Distance formula to calculate speed between two points

[Vlad]

I've spotted the InFlight thread about posting distance results of flights, so I wrote a script that parses the DBC data to extract this information, but I am stuck making this function properly:

// get delay between two points on a map and the movement speed modifier
function getDelay($from, $to, $speed) {
  $time = 0;
  if(is_array($from) && is_array($to)) {
    $m1 = $from['mapId']; $x1 = $from['x']; $y1 = $from['y']; $z1 = $from['z'];
    $m2 = $to['mapId'];   $x2 = $to['x'];   $y2 = $to['y'];   $z2 = $to['z'];
    $dx = abs($x1 - $x2); // TODO: are these correctly calculated?
    $dy = abs($y1 - $y2); // TODO: are these correctly calculated?
    $R = 1000; // NYI: mean radius of world (mapId)
    $a = pow(sin($dx/2), 2) + cos($x1)*cos($x2)*pow(sin($dy/2), 2);
    $c = 2*atan2(sqrt($a), sqrt(1-$a));
    $d = $R * $c;
    $S = 10; // NYI: speed constant that will be modified by $speed (%)
    $time = $d/($S*$speed);
  }
  return $time;
}

Basically, I have to calculate the distance between the two points (mapId1,x1,y1,z1) and (mapId2,x2,y2,z2) and I have the speed modifier here (100%, 150%, e.g.) but my speed constant and the radius of the mapId will be a challenge, anyone got any help on this matter?

If I get this to work sure I'll post source and best of all no flight addon will have to calculate on the fly, the time it will take to fly the path! One can in advance of a patch calculate the data from the DBC themselves and produce a LUA database with all the exact timers, cool right?

[Taryble]

That would work, assuming that all flight paths are perfectly straight lines.

[Seerah]

The way that InFlight and other timers work is by users recording how long it takes to fly from point A to point B. If a new flight is not in the addon's database, then it just measures how long it takes and stores that for next time.

[Vlad]

Thing is if the path isnt a straight line then you add more nodes and make the game slightly wobble (so it's not instant turns) but knowing the distances and angles between two coordinates would also allow you to figure out this wobble and include it in the time delay calculation, so you can achieve calculating the arrival time trough a path of nodes using their distances between each other.

For now my problem is that the paths have mapId relative coordinates so I have to figure out how big let's say northrend is, then outlands, e.g. Looking at MapDataLib for some info but havent gotten a proper formula, yet.

Anyway, there are advantages to calculating the times liek this, for once you can get all times without having to fly yourself to "time" it.

*Edit*

Saw your post SDPhantom, thanks. Gonna work it in, hehe. Yeah, I'm a bit unclear about the formulas, hence they look messy.

The coordinates in the DBC are raw, but not sure if it maters the size of the map, I guess not as long we dont fly across one map to the other (like to azuremyst but thats another problem to figure later on, hehe).

[Seerah]

I don't understand what you mean by "nodes" and "wobble"?

[SDPhantom]

Originally Posted by Vladinator Thing is if the path isnt a straight line then you add more nodes and make the game slightly wobble (so it's not instant turns) but knowing the distances and angles between two coordinates would also allow you to figure out this wobble and include it in the time delay calculation, so you can achieve calculating the arrival time trough a path of nodes using their distances between each other. For now my problem is that the paths have mapId relative coordinates so I have to figure out how big let's say northrend is, then outlands, e.g. Looking at MapDataLib for some info but havent gotten a proper formula, yet. Anyway, there are advantages to calculating the times liek this, for once you can get all times without having to fly yourself to "time" it. *Edit* Saw your post SDPhantom, thanks. Gonna work it in, hehe. Yeah, I'm a bit unclear about the formulas, hence they look messy. The coordinates in the DBC are raw, but not sure if it maters the size of the map, I guess not as long we dont fly across one map to the other (like to azuremyst but thats another problem to figure later on, hehe).

Internally, all objects are rendered at coordinates based on each continent. I'm not entirely sure what units such coordinates are based off of. I wouldn't automatically assume that it's still in yards.

Originally Posted by Seerah I don't understand what you mean by "nodes" and "wobble"?

I'm guessing "node" is each point that makes up the actual flight path and "wobble" is the method of which the game smooths out each turn by imposing a limit to the turning rate. However, the turn rate limit may just be enforced by adding more points in a turn to make it look smooth.

