Just want to say thanks to everyone who has chipped in with their thoughts and explanations regarding the discrepancies with the line. It’s all a learning curve (😉) and I’m certain that by the time I’ve fully digested all of your comments and emails Ill be fully equipped for any such issues come the next mission. Thanks everyone! You truly are the best fans in all of UA-cam.
There are a number of statistical measures of deviation and fit, so those are probably your best bet. For example, you could take the co-ordinates from the line you traveled and calculate the *standard deviation* from your 'perfect' line. Or you could do a *basic linear regression* of the y-coordinates from the traveled line on the x-coordinates from the traveled line, which will calculate the straight line of best fit for your travelled path. Then calculate the *R-squared* from this regression for a measure of fit. Both these methods can be done in various free softwares or programming languages e.g. R, which is free, just need to download R (the language) and R Studio. You might need to 'clean' your data from the GPS to take into account forests or deviations when standing still, but that isn't that difficult. It just depends how the data are collected.
Dropping some quick thoughts on this: 1. I feel like the spirit of the challenge is to move a far distance in as close to a straight line as possible, and the scoring should entirely be based on how straight your gps tracked line is, not at all connected to any planned line. 2. Having said that, now comes the scoring issue. Whether the top suggestion is followed wont matter much for my take on scoring, as it combines 2 sections. A well made computer program will easily be able to calculate an average deviation.(might have to be custom made though) This may be one good measure for scoring but will suffer an issue with single high devations barely impacting the average at all. Solution: Multiply average deviation with max deviation for a total score where both avoiding single time large deviations(cliffs n stuff) and sticking close to the line while strolling will impact the line. Here you can also introduce some multiplying constant to adjust balance, ending up with something like: AvgDev*(MaxDev*X) where 0
It probably has to do with the curvature of the Earth, as you are relatively close to the north pole. Your line actually goes completely straight in spherical geometry, and the yellow line only works on flat map projection. In this case, at both ends the two lines should get closer and meet at the end (i think you mentioned it in the video). If that is true, it should not be hard to calculate the pink line you followed. So you probably followed the truly straight line, and the other one was curved in terms of not being shortest distance connecting both ends on sphere.
I thought it might be that as well. Although some of the distances seem like they might be too far for that kind of error. It would be interesting to plot the curved line in GIS to see how well it matches with Tom's actual walked line.
@@kolklown I wonder if altitude could also cause some consistent offsset, GPS system should have this covered with triangulation. Maybe there is also some factor of closeness to the pole?
I think it’s important to remember that the series is called “Crossing Norway in A Straight Line” Not crossing Norway in THE straight line. No one much cares which line you use or send up following, we just care how close you were to any straight line.
Thats good but the problem is that he was following one specific line. That the line we should judge him by. He shouldn't be able to draw a perfect line after the fact. Imo
Disagree. He was following what his GPS told him, no one out in the field could know it was off from the original line. He didn’t draw a line to fit his final path, he drew one to more accurately represent the line his GPS directed him to follow. That is what the measuring stick should be.
Yes. But finding the perfect fit line afterwards is cheating a bit. Then you'd deviate left of it, and then right, during the missions, cause you know that'll help the best fit line. As long as he can prove it with GPS data it seems fair, but finding best fit lines in hind sight feels unfair to me
@@thelazymanatee2506 I don't see why the planning phase should affect how your actual physical line is judged. The challenge is to cross border to border in as straight a line as possible, not to walk along a straight line you planned, that's just a good tactic for succeeding in the challenge.
I'm a site positioning and gps technician in the U.S. and I feel I can shed some light on the line problem. You said to contact you by email but I couldn't find one so I thought I would add to what I've already seen some comments about. Whenever drawing a flat line on a map and then putting it on a 3d sphere like the earth the line will not stay completely straight. Your gps Is a map wrapped around a sphere and the map you are using in the video is flat so they will never be accurate to eachother. This is compounded when you add elevation changes and when you get closer to the poles (tightening the curve) this problem can be solved but in your case with all the massive elevation changes making a true straight line along a sphere is technically impossible. If anyone has his email or if you want to get in contact with me I can explain much more in depth than I can in a youtube comment. Hope that helps, keep up the awesome videos man.
What he really wants is a line/route that fits within a perpendicular plane and to calculate deviations by normals to that chosen plane which makes sense conceptually but I doubt the technology he is using is optimized towards that regard.
Well also a consumer grade GPS is also not 100% accurate either without correction signals like spotbeam, inmarsat and IALA. So that might also have been some of the problems.
I love how serious you take this and how you are effectively apologizing for 'misleading' us, even though you make the rules and it's not like you're cheating or anything
@@alfiewright1396 I don't believe that is what happened. I think the lines just drift apart because of earth's curvature and where it became apparent for him, he just happened to be switching out batteries and so it looked like a jump.
@@dmcdcm Maybe the jump happened on the battery change because the GPS receiver had calibrated itself somewhat in the run-up to the change, and reset once the batteries had been replaced - might also explain why the lines reconverged again towards the end.
Is there a media center of the news station that reported it that is accessible outside of Norway? I've been learning Norwegian for two years, so I SHOULD be able to at least understand some of it... NRK has at least some of their programm accessible, right?
GeoWizard: *Crosses an entire country in a straight line not even deviating 100 ft from the path* Also GeoWizard: "The harsh judges of you will say..."
