Floating-Point Filter for the Line Intersection Algorithm

Author(s):  
Andras Frankel ◽  
Doron Nussbaum ◽  
Jörg-Rudiger Sack
1994 ◽  
Vol 04 (01) ◽  
pp. 87-118 ◽  
Author(s):  
A. JAMES STEWART

The field of solid modeling makes extensive ve use of a variety of geometric algorithms. When implemented on a computer, these algorithms often fail because the computer only provides floating point arithmetic, while the algorithms are expecting infinite precision arithmetic on real numbers. These algorithms are not robust. This paper presents a formal theory of robustness. It is then argued that the elegant theoretical approach to robustness is not viable in practice: algorithms like those used in solid modeling are generally too complex for this approach. This paper presents a practical alternative to the formal theory of robustness; this alternative is called local robustness. Local robustness is applied to the design of a polyhedral intersection algorithm, which is an important component in many solid modelers. The intersection algorithm has been implemented, and, in extensive tests, has never failed to produce a valid polyhedron of intersection. A concise characterization of the locally robust intersection algorithm is presented; this characterization can be used to develop variants of the intersection algorithm, and to develop robust versions of other solid modeling algorithms.


2020 ◽  
Vol 33 (109) ◽  
pp. 21-31
Author(s):  
І. Ya. Zeleneva ◽  
Т. V. Golub ◽  
T. S. Diachuk ◽  
А. Ye. Didenko

The purpose of these studies is to develop an effective structure and internal functional blocks of a digital computing device – an adder, that performs addition and subtraction operations on floating- point numbers presented in IEEE Std 754TM-2008 format. To improve the characteristics of the adder, the circuit uses conveying, that is, division into levels, each of which performs a specific action on numbers. This allows you to perform addition / subtraction operations on several numbers at the same time, which increas- es the performance of calculations, and also makes the adder suitable for use in modern synchronous cir- cuits. Each block of the conveyor structure of the adder on FPGA is synthesized as a separate project of a digital functional unit, and thus, the overall task is divided into separate subtasks, which facilitates experi- mental testing and phased debugging of the entire device. Experimental studies were performed using EDA Quartus II. The developed circuit was modeled on FPGAs of the Stratix III and Cyclone III family. An ana- logue of the developed circuit was a functionally similar device from Altera. A comparative analysis is made and reasoned conclusions are drawn that the performance improvement is achieved due to the conveyor structure of the adder. Implementation of arithmetic over the floating-point numbers on programmable logic integrated cir- cuits, in particular on FPGA, has such advantages as flexibility of use and low production costs, and also provides the opportunity to solve problems for which there are no ready-made solutions in the form of stand- ard devices presented on the market. The developed adder has a wide scope, since most modern computing devices need to process floating-point numbers. The proposed conveyor model of the adder is quite simple to implement on the FPGA and can be an alternative to using built-in multipliers and processor cores in cases where the complex functionality of these devices is redundant for a specific task.


2012 ◽  
Vol 1 (6) ◽  
pp. 67-68
Author(s):  
M. Somasekhar M. Somasekhar ◽  
Keyword(s):  

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