Encyclopedia results for Quadric

1. Quadric
   
   for the computing company Quadrics In mathematics, a quadric , or quadric surface , is any D dimensional ... . In coordinates math x 0, x 1, x 2, ldots, x D math , the general quadric is defined by the algebraic ..
   
   
   
   
2. Klein quadric
   
   on a hyperbolic quadric Q known as the Klein quadric . If the underlying vector space of S is the 4 ... be reconstructed again from the quadric Q the planes contained in Q fall into two equivalence classes ..
   
   
   
   
3. Quadric (projective geometry)
   
   In projective geometry a quadric is the set of points of a projective space where a certain quadratic ... the set of all nonzero multiples of math v math . The projective quadric defined by math F math is the set ..
   
   
   
   
4. Ovoid (polar space)
   
   q 2n 1 1 math points. Hyperbolic quadrics An ovoid of a hyperbolic quadric math Q 2n 1,q n geq 2 math would contain math q n 1 1 math points. Parabolic quadrics An ovoid of a parabolic quadric math ..
   
   
   
   
5. Ovoid (projective geometry)
   
   q 2 1 math points of an elliptic quadric all of these are projectively equivalent . When q is odd, no other ovoids can be found than the elliptic Quadric quadrics . When math q 2 2 h 1 math another ..
   
   
   
   
6. Polar space
   
   a polar space of rank d 1 2. Let Q be a nonsingular quadric in PG n , q with character &omega . Then the index of Q will be g   n w 3 2. The set of all points on the quadric, together with the subspaces ..
   
   
   
   
7. Lie sphere geometry
   
   out to be a manifold known as the Lie quadric a quadric hypersurface in projective space . Lie sphere geometry is the geometry of the Lie quadric and the Lie transformations which preserve it. This geometry ..
   
   
   
   
8. List of surfaces
   
   Boy s surface Quadric s Sphere Spheroid Oblate Cone Ellipsoid Hyperboloid of one sheet Hyperboloid of two ..
   
   
   
   
9. Conical surface
   
   point not on the plane of math C math , one obtains a conical quadric , which is a special case of a quadric quadric surface . A cylindrical surface can be viewed as a limiting case of a conical ..
   
   
   
   
10. Grassmann?Cayley algebra
    
    create a useful framework for the modelling of conic s and quadric s, among other forms, and tensor ..
    
    
    
    
11. Complex projective plane
    
    , a non singular complex quadric in P sup 3 sup is obtained from the plane by blowing up two points ... can be seen by taking a point P on the quadric Q , blowing it up, and projecting onto a general plane ..
    
    
    
    
12. OpenGL Utility Library
    
    s, drawing of quadric surfaces, Nonuniform rational B spline NURBS , tessellation of polygonal primitives ..
    
    
    
    
13. DKBTrace
    
    DKBTrace was a graphical ray tracing program which was the forerunner of POV Ray . It had no GUI and ran via the command line . It featured quadric shapes spheres, ellipsoids, planes, etc , constructi ...
    
    
    
    
14. Segre embedding
    
    of the codomain . Examples Quadric For example with m n 1 we get an embedding of the product of the projective line with itself in P sup 3 sup . The image is a quadric , and is easily seen to contain ..
    
    
    
    
15. Generalized quadrangle
    
    them to rank 2, one finds these finite generalized quadrangles A hyperbolic quadric math Q 3,q math , a parabolic quadric math Q 4,q math and an elliptic quadric math Q 5,q math are the only possible ..
    
    
    
    
16. K3 surface
    
    of a quadric and a cubic in P sup 4 sup . The intersection of three quadric s in P sup 5 sup . A double ..
    
    
    
    
17. Enumerative geometry
    
    . Tangency to a given line L is one condition, so determined a quadric in P sup 5 sup . However ... each such quadric contains the Veronese surface , which parametrizes the conics aX bY cZ sup 2 sup ..
    
    
    
    
18. Rational singularity
    
    singularities are rational. Examples An example of a rational singularity is the singular point of the quadric ..
    
    
    
    
19. Plücker coordinates
    
    between the 4 dimensional space of lines in P sup 3 sup and points on a quadric projective geometry quadric in P sup 5 sup projective 5 space . A predecessor and special case of Grassmann coordinates ..
    
    
    
    
20. Cylinder (geometry)
    
    is a quadric surface , with the following equation in Cartesian coordinates math left frac x a right ... geometry cross section can be any curve. The cylinder is a degenerate quadric because at least one ..
    
    
    
    
21. Tutte?Coxeter graph
    
    . Coxeter title The chords of the non ruled quadric in PG 3,3 journal Canad. J. Math. volume 10 year ... title The chords of the non ruled quadric in PG 3,3 journal Canad. J. Math. volume 10 year 1958 pages ..
    
    
    
    
22. Hyperboloid
    
    Unreferenced date May 2008 Image HyperboloidOfOneSheet.png thumb Hyperboloid of one sheet Image HyperboloidOfTwoSheets.png thumb Hyperboloid of two sheets In mathematics , a hyperboloid is a quadric , ...
    
    
    
    
23. List of mathematical shapes
    
    solid dodecahedron hexahedron cube icosahedron octahedron tetrahedron torus doughnut quadric cone ..
    
    
    
    
24. Birational geometry
    
    is the birational isomorphism of the projective plane , and a non singular quadric Q in projective ..
    
    
    
    
25. Solid geometry
    
    other quadric s spheroid , ellipsoid , paraboloid and hyperboloid s. div Other topics More advanced ..
    
    
    
    

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