This news article was originally written in Spanish. It has been automatically translated for your convenience. Reasonable efforts have been made to provide an accurate translation, however, no automated translation is perfect nor is it intended to replace a human translator. The original article in Spanish can be viewed at Análisis de la posibilidad de implementación informática del método de los números característicos de una familia uniparamétrica de cónicas: aplicación a series y haces
CAD - CAM - CAE
Analysis on the possibility of computer implementation of the method of the characteristic of a family uniparamétrica of conical numbers: application to series and bundle
Esther Pascual Albarracín
Aeronautical school. PL Cardinal Cisneros 3. 28040 Madrid
Aeronautical school. PL Cardinal Cisneros 3. 28040 Madrid
91 336 63 12 epascual@aero.upm.es
01/12/20021. Introduction
Prior to this work there was some concern in our teaching unit by two conics-related issues. On the one hand, clearly abuse often suffer in CAD programs. On numerous occasions we have seen the lack of pre-programmed options enabling a simple layout of Conic sections of which is known, for example, five crossing points. Even, occasionally, seems that the input of the program data respond more to the ease of programming to the needs of the user. These limitations of CAD programmes in the implementation of the conical usually cover them by replacing them with B-splines curves or Bezier curves, thus losing much of the graphic wealth possessed by the Conic.
On the other hand, is seen in the design a true abandonment in the employment of conics. With the development and degree of current implementation of the numerical in manufacturing systems analysis, it is unthinkable to be due to the difficulty in its layout to produce the pieces. We assume that it may be because to translate required design specifications involving a conical, it must be defined by five simple data. But, in general, five data define a finite number of Conic sections, not a Conic single. It is necessary a tool that allows to know the possible Conic sections that meet the specifications and choose the most appropriate.
2 Results and discussion
In these circumstances arose the study of family uniparamétricas of Conic sections by the method of characteristics of Chasles and analytic geometry without equations of Lemoyne. However, this solution has brought associated a problem almost larger than we wanted to resolve. The theory that we wanted to build appeared as a subject lacking in consistency, developed as a casuistry without interrelate, unrelated studies, dark and dubious points, apparent inconsistencies in the theory and with lacking in rigour demonstrations even if they were true facts. Also proved to be a delicate theory, which is often the step to the imaginary field and the multiplicity of degenerate Conic sections, which may be cause of error with great ease.
3 Findings
It has developed this theory for the particular case of beams and series, trying as well to assess the possibilities of this method in two cases studied and known in other areas of the geometry. Using theorems based on this theory, Pascal and other more known as Brianchon is obtained for the Conic defined by five points of passage or five tangent lines (or degenerate cases) an output file of Exchange "device independent" that allows to use the results in large systems or as MICROSTATION SE CAD programs.