He is still 50km from the coast though, so not really an entire contry. There is more land on the other side of the fjord if he wanted to continue the line.
I just watched a man talk about how straight a line is for 30 minutes and I could not be happier, love how you're so passionate about sticking to the line exactly. Can't wait for the next one. Also GeoguessR released a Battle Royale mode, yep 2020 is a wild year. Quite fun though, looking forward to that video.
that'd be one expensive youtube video to film, this is his job so i don't know if he could justify 2 or 4 plane tickets (depening in if its solo) accross the globe
@@fisheatsyourhead He says he loves travel and he's travelled all around the world, so the straight line mission wouldn't have to be the whole trip- most of it could be a normal vacation
Considering this heavy GPS topic, I'd really wanna hear it from Garmin themselves. Maybe they have a special solution for future missions, they are the specialists afterall. Who knows, might even get random sponsorship :D Well done tho!
It's nearly impossible to get accurate. Altitude, rate of change the curve of the earth all affects the line that is ultimately mapped. The original one doesn't show the curvature of the earth, the distance from the poles etc.
Not to sound like a know it all....but the earth isn't flat... This sounds obvious after you hear it but think about it for a second. Matching up a line on a flat map to the sphere of earth isn't going to be easy. I'm pretty sure that's why your two lines don't match up in the middle but do at the ends.
It's off because you put a straight line on a flat map. Since the world is round, the actual path is going to bend slightly. It's more pronounced the closer to the poles you get, since flat maps get distorted more at the poles.
That was my first thought aswel during the intro, but it doesn't explain the sudden several meter jump after rebooting at 8:30. He also stated it happened in random points on the Wales route, instead of a steady progression with the peak being in the middle - the offset doesn't seem to progress smoothly along the route like it should if it's due to curvature. I'm clueless, but I'm reasonably sure its an issue with the gps device, or gps technology in general, with earth's curvature being a negligible deviation from the line considering the fairly short route length. The error was probably also not made during planning (using different maps, one being curved while the other is flat etc), as that wouldn't explain the sudden jumps and the camera footage of the gps tracker, it would be a consistant deviation throughout (which may well also be in the mix, but doesn't seem to be the main issue).
@@Die__Ene Could it be his altitude-offset is wrong, or barometric pressure sensor (if it has that) is blocked by dirt. Imagine most of the sattelites he receives are in the south it is like the line from the sattelite to "him" passes through a line about a couple meters above the programmed line and thus he is north of the line. He should do a trip in a straight line from south to north and see if he has the same problem.
im norwegian and yesterday i came over a newsarticle about you and your mission across Norway, from NRK. it really surprised me, but it was awesome to see them promoting you! From Wikipedia: NRK (an abbreviation of the Norwegian: Norsk rikskringkasting AS, generally expressed in English as the Norwegian Broadcasting Corporation) is the Norwegian government-owned radio and television public broadcasting company, and the largest media organisation in Norway.
We had been going over 10 minutes before we got an "are we recording?" and I was getting worried for a second there. Glad we got one in there eventually though.
Thanks Tom! Hey guys, the link to the process I went through to help Tom is in the description. Its a twitch VOD where I answered a lot of questions from the chat as well :)
Yeah, i was internally screaming ,,try to take the integral of the line (and divide it by the length of the entirely straight line, which he was aiming for)''. Don't continue if you don't like calculus. With doing that he could also vary the importance of maximum deviation through applying some sort of function( for example x^2) on the line function. So I would, if technically possibly, calculate the score as follows: score=(1/L)*∫(0 to L) dev(x)^2 dx where x is the distance from the start and dev(x) the deviation at that point x. Maybe ^2 is a bit too much, so maybe ^1.5. But you could experiment with that. If he can't calculate the deviation at every point, he could approximate the integral with a sum. The formula would change to score=(1/L)*∑(1 to n) dev(x)^2 dx where dx=L/n and where n is the number of points at which you would calculate/meassure the deviation. The distance(dx) between the meassuring points should definetly be set in advance(maybe 1m/5m/10m), it could approach 0 if a computer can do this, which would make it really accurate(comparing it to the real area). Then dev(x) gets calculated at every x=dx*k k=1,2,3,...,n until x=L(which is true when k=n). I probably annoyed you, if you read that. I just love applying maths to things like that :D
@@Ma7iT Yeah thats pretty good, I suppose for cases where there are two outputs (like when he is standing still and the signal is bouncing) you would just sample the further point. Also, we'd need to take abs(dev(x)) but if your squaring than it already takes care of that. One thing that we want out of this scale that Tom pointed out is he really wants a hefty penalty for going off course, and you could also just achieve by having your "weight" function that takes in dev(x) be a piecewise that after a certain threshold is when things get really bad. This would be sort of nice to keep it where there is still the concept of a band you want to stay in. Personally, i'd like to see maybe a 15m "safe zone" where there is no penalty, just to try and give some attempt to not penalize for random GPS jumps. The delta x in the actual sum needs to be pretty darn small, because if it said 5m then it would allow for you to do deviate arbitrarily far in the y aka dev(x) direction, and as long as you got back to line before moving 5m in the x-direction than your big deviation would go undetected.
Yeah I was trying to think back to A-level maths 30 odd years ago - calculating the area under the graph line before Tom mentioned it. This seems like the obvious standard, maybe with deviation from the mean factored in.
