X rotation angle
Y rotation angle
Z rotation angle
Data output panel 2
Layer Manager

The rod and the black paint marks

The second point that needs to be looked at before the geometry can be rotated in 3D is to determine a rotation axis for the rod and to check that there are no errors in the geometry that has been formed up to this point.

Click here to show some of the features from within the lower northern shaft that were identified earlier (page C6). The illustration shows four points of interest. They are, from left to right, the start of the hexagonal rod, the single scratched out black paint mark, the double scratched out black paint mark, and the piece of bent metal with two holes in it that is located at the start of the bend in the rod. The positions of these elements is taken from the description on the robotics engineer's website in conjunction with the measurements, from their technical drawings, of the stones that make up the shaft, the joints of which are shown on the interactive drawing.

If you start the clock (which, you will recall, sets the Earth rotating around the Sun) you can see the highlighted line of the ascending passage moving up and down the shaft and gallery areas.

If you let the animation run for a while it becomes apparent that the single scratched out black paint mark defines the lower extremity of the ascending passage line's movement, and if you stop the clock at this position you can see from the Y-axis rotation angle panel at the bottom of the screen that the Earth is at a 90° angle along its orbit - that is to say it is 9 months into its annual rotation around the Sun and therefore at an equinox.

If, instead of setting the Earth at this angle in its orbit, you set it at a 45° angle you can see that the ascending passage line coincides with the double scratched out black paint mark.

The rotation angles

These two angles, 45° and 90° are marker points in the shaft that draw your attention to the following two highly important fact.

The straight rod section's start and end points

This information can now be used to determine the start and end points of the straight section of the hexagonal rod which will also be the rod's rotation axis' start and end points.

If you consider how the geometry that plots out the hexagonal rod is being formed, any rotation axis must be a static object that has a defined fixed start and end point, irrespective of the moving geometry. The external stonework of the pyramid and the upper northern shaft were formed from two static ellipses, which have already been recorded as such earlier in this work (page B12 and page B3), and these are the only two static objects from which the rod's rotation axis can be formed.

If you place the dynamic rotating ellipse into the same position as that of the second static ellipse you would expect the start of the rod to be defined by this geometry. However, you can see that the highlighted green ascending passage line within the lower northern shaft has a substantial discrepancy from the actual start of the rod. Make a note of the distance between the two points.

If you place the dynamic rotating ellipse into the same position as that of the first static ellipse which is polar cross section of the Earth you can see that there is a similar discrepancy between the position of the highlighted green line and the point marked off in the shaft by the piece of metal with the two holes which identifies the end of the rod's straight section.

The two discrepancies at the two ends of the shaft's straight section are the same length, and it is in the advanced section of this work that the reason for this linear error is identified.

The angle of the axis of rotation that is defined by these two points, despite their linear positioning error, is correct and does not affect the 3D rotations that will be applied to the rod on the next page.

Last edited: 3rd July 2019
Last code/graphics edit: 29th March 2021