Abstract.
In [16] Stolfi developed a complete theory of Oriented Projective Geometry. He showed that assigning meaning to the sign of an otherwise homogeneous 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-spaces, inclusion within geometric entities and ordered intersections. It also illustrates the non-commutative nature of the meet. The paper concludes with some examples of applications in which Oriented Conformal Geometric Algebra is already providing benefits.
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Cameron, J., Lasenby, J. Oriented Conformal Geometric Algebra. AACA 18, 523–538 (2008). https://doi.org/10.1007/s00006-008-0084-9
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DOI: https://doi.org/10.1007/s00006-008-0084-9