Possibly the better way of calculating score for the run would be taking some quickly growing function, like exponent, and then integrating. That way every further meter from the line is weighted higher, so big deviation is punished, even if happened over a short distance.
@@vainbow4632 His solution of taking the distance from the line every meter and adding it up is *essentially* just numerical integration. You don't need a function representation of the curve to get a good estimate.
I think I've seen it suggested a couple of times, but the root mean square error would be a nice scoring metric. I basically entails squaring the deviation for the line at ever measurement point (for example every GPS update), taking the average of all the squared values and taking the route of that average. This still indicates the average deviation from the line, but squaring the errors and taking the root of the average has the beneficial effect of punishing large deviations with respect to small ones. That way you encompass both average deviation and punish large deviations in the same scoring metric. I definitely don't recommend doing this by hand, but a simple Python script or even an excel sheet could do the job, I think.
Boffin here, I would recommend using root mean square (RMS) of deviation measurements to get the best aggregate measure of success sticking to the line. RMS solves a couple problems you mentioned with the proposed rating systems, and is a good aggregate error method used in my field of electrical engineering and a lot of other fields of statistical analysis and the like. I'd be happy to explain further if you're interested in the technical details, and it wouldn't be that much harder to implement than a simple average of deviation lengths. I will outline some benefits below. 1) Disproportionate weight of larger deviations: Just taking an average of deviation from the line at any meter will, like you said, comparatively downplay the influence of more dramatic deviations over a shorter length. RMS uses the square of error values, so a 20 meter deviation actually has 16 times the weight per distance travelled than a 5 meter deviation. You may still want to set some hard limits on distance deviated, but this method has that built in to some extent. 2) Signed Cancelation: Taking a simple average of deviations could cancel out errors in either direction if you don't use the absolute value. RMS can take data in either direction and it contributes equally to the aggregate error calculation because the square of a positive or negative number is positive. 3) Recognized convention: RMS is a well-understood way to analyze problems like this, and when statisticians try to draw a line to interpolate data points, they do so to minimize RMS deviation (called residuals in that field), which seems similar to what you are trying to accomplish, and may lend your measurement standard more credibility and understandability. In electrical engineeting, signals are often recognized with a combination of peak-to-peak amplitude and RMS, which is basically analogous to your proposed standard of looking at both peak deviation and average deviation for an overall rating of the accuracy of the run. 4) Similarity to Average/Intuitiveness: An RMS of deviation is exactly the same as an average in the special case of a constant deviation (e.g. walking 10 meters to the left of the line the whole time) it mainly differs from an average by placing higher weight on bigger deviations. What this means though is you will still get a final number that is intuitively understandable in meters. You could say "my RMS deviation was 10 meters, which is just an average that weights bigger deviations higher" and I think most people unfamiliar with the concept would still understand.
That's not a culture anyone should want to be a part of to be honest. Tom is an honest guy and I can't even remember if he has even done any sponsorships on his videos besides the regular UA-cam ads. There's no reason why fame should be an access to a ton of random free stuff for the sole reason of marketing. There are so many people who need it much harder and I reckon Tom thinks the same way about it. Else you would have seen your fair share of skillshare/honey/raid shadow legends on this channel already. I think Tom wants to remain genuine, not some sellout influencer and to be fair, genuinity is kinda his trademark. Sure, he has tried persuading some people in his "How To Not Travel Europe" videos, but that was part of the challenge really.
Hey, I live in Portugal and I'm pretty sure it is possible to cross Portugal in a straight line, from east to west. If you want to try it, I will help you. I'm even thinking of doing it myself.
The lake anomaly might have to do with the fact that it's an artificial reservoir whose level changes over time. The software line and the GPS line might have both made different assumptions about the lake level and that placed you on a slightly different part of the geoid than expected.
Combine this with some kind of callibration the GPS performs to cancel out margin-of-error when it's restarted, and you might be onto something here...
This seems by far the most believable ipothesis I've read so far. It's definitely not due due earth curvature because the change is sudden and coincided with the battery change so it's definitely something related to the device
Do GPS devices (like the handheld GPS, obviously not something for usage in an aircraft) assume you're moving on the ground and then use this assumption in calculating your position? Or do they calculate your position in three spatial dimension, ignoring the ground completely?
@@v0ldy54 Totally agree. There could be problems with curvature, but they don't seem like the problem encountered here. And this makes a lot of sense. Especially if a limited number of satellites are in view, it seems plausible than an expected altitude vs actual altitude could make a difference.
The only problem with this theory is that Tom mentioned this problem occuring in Wales as well. If that's true, it couldn't have just been the artificial reservoir at fault. This could well be an altitude calculation problem though, that still makes sense.
I think it was smart to separate this into a dedicated video. I don't think these details make the mission any less successful, but I understand your desire to figure out exactly what went wrong. I wish you the best of luck with future missions and figuring out all of the crazy maps and GPS stuff! Always a joy to watch. As you said yourself, if anything, it's your amazing success that makes these minor discrepancies visible at all!
Very interesting thoughts on how to score it. I'm still interested in the definition of across a country especially in the extreme case of Norway, land of the fjords! 1.Border to 1st fjord (seawater). 2. Full country crossing: if continuing straight line over the sea reaches more mainland of the same country, that too must be crossed (if significant % X of land).
