
Author(s):  
MICHAEL E. HOHMEYER
Keyword(s):  
Gauss Map ◽  
Algebraic Surfaces ◽  
Boundary Representation ◽  
Intersection Curve ◽  
Closed Loops ◽  
Detection Algorithms ◽  
Surface Intersection ◽  
Loop Detection ◽  
Intersection Algorithm ◽  
New Strategies

A robust and efficient surface intersection algorithm that is implementable in floating point arithmetic, accepts surfaces algebraic or otherwise and which operates without human supervision is critical to boundary representation solid modeling. To the author's knowledge, no such algorithms has been developed. All tolerance-based subdivision algorithms will fail on surfaces with sufficiently small intersections. Algebraic techniques, while promising robustness, are presently too slow to be practical and do not accept non-algebraic surfaces. Algorithms based on loop detection hold promise. They do not require tolerances except those associated with machine associated with machine arithmetic, and can handle any surface for which there is a method to construct bounds on the surface and its Gauss map. Published loop detection algorithms are, however, still too slow and do not deal with singularities. We present a new loop detection criterion and discuss its use in a surface intersection algorithms. The algorithm, like other loop detection based intersection algorithms, subdivides the surfaces into pairs of sub-patches which do not intersect in any closed loops. This paper presents new strategies for subdividing surfaces in a way that causes the algorithms to run quickly even when the intersection curve(s) contain(s) singularities.

A proposed method for assessing the quality of sealants - the CCC Sealant Evaluation System

2001 ◽  
Vol 29 (2) ◽  
pp. 83-91 ◽  
Author(s):  
Christopher Deery ◽  
Hazel E. Fyffe ◽  
Zoann J. Nugent ◽  
Nigel M. Nuttall ◽  
Nigel B. Pitts
Keyword(s):  
Evaluation System

Intelligent system of English composition scoring model based on improved machine learning algorithm

2020 ◽  
pp. 1-11
Author(s):  
Jie Liu ◽  
Lin Lin ◽  
Xiufang Liang
Keyword(s):  
Machine Learning ◽  
Evaluation System ◽  
Intelligent System ◽  
Learning Algorithm ◽  
Learning Algorithms ◽  
Machine Learning Algorithms ◽  
Assessment System ◽  
English Composition ◽  
Region Extraction ◽  
Constraint Model

The online English teaching system has certain requirements for the intelligent scoring system, and the most difficult stage of intelligent scoring in the English test is to score the English composition through the intelligent model. In order to improve the intelligence of English composition scoring, based on machine learning algorithms, this study combines intelligent image recognition technology to improve machine learning algorithms, and proposes an improved MSER-based character candidate region extraction algorithm and a convolutional neural network-based pseudo-character region filtering algorithm. In addition, in order to verify whether the algorithm model proposed in this paper meets the requirements of the group text, that is, to verify the feasibility of the algorithm, the performance of the model proposed in this study is analyzed through design experiments. Moreover, the basic conditions for composition scoring are input into the model as a constraint model. The research results show that the algorithm proposed in this paper has a certain practical effect, and it can be applied to the English assessment system and the online assessment system of the homework evaluation system algorithm system.

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