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searching for Homogeneous coordinates 24 found (172 total)

Real projective space (2,083 words) [view diff] exact match in snippet view article find links to article

sphere. Real projective spaces are smooth manifolds. On Sn, in homogeneous coordinates, (x1, ..., xn+1), consider the subset Ui with xi ≠ 0. Each Ui is

Plücker embedding (1,332 words) [view diff] exact match in snippet view article find links to article

Grassmann generalized Plücker's embedding to arbitrary k and n. The homogeneous coordinates of the image of the Grassmannian G r ( k , V ) {\displaystyle \mathrm

Multivector (4,882 words) [view diff] exact match in snippet view article find links to article

lines, planes and hyperplanes that have properties similar to the homogeneous coordinates of points, called Grassmann coordinates. Points in a real projective

Pappus's hexagon theorem (2,865 words) [view diff] exact match in snippet view article find links to article

parallelity A c ∥ C a {\displaystyle \;Ac\parallel Ca\;} . Choose homogeneous coordinates with C = ( 1 , 0 , 0 ) , c = ( 0 , 1 , 0 ) , X = ( 0 , 0 , 1 )

Homersham Cox (mathematician) (1,348 words) [view diff] exact match in snippet view article

(which was published in two parts in 1881 and 1882) he described homogeneous coordinates for hyperbolic geometry, now called Weierstrass coordinates of

Calabi–Yau manifold (3,256 words) [view diff] exact match in snippet view article find links to article

of all of the zeros of a homogeneous quintic polynomial in the homogeneous coordinates of the CP4. Another example is a smooth model of the Barth–Nieto

Conifold (865 words) [view diff] exact match in snippet view article find links to article

}^{5}+z_{5}^{5}-5\psi z_{1}z_{2}z_{3}z_{4}z_{5}=0} in terms of homogeneous coordinates z i {\displaystyle z_{i}} on C P 4 {\displaystyle \mathbb {CP}

Hyperboloid model (3,520 words) [view diff] exact match in snippet view article find links to article

Geometry p.266 in English version (Springer 1988). Cox, H. (1881). "Homogeneous coordinates in imaginary geometry and their application to systems of forces"

Triangulation (computer vision) (2,384 words) [view diff] exact match in snippet view article

′ {\displaystyle \mathbf {y} '_{1},\mathbf {y} '_{2}} are the homogeneous coordinates of the detected image points and C 1 , C 2 {\displaystyle \mathbf

Morphism of algebraic varieties (4,397 words) [view diff] exact match in snippet view article find links to article

\mathbf {P} ^{m}-\{y_{0}=0\}} is a morphism, where yi are the homogeneous coordinates. Note the target space is the affine space Am through the identification

Curve (3,656 words) [view diff] exact match in snippet view article find links to article

degree d. The values of u, v, w such that g(u, v, w) = 0 are the homogeneous coordinates of the points of the completion of the curve in the projective

Six-dimensional space (2,020 words) [view diff] exact match in snippet view article find links to article

related to general transformations in three dimensions through homogeneous coordinates, which can be thought of as modified rotations in R 4 {\displaystyle

Cayley transform (2,249 words) [view diff] exact match in snippet view article find links to article

quaternions are non-commutative, elements of its projective line have homogeneous coordinates written U [ a , b ] {\displaystyle U[a,b]} to indicate that the

Partial differential equation (6,795 words) [view diff] exact match in snippet view article find links to article

characteristic form Q(ζ) = 0 defines a cone (the normal cone) with homogeneous coordinates ζ. In the hyperbolic case, this cone has nm sheets, and the axis

Five points determine a conic (2,331 words) [view diff] exact match in snippet view article find links to article

(n-dimensional projective space has n + 1 {\displaystyle n+1} homogeneous coordinates) is ( ( n + 1 d ) ) , {\displaystyle \textstyle {\left(\!\!{n+1

Complex multiplication (2,071 words) [view diff] exact match in snippet view article find links to article

\mathbb {C} /\Lambda } to the projective elliptic curve defined in homogeneous coordinates by E = { ( x : y : z ) ∈ C 3 ∣ y 2 z = 4 x 3 − g 2 x z 2 − g 3

Projective line over a ring (2,979 words) [view diff] exact match in snippet view article find links to article

and Julius Plücker are also credited with originating the use of homogeneous coordinates. Eduard Study in 1898, and Élie Cartan in 1908, wrote articles

Division by zero (5,706 words) [view diff] exact match in snippet view article find links to article

JSTOR 20876802 Wegman, Edward J.; Said, Yasmin H. (2010), "Natural homogeneous coordinates", Wiley Interdisciplinary Reviews: Computational Statistics, 2

Thin plate spline (1,593 words) [view diff] exact match in snippet view article find links to article

are in 2 dimensions ( D = 2 {\displaystyle D=2} ). One can use homogeneous coordinates for the point-set where a point y i {\displaystyle y_{i}} is represented

Hilbert's Nullstellensatz (4,332 words) [view diff] exact match in snippet view article find links to article

0 on S {\displaystyle f=0{\text{ on }}S} we mean: for every homogeneous coordinates ( a 0 : ⋯ : a n ) {\displaystyle (a_{0}:\cdots :a_{n})} of a point

Divisor (algebraic geometry) (6,612 words) [view diff] exact match in snippet view article

dimension of X. Example: Let X = Pn be the projective n-space with the homogeneous coordinates x0, ..., xn. Let U = {x0 ≠ 0}. Then U is isomorphic to the affine

Steiner conic (2,205 words) [view diff] exact match in snippet view article find links to article

of a pappian plane is pappian and can also be coordinatized by homogeneous coordinates. A nondegenerate dual conic section is analogously defined by a

Pedal equation (1,591 words) [view diff] exact match in snippet view article find links to article

p may be simplified if the equation of the curve is written in homogeneous coordinates by introducing a variable z, so that the equation of the curve

Conformal geometric algebra (3,303 words) [view diff] case mismatch in snippet view article find links to article

New algebraic tools for classical geometry Ch. 2: Generalized Homogeneous Coordinates for Computational Geometry Ch. 3: Spherical Conformal Geometry