Search results

...int.svg|400px|thumb|right|'''Figure 1.''' The various properties of a flat point.]] In the 5D conformal geometric algebra $$\mathcal G_{4,1}$$, a ''flat point'' $$\mathbf p$$ is a bivector having the general form ...

...can be viewed as an infinitely large [[sphere]] containing the [[point at infinity]]. A plane in conformal geometric algebra is the precise analog of a [http: * [[Flat point]] ...

...n be viewed as an infinitely large [[circle]] that contains the [[point at infinity]]. A line in conformal geometric algebra is the precise analog of a [http:/ * [[Flat point]] ...

...{x7E}}{T}}}$$. This can be interpreted as a rotation about the [[line]] at infinity perpendicular to the direction $$\boldsymbol \tau$$, where the magnitude of ...$$ is applied to a [[round point]], it is equivalent to premultiplying the point by the $$5 \times 5$$ matrix ...

If the $$s_u$$ component is zero, then the sphere contains the [[point at infinity]], and it is thus a flat [[plane]]. The round [[center]] of a sphere $$\mathbf s$$ is the [[round point]] having the same center and radius as $$\mathbf s$$, and it is given by ...

...hen the dipole contains the [[point at infinity]], and it is thus a [[flat point]]. ...arrier meet at the flat center of the dipole, which is given by the [[flat point]] ...

...nd $$gw$$ components are all zero, then the circle contains the [[point at infinity]], and it is thus a straight [[line]]. ...arrier meet at the flat center of the circle, which is given by the [[flat point]] ...

...ng 3D Euclidean space as an example, we begin by considering a homogeneous point ...projected is $$\mathbf e_- + \mathbf e_+$$. This projection transforms the point $$\mathbf p$$ into ...