@@GrumpySalmon I love how they say "he could have chosen an easier route if he went to the Finnmark instead" and the guy from Visit Norway also seems quite happy about the publicity. At least, that's what I get from the article with my limited Norwegian skills. :)
Surprised you only used one GPS in case one broke or anything plus you can then cross reference the reading from the second one. Bloody impressive still, great series
I'm getting hyped for Scotland, and it's just before midge season too! Remember to get wrapped up though, February/March can be real cold up here with all the wind, rain & snow. I usually go skiing at that time of the year in Glencoe.
The software you are looking for is known as Excel ;-)) Also the two suggestions you have made are kind of the same. The surface method is just a higher resolution version of your first suggestion. Using the length of the line is bad idea, because a more accurate calculation will always result in a worse score. It's the same paradox of measuring the circumference of a country.
But you have a similar Problem when you use the "integral" of the line; everytime you calculate something with the entirety of the line it depends on it's resolution. You could get around that with setting a resolution to calculate, ie you connect every 1m mark with a straight line (or some curvature function, idk).
@@maxkr8285 integral does not cause the coastline paradox, interestingly (hence why it's the coastline that causes a problem not the area of the problem). This is a good video that touches on the topic (and finds there IS a similar paradox when it comes to surface area when you introduce topography, it's basically when the "number of dimensions" is off) ua-cam.com/video/PtKhbbcc1Rc/v-deo.html
Method 2 won't work. What happens if you walk perpendicular to the line for 100m and go back the same way ? The integral (area between the staight line and your path) would be zero although you were 100m away from the line. Method 1 is the best calculation imo.
@Mum Blinc I agree with you the two methods mentioned at the end are basicly the same, with the difference that one time you multiply the average distance with the length of the line. So I think for better comparison between different missions I would use the average distance. However I think the max deviation is also an important factor for "judging the success of a mission". So I would use these two variable to compare missions.
It might be decimal precision differences. Like on the PC you planned it used 5 decimal points so 14.43245 but the gps is only precise to 4 so it read as 14.4325
That would actually explain the line changing right during the mission, because the GPS suddenly starts rounding up the coordinates instead of down, or vice-versa. Makes a lot of sense to me
@@finnluis1409 I’m not to sure how it would explain the line being right in the first part of the journey then getting displaced when he changes the batteries at 8:30, then correcting itself at 20:55. You could probably get away with saying that the first displacement is caused by the batteries being changed but how does the pink line go back into the original line at 20:55 without anything occurring. Doesn’t add up to me 🤔🤔
@@platyguy maybe the was calculating the line at battery changing with the current location and the point where the lines meet again, which was looking like the middle between battery changing and the end. But that's a pretty wild theorie, some others probably make more sense Edit: was there a bend in the new line or why do they meet up again and then stay on top? Ok now I'm totally confused
All the answers I've seen are really good ones. You have some point on decimal precision, however I think it is a lesser factor and the rounding error is more likely to come in with some of the other calculations. Strictly, for these calculations you shouldn't be computationally using decimal, or floating point numbers ;) if the gps does that would be a factor certainly.
Thoroughly enjoyed your Norway expedition Tom. Feel I need to remind you of the most important bit though - you made it across! Like Bruce Lee said, It's like the finger pointing away at the moon. Concentrate on the finger for too long you miss all that heavenly glory ;-)
I might be a bit late, but this is what I came up with (i'll mail this to Tom as well). -Get the .gpx data (this gives your postions in ??°N ??°E ??? meters altitude) -Rotate/move all the .gpx points so that the start point is now on 0°N 0°E -Rotate all these points again so that the end point is on 0°E (so that all your deviations are now in the north-south direction) -Convert these degree-values (polar coordinates) into meters (cartesian coordinates) so you now have simple XY-data, where X tells you how far along the path you are and Y tells you how far away you are from the ideal path (fyi, the ideal path is an arc on the ball-shaped surface of the earth.) -At this point you could output this data to excel and work from there (or keep it in software, your choise) -You could calculate the best fitting straight line and use that as baseline to calcutate your deviation (you need to do another transformation on the data but no biggie) -Sort all positions according to the X-values from smallest to biggest -Take the X value of each coordinate, subtract the X-value of the next coordinate and multiply with the average Y-value of both coordinates (ie, calculate the surface area between the line and the x-axis) -Add all the calculated values up and you get the surface area between the best path and the one you took -Divide the area by the total length and you get a nice numerical score. This is all very doable in any programming language of choise. Also, the twitch-stream videos of Noah are already deleted so I dont know how he did it, but if the LIDAR data is publicly availible, you could automatically calculate all the gradients, say how steep they are and in what direction they are going (you need to go up? down? or is the gradient sideways and your just walking on a the same hight)
I'm more excited at the prospect of your Scotland mission and smaller missions than I am of any film, series or game announcement, and that's saying something.. Well done mate, you've created a new exciting concept and your videos are made and edited wonderfully.
In the field of statistics there is a way to measure how well data points fit on a line called the *mean squared error*. To calculate it: for each data point take the length of the line segment from the data point perpendicular to the golden line and square it. The average of these squared lengths will be your score. This has two advantages: 1. straying far from the line a few times will be penalized harder than having many small deviations (due to the squaring). 2. staying still, going backwards, experiencing bad signal reception or other small anomalies will not change the result significantly (due to the mean).
the 10-meter error is probably because the data is planed/imported/recorded in the wrong coordinate datum. like recorded in WGS 72 but imported as WGS 84 (or any other datums). Another theory that can result in a consistent error like this is that the GPS and the mapping software are configured with a different coordinate system that on the surface is interchangeable, but uses different reference ellipsoids (for localization purposes), like NAD83 and WGS84.
