Geometry

1712 Submissions

[2] viXra:1712.0524 [pdf] submitted on 2017-12-19 13:56:07

Projection of a Vector upon a Plane from an Arbitrary Angle, via Geometric (Clifford) Algebra

Authors: James A. Smith
Comments: 8 Pages.

We show how to calculate the projection of a vector, from an arbitrary direction, upon a given plane whose orientation is characterized by its normal vector, and by a bivector to which the plane is parallel. The resulting solutions are tested by means of an interactive GeoGebra construction.
Category: Geometry

[1] viXra:1712.0393 [pdf] submitted on 2017-12-11 16:46:30

Formulas and Spreadsheets for Simple, Composite, and Complex Rotations of Vectors and Bivectors in Geometric (Clifford) Algebra

Authors: James A. Smith
Comments: 29 Pages. Formulas and Spreadsheets for Simple, Composite, and Complex Rotations of Vectors and Bivectors in Geometric (Clifford) Algebra

We show how to express the representations of single, composite, and ``rotated" rotations in GA terms that allow rotations to be calculated conveniently via spreadsheets. Worked examples include rotation of a single vector by a bivector angle; rotation of a vector about an axis; composite rotation of a vector; rotation of a bivector; and the ``rotation of a rotation". Spreadsheets for doing the calculations are made available via live links.
Category: Geometry