Projecting multivector directions
Figure 1.2.1: Multivector directions in (1,1) spacetime and their projections
Figure 1.2.2: Stereographic projection of (1,1) spacetime directions
Figure 1.2.3: Vector and Bivector directions in (1,2) spacetime
Dynamic app 1.2.1: Bivector directions in (1,2) spacetime
Caption for dynamic app 1.2.1: Bivector directions in (1,2) spacetime
Left: Bivector direction (projective space), Right: Stereographic projection
Drag green slider (P) on the projective space to move the polar direction E around the sphere.
The bivector direction is a red circular diameter (right) whose projection is a red circumference in the projective plane.
This circumference crosses the unit circumference at diametral points.
Figure 1.2.4: Multivector directions in (1,2) spacetime projection
Dynamic app 1.2.2: Vector and Bivector directions in (1,2) spacetime
Vector and Bivector directions (caption for dynamic app 1.2.2)
Drag the green slider A to change the vector direction (green line) and the red slider B to change the bivector direction (red plane).
Placing (on the left projective plane) the slider A over the red circle centered at B, verify (at the right spacetime) that the vector direction (green line) lies on the bivector direction (red plane). You should rotate the right figure to find the appropriate perspective.
Dynamic app 1.2.3: Two Bivector and one vector directions in (1,2) spacetime
Two Bivector and one vector directions (caption for dynamic app 1.2.3)
Drag the sliders A, B and C to change the relative positions of the corresponding spacetime directions.
Rotating the spacetime figure (right side) try to find the best perspective to observe the correspondences between both planes and the green line. Compare with the relative positions of the green point A and the blue and red circles.
Figure 1.2.5: Multivector directions in (1,3) spacetime: 3d projection
Dynamic app 1.2.4: Bivector and Trivector projected on 3d space
Bivector and Trivector Projected on 3d space (caption for dynamic app 1.2.4)
Drag the three red points (two, Ao and Bo, on the surface of the unit grey sphere to select the orientation, and the third (B) to define the size of the red circle representing the projection of a (1,3) bivector direction on the 3d projection space.
Drag the blue point Co on the surface of the unit sphere and C on the blue line to define the spherical surface corresponding to the projection of a trivector direction.
Check the relative positions of those projected multivector directions.