Search results for "Conic section"
showing 4 items of 14 documents
Die Schmieghyperebenen an die Veronese-Mannigfaltigkeit bei Beliebiger Charakteristik
1982
By means of linear algebra a base-free definition of a Veronese variety V(n,r) is given and also an illuminating description of its osculating primes from which can be deduced in a general form and without difficulty the phenomena of degeneracy in case of small characteristics. (Instance best known: For characteristic 2 all tangents of a conic are confluent.) The last section investigates special problems for the V(1,r) in characteristic p: So the osculating primes of a V(1,p) intersect its node in a V(1,p-2). Furthermore it becomes clearer why for 2<r<¦K¦−1 no elation can fix a V(1,r) (in case of a perfect field).
Subdivisions of Ring Dupin Cyclides Using Bézier Curves with Mass Points
2021
Dupin cyclides are algebraic surfaces introduced for the first time in 1822 by the French mathematician Pierre-Charles Dupin. A Dupin cyclide can be defined as the envelope of a one-parameter family of oriented spheres, in two different ways. R. Martin is the first author who thought to use these surfaces in CAD/CAM and geometric modeling. The Minkowski-Lorentz space is a generalization of the space-time used in Einstein’s theory, equipped of the non-degenerate indefinite quadratic form $$Q_{M} ( \vec{u} ) = x^{2} + y^{2} + z^{2} - c^{2} t^{2}$$ where (x, y, z) are the spacial components of the vector $$ \vec{u}$$ and t is the time component of $$ \vec{u}$$ and c is the constant of the spee…
Projective Architecture
2009
Sbacchi indaga su quale sia stata la reale influenza della nozione di "proiezione" nell'ambito della progettazione architettonica a partire da Guarini. Per fare ciò vengono presi in considerazione i concetti di luce e ombra così come quelli di linea astratta, piano, sezione, geometria proiettiva e prospettiva. Michele Sbacchi investigates the real influence of the notion of projection on architectural design before and during the age of Guarini. He takes into consideration concepts such as light and shadow, abstract line, plane, section, projective geometry and perspective. To do this he looks at the ideas of Gregorius Saint Vincent, Alberti, Guarini, Desargues and de l’Orme, among others.
The non-degenerate Dupin cyclides in the space of spheres using Geometric Algebra
2012
International audience; Dupin cyclides are algebraic surfaces of degree 4 discovered by the French mathematician Pierre-Charles Dupin early in the 19th century and \textcolor{black}{were} introduced in CAD by R. Martin in 1982. A Dupin cyclide can be defined, in two different ways, as the envelope of a one-parameter family of oriented spheres. So, it is very interesting to model the Dupin cyclides in the space of spheres, space wherein each family of spheres can be seen as a conic curve. In this paper, we model the non-degenerate Dupin cyclides and the space of spheres using Conformal Geometric Algebra. This new approach permits us to benefit from the advantages of the use of Geometric Alge…