[Vlad]

It's a bit hard to explain, so I'll show some examples of what I mean;

TaxiNodes.dbc contains the columns:
TaxiId, mapId, x, y, z, name, ...

TaxiPath.dbc contains the columns:
PathId, fromTaxiId, toTaxiId, cost

TaxiPathNode.dbc contains the columns:
PathNodeId, PathId, counter, mapId, x, y, z, ...

Combining these information tables you can combine a start and a destination, for example in TaxiNodes.dbc Stormwind is #2 and Goldshire is #582.

Then you check TaxiPath.dbc if you have a PathId for a path fromTaxiId=2 and toTaxiId=582, if not then that taxi path does not exist.

If you do on the other hand, you look the nodes in the path (the mount follows these node by node) in TaxiPathNode.dbc where you look up all PathNodeId where PathId=TaxiPath.PathId and you get a list where counter goes from 0 up to the last node (SW->GS has 16 nodes along the flight path).

Each flight position has coordinates, they are relative to the map and we know the mapId in case we need to translate coordinates (i.e. flying from one map to the other, e.g. maybe it affects the distance calculations, not sure, maybe not).

Anyway, mathematically you can iterate a path of many nodes and each step you take you compare this with the previous (or next, depending how you program it) and get a distance difference by putting the coordinates in a formula, then if you know how fast you are moving you can calculate the time between each node and sum them all up for the total travel time from start to finish.

The only problem so far is the possibility of a "wobble", like this:

Fig. 1 is how the math would calculate distances, straight lines from one point to the other. Fig. 2 is how it feels in the game, you don't fly and instantly turn once you hit a node, instead the game does some sort of wobble to make the transition smooth between nodes.

TaxiNodes = positions you can land and take off
FlightNodes/(I call them nodes in this post) = the orange dots in between the air, not visible but you go from one to the next like waypoints.

*Edit*

SDPhantom the coordinates are on this form (one random line from both files that contain coordinates):
2,0,-8841.05957031,489.656005859,109.607002258,"Stormwind, Elwynn",0,541,1,0.00998003967106,0.0101744187996,
35,6,0,0,-8852.65039063,496.459991455,111.040000916,0x0,0,0,0,
You have the mapId (0 in this case) and the coordinates, it does look like continent coordinates, yes.

*Edit 2*
Just figured I'd put an example output so far, the time is about right for this specific path, but need to find the speed value, it may be variable or constant if lucky. At the moment the speed was set to 30.33... but need to test with more FP to see if it applies to them or not, I think not because of this wobble I mentioned in the post.

Flying path #557 for 1020 copper: - #128; Shattrath, Terokkar Forest - #121; Allerian Stronghold, Terokkar Forest - parsing nodes along path... -> #start to #14252 (+0.15 seconds) -> #14252 to #14251 (+0.71 seconds) -> #14251 to #14250 (+1.48 seconds) -> #14250 to #14249 (+2.33 seconds) -> #14249 to #14248 (+2.47 seconds) -> #14248 to #14247 (+3.21 seconds) -> #14247 to #14246 (+5.81 seconds) -> #14246 to #14245 (+13.83 seconds) -> #14245 to #14244 (+7.16 seconds) -> #14244 to #14243 (+4.55 seconds) -> #14243 to #14242 (+4.87 seconds) -> #14242 to #14241 (+6.92 seconds) -> #14241 to #14240 (+4.93 seconds) -> #14240 to #14239 (+5.49 seconds) -> #14239 to #14238 (+5.59 seconds) -> #14238 to #14237 (+3.15 seconds) -> #14237 to #14236 (+1.66 seconds) -> #14236 to #end (+0.06 seconds) => arrived destination after 74.36 seconds!

[SDPhantom]

If you have absolute coordinates, you don't need MapID. You're also using a bunch of unneeded trig functions.

PHP Code:

function getDistance($x1,$y1,$z1,$x2,$y2,$z2,$speed)
    return sqrt(pow($x1-$x2,2)+pow($y1-$y2,2)+pow($z1-$z2,2))/$speed;
end 


Note: $speed needs to be in the same units as the coordinates, this means since the absolute coordinates of a map are measured in yards, $speed needs to match it too. For 100% speed, this would be a value of 7.

[Seerah]

(Don't forget that we do not have access to z-coordinates.)