Projective Geometric Algebra as a Subalgebra of Conformal Geometric algebra

Projective Geometric Algebra

Oriented Conformal Geometric Algebra

In [12] Stolfi developed a complete theory of Oriented Projective Geometry. He showed that assigning meaning to the sign of an otherwise homogenous representation of geometry could provide a multitude of benefits. This paper extends his work by applying the same approach to Conformal Geometric Algebra. Oriented Conformal Geometric Algebra allows intuitive manipulation of such concepts as half-s...

Conformal Mappings in Geometric Algebra

I n 1878 William Kingdon Clifford wrote down the rules for his geometric algebra, also known as Clifford algebra. We argue in this paper that in doing so he laid down the groundwork that is profoundly altering the language used by the mathematical community to express geometrical ideas. In the real estate business everyone knows that what is most important is location. We demonstrate here that ...

Recent Applications of Conformal Geometric Algebra

We discuss a new covariant approach to geometry, called conformal geometric algebra, concentrating particularly on applications to projective geometry and new hybrid geometries. In addition, a new method of working, which can achieve similar results, but using only one extra dimension instead of two, is also discussed.

Three-Dimensional Projective Geometry with Geometric Algebra

The line geometric model of 3-D projective geometry has the nice property that the Lie algebra sl(4) of 3-D projective transformations is isomorphic to the bivector algebra of Cl(3, 3), and line geometry is closely related to the classical screw theory for 3-D rigid-body motions. The canonical homomorphism from SL(4) to Spin(3, 3) is not satisfying because it is not surjective, and the projecti...