Hey there, I tried to keep everything the same coordinate system so all my data was generated in the UTM Zone that Norway uses for their geospatial data.
I'm in awe watching this, if that was the amount of error that you are aiming for then you are undoubtedly a perfectionist. The fact that you were able get that close to the line all the way is mind blowing to me
How about dividing the entire line into 100 equal sections. Each section is 1% of the total 100% points available. You pick the widest point in that section and that is your deciding factor. The widest point in a section under 20 meters is a point and anything over that number is 0 points. Platinum could be 95% or higher, gold is 90%, silver is 85% etc.
@@jakebrennan7685 I know nothing about what causes the deviation or how to fix it. This was just a suggestion on how to score the attempt without automatically losing the platinum from one instance of deviating too far from the line. I'm sure smarter people will come up with better solutions for the other stuff
@@RecBr0wn Might not have been clear. Your system allows for him to deviate massively for one of the sections and only penalised 1 percentage point. Maybe a deviation scale could be put in for set amounts but that's kinda just moving the problem. It's a good starting point though.
@@jakebrennan7685 you could integrate all the deveation over the total length of the line. then divide that over the line length. that way, you can compare different runs more easily. going off by 500m would then punish you harder
I think the easier thing would say platinum for staying within 15m with 1 exception per 20 miles or something, gold is within 25m with maybe just 1 exception overall, silver within 35 or 40m, with 1 exception overall. Bronze within 100m with 0 exceptions, go farther outside then 100m its not even bronze
I think the reason for the deviation from the yellow line is due to being close to the north pole. At the poles the earth's curvature has a more significant impact on we would consider straight lines across the globe and what could be considered the shortest route. If choose two waypoints on a map and draw a line between them, then use a compass to work out which direction would will go, this will give you a Rhumb line, which is the line of constant bearing from north. However your GPS has probably worked out the shortest route between those two points, which as we're on a globe will always bow slightly towards the nearest pole - Called a Great Circle. The most obvious example of this is if you look at the routes of long haul aircraft. For example if you look at a map (let's choose a Mercator projection) and draw a line between Seoul, South Korea and New York, USA, you'd assume the best route would be out over Japan, past Hawaii and then across the USA in almost an exact west to east direction. However this route turns out to be 15,800 miles, compared to the much shorter route of 12,700 miles if you travel almost directly north from Seoul and up over the north pole. At the end of the day, both of these routes are straight lines on a sphere, but depending on the map projection you use can appear to bend.
"length of the line" division measurements is bit of a "coastline paradox", the "wiggles" make it potentially infinate! You could do "length of the line" if you did a standard sample distance every 1m along the line etc, similar to the area of land.
In the coastline case the measured number gets bigger and bigger and in this case it would get closer and closer to an finite number. It is converging.
As far as I see, if you still committed to staying as close to a line as possible (without changing the line on purpose) then it’s just as good as the “actual” line. Loving your content! Keep up the great work!
I am going to ask my dad what he thinks about that problem. He is working for the bkg in germany (those are the people google buys their maps from). I am pretty sure he will find the solution, i will write an update tomorrow.
Reset GPS - new starting point and old finish point. Fully explains the video for me. Yellow one - calculated before walk, so predictions calculated are right. Pink - after reset, that is what he was looking onto during walk.
Do a calibration pattern/movement every time you restart the system, or at random distance intervals during the trek. It will make the line correlation post mission easier and accurate.
If you need a new measurement for your runs how about this: You look at the total distance of your line and just simply calculate the percentage of track outside of the 25 meter radius. If 99% of your track is within this limit you get platinum, 97.5% is gold 95% silver and 90% bronze.
Really great suggestions for the ranking system, funnily the area between the drawn and the actual line divided by the line length is roughly the same concept as calculating the average of the distances calculated after every meter. You can think of the area concept as calculating the distance infinitely many times (the same way Riemann integral calculation is taught), basically you would get the same result both ways.
Hi Tom! My name is Cam, from Ontario Canada. Made some friends from UK, playing video games. Found out we both watched your videos. Spent a long time watching your videos together on discord, what a blast. Absolutely love your content. LEGEND. * Shout out to Vagas :) *
@@Jeff321 Yes, I love it. Does also make you think how many times he has been 12 minutes into a recording and it WASNT recording!! lol, makes me laugh.
Technically you can't really cross any country in a straight line because of the Earth's curvature... :) But basically what I wanna say is - don't worry about it so much. You might not have followed THE line, but you followed A line and you did a great job. It's your own challenge with your own rules anyways. You did your best, you succeeded at least on 99% in my eyes (and I believe most of your subscribers think the same), and you had a great trip and a nice adventure. So, well done, you're still a winner! Keep doing what you're doing.
This was a wonderful series! Thank you very much. I'm sure someone has suggested this before - but Finland might actually be pretty doable due to the relative flatness of the landscape. The country is actually quite thin between the Russian border and Oulu on the western coast - around 200 km. There's one big lake to be crossed, but other than that I think you could draw a line with just a few smaller puddles remaining in the way. Anyways, cheers and thanks again for the content!
