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On combinatorial and projective geometry
Geometriae Dedicata, 1990Cross ratios constitute an important tool in classical projective geometry. Using the theory of Tutte groups as discussed in [6] it will be shown in this note that the concept of cross ratios extends naturally to combinatorial geometries or matroids.
Dress, Andreas, Wenzel, Walter
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The geometry of projections [PDF]
Tschermaks Mineralogische und Petrographische Mitteilungen, 1965 A complete crystal structure can be projected usefully only in a rational direction, although an appropriate portion of a structure, such as a unit cell, can be projected in any arbitrary direction. The plane of the projection can be any plane not parallel with the projection direction, but only the plarie normal to the projection direction has ...
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Oriented Projective Geometry: A Framework for Geometric Computations
, 2014Part 1 Projective geometry: the classic projective plane advantages of projective geometry drawbacks of classical projective geometry oriented projective geometry related work.
J. Stolfi
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1992
So far all of the varieties we have studied have been subsets of affine space kn. In this chapter, we will enlarge kn by adding certain “points at ∞” to create n-dimensional projective space \(\mathbb{P}^{n}(k)\). We will then define projective varieties in \(\mathbb{P}^{n}(k)\) and study the projective version of the algebra–geometry dictionary.
David A. Cox +2 more
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So far all of the varieties we have studied have been subsets of affine space kn. In this chapter, we will enlarge kn by adding certain “points at ∞” to create n-dimensional projective space \(\mathbb{P}^{n}(k)\). We will then define projective varieties in \(\mathbb{P}^{n}(k)\) and study the projective version of the algebra–geometry dictionary.
David A. Cox +2 more
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Projective Geometry of Attitude Parameterizations with Applications to Control
, 2013This paper examines the projective geometry of three-parameter attitude representations that are constructed by projecting a four-parameter unit quaternion representation from its unit hypersphere onto a three-dimensional hyperplane.
S. Tanygin
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Projective Geometry as the Fundamental Geometry
2011Projective geometry became regarded by the mid 19th century as the fundamental geometry. This was very much the view of the English mathematicians Arthur Cayley, James Joseph Sylvester, and Henry Smith, and of George Salmon in Ireland, as it was of the Italian mathematician Luigi Cremona, whose book Elementi di geometria projettiva may be the first to ...
Jeremy Gray, Jeremy Gray
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The birational geometry of moduli spaces of sheaves on the projective plane
, 2013We describe a close relation between wall crossings in the birational geometry of moduli space of Gieseker stable sheaves $$M_H(v)$$MH(v) on $$\mathbb {P}^2$$P2 and mini-wall crossings in the stability manifold $$Stab(D^b(\mathbb {P}^2))$$Stab(Db(P2)).
A. Bertram, Cristian Martinez, Jie Wang
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Basics of Projective Geometry [PDF]
, 2001 For a novice, projective geometry usually appears to be a bit odd, and it is not obvious to motivate why its introduction is inevitable and in fact fruitful. One of the main motivations arises from algebraic geometry.
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