Eine Plattform für die Wissenschaft: Bauingenieurwesen, Architektur und Urbanistik
Eine Plattform für die Wissenschaft: Bauingenieurwesen, Architektur und Urbanistik
Projective configurations in projectivegeometrical drawings
The article focuses on the optimization of the earlier discussed computer method of obtaining new forms of polyhedra based on projective geometry drawings (trace Diagrams).While working on getting new multifaceted forms by projective geometry methods based on the well-known models of polyhedra on the first stage of the work it is required to calculate the parameters of projective geometry drawings, and then to build them. This is an often used apparatus of analytical geometry. According to it, at first the parameters of the polyhedron (core system of planes) are calculated, then we obtain the equation of the plane of the face of the polyhedron, and finally we obtain the equations of lines the next plane faces on the selected curve plane. At each stage of application such a method requires the use of the algorithms of floating point arithmetic, on the one hand, leads to some loss of accuracy of the results and, on the other hand, the large amount of computer time to perform these operations in comparison with integer arithmetic operations.The proposed method is based on the laws existing between the lines that make up the drawing - the known configurations of projective geometry (complete quadrilaterals, configuration of Desargues, Pappus et al.).The authors discussed in detail the analysis procedure of projective geometry drawing and the presence of full quadrilaterals, Desargues and Pappus configurations in it.Since the composition of these configurations is invariant with respect to projective change of the original nucleus, knowing them, you can avoid the calculations when solving the equations for finding direct projective geometry drawing analytically, getting them on the basis of belonging to a particular configuration. So you can get a definite advantage in accuracy of the results, and in the cost of computer time. Finding these basic configurations significantly enriches the set of methods and the use of projective geometry drawings.
Projective configurations in projectivegeometrical drawings
The article focuses on the optimization of the earlier discussed computer method of obtaining new forms of polyhedra based on projective geometry drawings (trace Diagrams).While working on getting new multifaceted forms by projective geometry methods based on the well-known models of polyhedra on the first stage of the work it is required to calculate the parameters of projective geometry drawings, and then to build them. This is an often used apparatus of analytical geometry. According to it, at first the parameters of the polyhedron (core system of planes) are calculated, then we obtain the equation of the plane of the face of the polyhedron, and finally we obtain the equations of lines the next plane faces on the selected curve plane. At each stage of application such a method requires the use of the algorithms of floating point arithmetic, on the one hand, leads to some loss of accuracy of the results and, on the other hand, the large amount of computer time to perform these operations in comparison with integer arithmetic operations.The proposed method is based on the laws existing between the lines that make up the drawing - the known configurations of projective geometry (complete quadrilaterals, configuration of Desargues, Pappus et al.).The authors discussed in detail the analysis procedure of projective geometry drawing and the presence of full quadrilaterals, Desargues and Pappus configurations in it.Since the composition of these configurations is invariant with respect to projective change of the original nucleus, knowing them, you can avoid the calculations when solving the equations for finding direct projective geometry drawing analytically, getting them on the basis of belonging to a particular configuration. So you can get a definite advantage in accuracy of the results, and in the cost of computer time. Finding these basic configurations significantly enriches the set of methods and the use of projective geometry drawings.
Projective configurations in projectivegeometrical drawings
Ivashchenko Andrey Viktorovich (Autor:in) / Kondrat’eva Tat’yana Mikhaylovna (Autor:in)
2015
Aufsatz (Zeitschrift)
Elektronische Ressource
Unbekannt
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