LOS Hex Geometry Articles
- Thread starter Augie
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bendizoid
Official ***** Dickweed
The midpoint between two hexes is either a hex center or most likely the midpoint of a hexside. At 5 hex range (4 up one over) the line goes through two vertices and a hexside midpoint. Just say'in.
Thanks, but that is the obvious one known by me (and about the only one I know). I'm looking for the more complex and non-intuitive geometric LOS hex math.
rreinesch
Elder Member
Then head to the reference to the Banzai article that Jim references above. This'll fit your bill.
This article is hugely helpful. Thanks for everyone's responses. Mid-hex on simple geometry was obvious to me. This article helps break it down for additional hexes for longer and/or more complex LOS.
Philippe D.
Elder Member
Well, I admit a lot of math seems more intuitive to me than to most people, but here's a trick that some might find useful.
If you trace straight lines through a hexagon between opposing vertices, you'll divide the hexagon into six equilateral triangles. Do this for the whole hex grid, and you're dividing your map into equal triangles. On this (fictive) triangle grid, it's pretty easy to figure geometry - whenever you are tracing a LOS from one hex center or hex vertex to another, you're actually tracing a LOS from one vertex to another of the triangle grid. If it helps, you can pair adjacent triangles into lozenges, and then the geometry of lines through a grid of lozenges is essentially the same as it is in a grid of squares - and note that the vertices for the triangle gris are the same as for the square grid.
Basically, on a square grid, if you need to figure out whether a line from one vertex A to another vertex B goes exactly through a vertex C or not, this is the "rule": count the ticks along each axis from A to B, and from A to C (or from B to C). The ratios must be the same, or the line doesn't go through C. In the "triangle grid as a kind of square grid", you need to pick two line directions as your "axes", and they won't be orthogonal, but the same holds (and "ticks" in this setting will be the length of a hexside, or, in the language of the Banzai! article, a hex radius).
(I realize this isn't easy to follow without pictures, but I don't have pics of a hex grid that I could easily post here)
If you trace straight lines through a hexagon between opposing vertices, you'll divide the hexagon into six equilateral triangles. Do this for the whole hex grid, and you're dividing your map into equal triangles. On this (fictive) triangle grid, it's pretty easy to figure geometry - whenever you are tracing a LOS from one hex center or hex vertex to another, you're actually tracing a LOS from one vertex to another of the triangle grid. If it helps, you can pair adjacent triangles into lozenges, and then the geometry of lines through a grid of lozenges is essentially the same as it is in a grid of squares - and note that the vertices for the triangle gris are the same as for the square grid.
Basically, on a square grid, if you need to figure out whether a line from one vertex A to another vertex B goes exactly through a vertex C or not, this is the "rule": count the ticks along each axis from A to B, and from A to C (or from B to C). The ratios must be the same, or the line doesn't go through C. In the "triangle grid as a kind of square grid", you need to pick two line directions as your "axes", and they won't be orthogonal, but the same holds (and "ticks" in this setting will be the length of a hexside, or, in the language of the Banzai! article, a hex radius).
(I realize this isn't easy to follow without pictures, but I don't have pics of a hex grid that I could easily post here)
Yup, someone is going to need post pics for this
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Ganjulama
Tuco B.P.J. Maria Ramirez
Grok failure
Eyes glaze over. I failed Geometry in High School. I just take my chances and draw the thread
bendizoid
Official ***** Dickweed
Grok failure
Eyes glaze over. I failed Geometry in High School. I just take my chances and draw the thread
Doug, Next time I see you lets take two minutes and I'll show you what We're taking about. It is such a advantage to quickly and accurately gauge tacky LOS's. I've only met a few players with better LOS skills than me (Paul Chamberland for one). It's really worth learning and not that difficult once you visualize. Once you establish a midpoint (rather easy) you can break the LOS line into two line segments and get a easier look.Grok failure
Eyes glaze over. I failed Geometry in High School. I just take my chances and draw the thread
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bendizoid
Official ***** Dickweed
Another cool LOS idea is for those on the board edge with no center dot. Instead of guessing, count the pattern of hexes toward the target hex on the edge, then count the exact same pattern in the opposite direction and extrapolate from your new hex through the 'center' hex to the target 'edge' hex.
Philippe D.
Elder Member
For those who have trouble with this geometry - is the Banzai! article that was linked a little above any clearer than my own triangle explanations? Everything in there is correct, as far as I can see. I'd like to know where the difficulties are if I'm to try and write down some explanations.
sarfs
Senior Member
This one of the best things you ever taught me about this game. Thanks Bob!
bendizoid
Official ***** Dickweed
Because you have to announce before and then shoot after you string the LOS. It's not that much brain drain and simple with a little practice. It's probably one of the best advantages a player could have.Why waste the brain power, string the thread and see, bet it is quicker than killing brain cells doing the math
Philippe D.
Elder Member
You can play with a house rule for free LOS checks, but the rules ask that before you draw the string, you commit to firing - unless you're checking for something like concealment loss.
Also, there is the question of whether the LOS, geometrically, goes exactly through a vertex, mostly for inherent terrain reasons. The hex grid printed on cardboard is not perfect, and hex centers are not exact points (some of them are even big squares or circles). A little geometry can tell you exactly when a LOS is supposed to go through a vertex, and this works for center-to-center, for center-to-vertex, or for vertex-to-vertex. Also, being able to figure out which exact points the LOS is going along the way, often lets you see whether it will cross some drawn terrain feature.
Ganjulama
Tuco B.P.J. Maria Ramirez
The biggest advantage is to Attack Without Mercy. It is always a surprise