The following seems to be invalid for the newer PC
versions of the game.
A ship can jump very large distances due to a modulo
effect in the hyperspace continuum with a base of #math163#Wsect = 81.62 sector
lengths (#math164#655.36 lj). One can use this behavior to find jump paths
that are much shorter in time and fuel consumption than the straight
distance. This also allows you to use a smaller hyperdrive and leaves more
room for fuel and cargo.
The optimal jump points for a journey between two systems with one
intermediate stop are found on the intersections of circles around the two
endpoints of the journey. On such a circle lie the systems that can be
reached from the center of the circle with a minimum amount of fuel and
time. A system at the intersection of such circles can be reached easily
from the centers of both circles, making it an ideal intermediate jump
point. The circles have multiples of the wormhole distance (#math165#655.36 lj) as
radii.
To make the calculations simple we assume at first, that the ``thickness''
of a sector can be neglected and that two jumps with equal distance shall be
made, resulting in circles with equal radius. The coordinates of the ideal
intermediate jump points can now be found on a line that perpendicular
bisects the segment between the two endpoints of your journey, at the points
of intersection of the circles around the endpoints.
<#2095#>Figure<#2095#>:
<#2096#>Location of intermediate jump points for
equal distance wormhole jumps<#2096#>
| #figure268# |
For two star systems at the coordinates (x, y) and (u, v) we define:
#math166#
|
, *1cm#tex2html_wrap_indisplay2102#
|
(6) |
We choose a jump distance of #math167#Wn = n×Wsect
sectors. With this definitions we get as coordinates for the intermediate
jump (p, q):
#math168#
|
| p = #tex2html_wrap_indisplay2107# + b#tex2html_wrap_indisplay2108# |
, *1cm#tex2html_wrap_indisplay2109#
|
(7) |
or
#math169#
|
| p = #tex2html_wrap_indisplay2112# - b#tex2html_wrap_indisplay2113# |
, *1cm#tex2html_wrap_indisplay2114#
|
(8) |
Now n has to be chosen such that the square root has a
real solution (the jump radius is larger than the half distance between the
systems) and we have to find a system near one of the intermediate jump
points. If such a system cannot be found, we simply increment n and try
again with a wormhole distance of the next greater order.
If you want to perform two jumps with different jump sizes the equations
have essentially the same structure but get a bit more complicated. We
define a and b as in (#shortcut#337>) and choose the jump distances
#math170#Wm = m×Wsect for the first jump and #math171#Wn = n×Wsect for the second jump. m and n must be chosen such that:
#math172#
|
#tex2html_wrap_indisplay2124#m - #tex2html_wrap_indisplay2125##tex2html_wrap_indisplay2126#≤n≤m + #tex2html_wrap_indisplay2127#
|
(9) |
This ensures, that there exists an intermediate jump point at all. With
#math173#
|
α = #tex2html_wrap_indisplay2129# + #tex2html_wrap_indisplay2130#
|
(10) |
we get for the coordinates of the intermediate jump point (p, q):
#math174#
|
| p = (1 - α)x + αu + b#tex2html_wrap_indisplay2134# |
, *1cm#tex2html_wrap_indisplay2135#
|
(11) |
or
#math175#
|
| p = (1 - α)x + αu - b#tex2html_wrap_indisplay2138# |
, *1cm#tex2html_wrap_indisplay2139#
|
(12) |