I think the best way to measure success would be to do a linear regression. Take all of the points (lat, long). The closer the r2 is to 1 the better. And would account for any error in the gps
This is what I’m thinking too. There are a couple of complications here. 1. The earth is not a plane. It more closely resembles a sphere. So we’d be fitting the points to an arc on a sphere, not a line on a plane. 2. Is that we don’t have a perfect arc on a sphere either, we have elevation to contend with. e.g imagine an arc A being the true line, which goes over a large hill. Next the path B goes around the large hill. You can calculate the distance from a point a on A and a point b on B using spherical geometry, but it will not take elevation into account. Spherical geometry will assume the sphere has constant radius. Therefore we need to use geographical data for our distance function in the regression.
Hey Tom, im a researcher in the states. I specialize in meteorology but I have a method we use to compute forecasting errors that might be applicable to your mission. Consider Root Mean Squared Error. If you look it up online its fairly self explanatory but I wanted to mention a few caveats. For your "actual location minus optimal location" it is just the distance from the line, perpendicular. You will of course need some weighting. We will weight each point based on midpoint distance between the 2 surrounding points... for example if you travel 10 meters before a point and 20 meters after a point, that point is weighted 15 meters. Look for the largest midpoint distance in your journey. Divide all your midpoint distances by that distance. This will have them all be a fraction between 0 and 1. Thus, large lines are weighted alot... small distances (like when still) are weighted a little. The metric is calculated for the whole journey since it is a summation in the numerator and denominator. The output is a single number that represents your mean error in meters. Using this you could set your platinum, gold, silver. Feel free to reach out if you care. Additionally, if you see this could you like so it gets to tom! Cheers, Colton
My review: You got a line on the GPS in the field and followed it. I would say that is a success, even if the line on the computer is in another place. As a selfish norwegian, I'd love to see an attempt #2 next year :)
I think after all this practice it’s about time you took on the equator. 😅 loving your videos. Really good to see some outside world during this pandemic. Keep up the great work you absolute legend!
Still feel of regardless of how you decide to evaluate your run, you can either find ways to game it, or find ways to feel worst about it. These videos were a lot of fun to watch. Thank you.
Great work! A possible explanation for the deviation in the GPS path and the yellow line may relate to different S2 projections between GIS systems (such as WGS84 vs. Mercator, etc., and the computer's maps vs. GPS device schemas)? Another possibility is that straight lines from an S2 projection translate to curved geodesics on S2 in the real world? This was likely handled in the planning GIS phase, but add in elevation, terrain, and location of the path on the Earth can compound to a systematic error (ie, point-to-point bowing) you've experienced. Google 'wgs84 straight line projection' to see some articles on the subject. If you make the raw data captures available for public download, someone with better GIS knowledge could be able to help further, idk, hope that all helps!
Yeah, this seems plausible to me. It is just a bit weird that the problems suddenly occurs when he restarts his GPS device. The only explanation I can come up with is that the device switched projection when he restarted it, this could be plausible since Garmin apparently has some specific projection options for Sweden, but only the global MGRS for Norway (support.garmin.com/en-US/?faq=lvWzTYlPsx6BvUDTyKfqC8). Maybe the device started out with one of the Swedish projections because of the proximity, but switched to one of the other. IDK total speculation though, really weird.
I think that line is a brilliant achievement, regardless of the vagaries from the gps. As far as measuring the straightness, I think your original approach of looking at maximum deviation is fine. I would just imagine the line more as a strip of tape on the map, rather than as a mathematical line with no thickness. Set a width for the line (maybe 5-10m) that you can freely move within without that counting as deviation. This should allow for the slight randomness of the gps and of yourself. Then, measure only deviation from that narrow zone, and set maximum deviation for platinum, gold etc, as you did. Also, look at getting sponsored by Garmin! They'd love this, it's fantastic!
I feel like there's always gonna be some sort of inaccuracy when measuring the line. I had this too with my mission and some of it is just inevitable (standing still, forests, gps doing weird things sometimes, etc).
Bottom line, you were still within ~40 meters? That's still insane. The physical achievement alone is laudable. It's definitely curious as to why there is this variation. But if I were you I'd take it as an academic issue rather than one of credibility or honesty. You put all your cards on the table; So long as you don't hide things people will understand just about anything and support you the whole way. Really amazing achievement mate. Outstanding work. Hope you find the cause of the issue and post a video about it. Good luck with your future endeavors.
I feel in a general sense that for any attempt when thinking about the line it's totally fine to just redraw it after the fact, and see the one you planned as a guide. So long as it's still a straight line I don't really see how you'd be able to game that and it would account for any weirdness like this
Dude your straight line videos are epic but I have to say none of them have been as good as the first! I loved the first one especially when you’re trying to stick to your plans doing 8-9 hours a day pushing on to your next camp spot! I didn’t enjoy the Norway one as much as there wasn’t as much epic content like camping and also bumping into people and running through dodgy places! Honestly though a credit to you especially all that rowing near the start! Please keep doing them!
A better score would be to calculate the Mean Squared Error between the target line and the travelled route. Another option is to calculate the Linear Regression of the travelled route and compare it to the target line (can't remember a good method for it right now).
But for that, like every other calculation method involving calculations with the line as a function, you'd have to use the line with a given resolution, because you can't calculate that with infinite points, what the line currently is. And with that I think there are better ways like just the integral. But none of those methods really are perfect, but I can't think of anything better
Yep, he could regress the actual line traveled on his hypothetically perfect line, calculate the R^2 and he has a measure of fit. Ofcourse to account for forrests and deviations when stood still, he would have to 'clean' the data from the GPS, but that shouldn't be that difficult.
both as he explained. Otherwise you can deviate once by a far bit, then keep close to the line. Depending on the length of the route that could mean you could briefly deviate miles from the line.
