What happens if you construct the three tessellations based on the same set of points?

Below you find 2 combined drawings. The hexagonal part is devided in two ways, the lower one comes closer in comparisation with the voronoi and delaunay part.

In these two dwawings the amount of points are chosen by using factors of 2. Thats why the structure is more regular. The second one is the best. Because the density of the hexagonal structure is more equal to the others.

For the research it would be interesting to test the three types of structures and compare them. In the next scheme, I defined a try-out set up of the comparisation.

These domes are all constructed based on the same set of points. The amount of points per ring are random. Thats why the Delaunay and Voronoi version are a bit irregular. The errors in the hexagon sample are because it took too long to draw all lines manually and I arrayed one quarter. but it gives an idea. The size of the dome can be a parameter as well!! (unlike i noted on this picture) But to compare them, the size should be the same for all 3 domes.

How to define the circels and points (in GC), which define the tesselations?

In the picture below is illustrated how a plane is projected onto the dome. the set-up size of the plane has a diameter of 32 m, while the dome itselves has a diameter of 20.37 m. I defined the plane first, in order to get a regular division of rings possible.

The overal size can be changed afterwards by adjusting the diameter of the projection plane.

RULES RINGS

The rings can vary in number. They are always linear distributed on the plane.

Number of rings: n_ring

Diameter of projection plane: d_plane

The max distance between the rings is 4 meter.

The min distance between the rings is 0.5 meter.

The formula which defines this relation is: 1/2 = smaller than: (0.25*pi*d_plane)/n_ring = smaller than: 4

RULES POINTS

The points on each ring can vary in number. They are always linear distributed along the ring.

A similar system rules the division of points onto the rings

Number of points: n_point

Diameter of ring: d_ring

The max distance between the points is 4 meter.

The min distance between the points is 0.5 meter.

The formula which defines this relation is: 1/2 = smaller than: (d_ring*pi)/n_point = smaller than: 4.

definition of the projection plane & rings

Diagram of GC hierarchy.

## Saturday, July 25, 2009

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