BDS Software

Stellar System Thoughts - Page 9



I like the uniformity of keeping my game screens all the same size wherever possible. I've standardized on a size of 641 pixels wide by 641 pixels high. This seems to work particularly well in Rectangular Grid scenarios.

A Hexagonal Grid scenario is significantly different however. Nevertheless, I want to use a Hex Grid for Stellar System modeling because it lends itself well to modeling orbital mechanics (at the game "approximation" level).

In modeling our own Solar System, it's appropriate to allow for eleven (11) "orbits", numbered zero through ten. The zeroth orbit is actually modeled as a stationary point: the unchanging location of the Sun itself at the center of the system.

Then, orbits 1-4 and 6-10 are reserved for the nine planets (I don't care WHAT you say; I STILL think of Pluto as a planet. :-)

Orbit #5 is reserved for the asteroid belt which, for simplicity in this model, will just consist of the three major asteroids: Ceres, Juno, and Vesta.

This is going to be a long page: Hold on tight!

*****

Given these eleven orbits, our grid must be at least 21 hexes high by 21 hexes wide (1 hex high by wide for the Sun, plus 2 hexes high by wide for each of the other orbits.

That is, the Sun (Orbit zero) will occupy one hex. The first planet (Orbit one) will sweep-out a 3-hex by 3-hex path with the Sun at the center. The second planet (Orbit two) will sweep-out a 5-hex by 5-hex path with the Sun at the center.... The last planet (Orbit ten) will sweep-out a 21-hex by 21-hex path with the Sun at the center.

So a minimum 21-hex high by 21-hex wide space is required.

And, comparative rectangular and hexagonal geometries dictate that a set of columns, each 21 hexes high, contained in a square space, will actually result in the collection being 23 columns wide.

To make sure all of these hexes are complete hexes (i.e. not cut-off by the edges of the 641 by 641 square space, it's helpful to generate a hex space larger than 21 by 23 hexes. I used Worldographer to generate a 29 by 29 hex map with hexes 29 pixels high by 34 pixels wide.

The result was the 748 by 855 pixel map shown here.










I then cropped this image to 641 by 641 pixels as shown here:










Resulting in this 641 by 641 pixel image containing 483 complete hexes, arranged 23 wide by 21 high, and also showing numerous incomplete hexes around the edges of the square:










However, blowing that image up ten times reveals that the diagonal lines are overly thick and lacking in precision. Also, alternate columns show further imprecision in having two lines per horizontal edge instead of only one. Some incidental artifacts (remnants of removed Worldographer-generated hex numbers) are also apparent:










So I prepared an 841 by 841 pixel blank image with croplines to a 641 by 641 pixel space as shown here:










This would allow me to produce a more precise Hex Grid via the following manually developed layout:










Blowing this layout up ten times reveals its arrangement. The yellow lines are hairline guides; the blue dots are Hex centers; and the red dots are Hex corners. The purple lines are a portion of the 641 by 641 croplines:










This is the final base Hex Grid which this manual process produced:










Blowing it up ten times shows the significantly improved precision:










And, this ten-times blowup of the upper-left corner also shows that the extraneous fractional border hexes have been removed from this manual plot:










This is the final Hex Grid which I will be using for my further Hex Grid-based game research and development.




                                                                                                                                                                M.D.J. 2022/07/29