I have an idea to tackle the measurements regarding medal selection: Lets just divide the medals into two categories: Highest Deviation & Persistence Deviation. Essentially in case of highest deviation, you can work with the tools you already have established: 25m Platinum, 50m Gold, etc. In case of persistence deviation rewarding the idea of sticking as close to the line as possible and overcoming obstacles, you can compute the area under the straight line (like when you say you deviated by 10m at some place, just compute the area of that triangle of 10m vertex meaning for a small 10m deviation you'd be penalised low but for 10m deviation across long distance, area would be higher and hence high penalty). Its very easy to calculate these area using programming by feeding it logs files. In case of standing still or walking back (GPS inconsistencies) just add a rule in program to eliminate those coordinates and have manual inspection to ensure you only take GPS ones and not actual mistakes (trust and honesty). And now finally about GPS moving 2-5m zig zag when you are under tree-cover: Compute the area under straight-line from a 3-5m pathway meaning anytime you deviate more than 3-5m on any direction, the area of the deviation will be added to your deviated path. Medals of persistence deviation could be: 5% Deviated Area Platinum, 10% Gold, etc. Hence, even if you at one point deviated more than 25m and fell below Platinum category of Highest Deviation, you would still have the Platinum of Persistence Deviation to fight for! Now final medal can have categories like Pure Platinum (Platinum of HD AND Platinum of PD), Impure Platinum (Platinum of either HD or PD AND Gold of other), Pure Gold, Impure Gold, etc. --- Lastly on the yellow and pink line deviation - its the result of Great Circle and Thumb line projections (orthodrome and loxodrome) inconsistency where your map is working on one projection while GPS being on another - such that they take separate paths but have the same starting and ending point.
I think a better way to determine how close you were to the target line is to turn your line into a series of sampled points. Then find the best fit line for those series of points. Then determine the translation (in distance and angle) between this best fit line and your target line. Then give distance and angle a weight to determine if it was a platinum, gold, or silver run. A*x + B*phi = GWLM (GeoWizard Line Metric). Where A and B are the weights (0 to 1), x is the translation distance, and phi is the translation angle. Based on the GWLM, determine if it was a platinum, gold, or silver. Loved the series by the way. I don't think your GPS error makes it any less epic.
I´d like to say, that for my part... it is not an issue you deviated from the Yellow line. If you followed your own line from start to finish, it is still a straight line. Doesn´t matter if its not the one you calculated beforehand. Your explainations and motivations to make sure you have the ´perfect´ line, are really commendable though. Ofcourse if you can improve the whole GPS issue on your next adventure, i´d be great. But for this one, I´d say you did a really nice job! Love the content, it is really something special and I hope you keep it coming!. Greetings from a fan from the Netherlands ;) ps. A straight line through the Netherlands is always something i'd be looking forward to. Don't worry about steep hill/slope 1, it wont come. Might be a little bit overcrowded though!
27:50 lol you essentially stumbled across integral calculus here 😅 I feel that "how straight is this line" is something mathematicians can almost certainly help you answer.
I think he mentions in the Norway series an upcoming Scotland trip with Welsh Greg. I think it was why he had such a short window for the Norway trip because he had to squeeze it in before that trip
![Introducing the "No Roads Mission" ..a very urban adventure [PART 1]](http://i.ytimg.com/vi/pDU9BOtX80A/mqdefault.jpg)
Just want to say thanks to everyone who has chipped in with their thoughts and explanations regarding the discrepancies with the line. It’s all a learning curve (😉) and I’m certain that by the time I’ve fully digested all of your comments and emails Ill be fully equipped for any such issues come the next mission. Thanks everyone! You truly are the best fans in all of UA-cam.
👍
Nice pun
There are a number of statistical measures of deviation and fit, so those are probably your best bet. For example, you could take the co-ordinates from the line you traveled and calculate the *standard deviation* from your 'perfect' line. Or you could do a *basic linear regression* of the y-coordinates from the traveled line on the x-coordinates from the traveled line, which will calculate the straight line of best fit for your travelled path. Then calculate the *R-squared* from this regression for a measure of fit. Both these methods can be done in various free softwares or programming languages e.g. R, which is free, just need to download R (the language) and R Studio. You might need to 'clean' your data from the GPS to take into account forests or deviations when standing still, but that isn't that difficult. It just depends how the data are collected.
Dropping some quick thoughts on this:
1. I feel like the spirit of the challenge is to move a far distance in as close to a straight line as possible, and the scoring should entirely be based on how straight your gps tracked line is, not at all connected to any planned line.
2. Having said that, now comes the scoring issue. Whether the top suggestion is followed wont matter much for my take on scoring, as it combines 2 sections.
A well made computer program will easily be able to calculate an average deviation.(might have to be custom made though)
This may be one good measure for scoring but will suffer an issue with single high devations barely impacting the average at all.
Solution: Multiply average deviation with max deviation for a total score where both avoiding single time large deviations(cliffs n stuff) and sticking close to the line while strolling will impact the line.
Here you can also introduce some multiplying constant to adjust balance, ending up with something like:
AvgDev*(MaxDev*X) where 0
Can we get an update on that GPS issue once you've figured it out? Curious to know what happened.
Geowizard About to die in a Bog: Calm, collected
Geowizard noticing the line was off: Panik
Its a matter of priorities
Professionals have standards
Stonks
Watching him in that bog gave ME a panic attack.
@@BibleStorm i couldn't watch it, i knew he came out of it (i mean, i saw the video, so he atleast posted it) but is couldn't watch.
Cop: You didn't walk on a straight line. Have you been drinking? Tom: Let me explain [pulls his GPS out]. See the yellow line?
*pink
@@thijssmudde cry
@@thijssmudde no because the yellow line is the one he would have seen on his gps
It probably has to do with the curvature of the Earth, as you are relatively close to the north pole. Your line actually goes completely straight in spherical geometry, and the yellow line only works on flat map projection. In this case, at both ends the two lines should get closer and meet at the end (i think you mentioned it in the video). If that is true, it should not be hard to calculate the pink line you followed.
So you probably followed the truly straight line, and the other one was curved in terms of not being shortest distance connecting both ends on sphere.
I think this combined with changes in altitude above sea level is the culprit.
I thought it might be that as well. Although some of the distances seem like they might be too far for that kind of error. It would be interesting to plot the curved line in GIS to see how well it matches with Tom's actual walked line.
@@kolklown I wonder if altitude could also cause some consistent offsset, GPS system should have this covered with triangulation. Maybe there is also some factor of closeness to the pole?
@@kolklown how would the altitude affect it?
You are probably familiar with this effect in flight paths. Planes usually go into higher lattitudes rather than seemingly "straight" line on the map.
I think it’s important to remember that the series is called “Crossing Norway in A Straight Line”
Not crossing Norway in THE straight line. No one much cares which line you use or send up following, we just care how close you were to any straight line.
Thats good but the problem is that he was following one specific line. That the line we should judge him by. He shouldn't be able to draw a perfect line after the fact. Imo
Disagree. He was following what his GPS told him, no one out in the field could know it was off from the original line. He didn’t draw a line to fit his final path, he drew one to more accurately represent the line his GPS directed him to follow. That is what the measuring stick should be.
@@Xeroc_ well he literally followed the specific line. video evidence. not his fault there was a tech problem.
Yes. But finding the perfect fit line afterwards is cheating a bit. Then you'd deviate left of it, and then right, during the missions, cause you know that'll help the best fit line. As long as he can prove it with GPS data it seems fair, but finding best fit lines in hind sight feels unfair to me
@@thelazymanatee2506 I don't see why the planning phase should affect how your actual physical line is judged. The challenge is to cross border to border in as straight a line as possible, not to walk along a straight line you planned, that's just a good tactic for succeeding in the challenge.
I'm a site positioning and gps technician in the U.S. and I feel I can shed some light on the line problem. You said to contact you by email but I couldn't find one so I thought I would add to what I've already seen some comments about. Whenever drawing a flat line on a map and then putting it on a 3d sphere like the earth the line will not stay completely straight. Your gps Is a map wrapped around a sphere and the map you are using in the video is flat so they will never be accurate to eachother. This is compounded when you add elevation changes and when you get closer to the poles (tightening the curve) this problem can be solved but in your case with all the massive elevation changes making a true straight line along a sphere is technically impossible. If anyone has his email or if you want to get in contact with me I can explain much more in depth than I can in a youtube comment. Hope that helps, keep up the awesome videos man.
His email is: tomdavies2286@gmail.com
You can find it in the about section on his youtube channel.
What he really wants is a line/route that fits within a perpendicular plane and to calculate deviations by normals to that chosen plane which makes sense conceptually but I doubt the technology he is using is optimized towards that regard.
Straight line mission across Ecuador it is then. 😄
Well also a consumer grade GPS is also not 100% accurate either without correction signals like spotbeam, inmarsat and IALA. So that might also have been some of the problems.
Yeah in future I think he just simply needs to video his GPS more for evidence when editing.
Just dropping a comment to say - keep being a legend Tom.
how do you feel about Checo taking your seat
GeoWizzard viewers here
Hello viewee
Fancy seeing super GT here!
How random haha.
Maybe this is how I discovered Tom.....
Love a bit of R4M
I love how serious you take this and how you are effectively apologizing for 'misleading' us, even though you make the rules and it's not like you're cheating or anything
Such a genuine guy love these videos
I mean, if you make rules and they don’t mean anything, they aren’t really rules then. It’s just a dude taking a very long walk.
@@leeartlee915 It is a dude taking a very long walk. What else is it supposed to be, an Olympic event? Who the hell cares.
@@Peksisarvinen Then why are you watching?
Technically it doesn't matter if you followed the original line that you set, just that you walked ANY straight line across a country
Sadly it does matter if you started the route on one line and switched to another part way through
@@alfiewright1396 well if you switch lines then that isn't a line. It doesn't matter if it's the preset line or simply a line
@@alfiewright1396 I don't believe that is what happened. I think the lines just drift apart because of earth's curvature and where it became apparent for him, he just happened to be switching out batteries and so it looked like a jump.
@@dmcdcm Maybe the jump happened on the battery change because the GPS receiver had calibrated itself somewhat in the run-up to the change, and reset once the batteries had been replaced - might also explain why the lines reconverged again towards the end.
this is what i was thinking! if he draws a regression line of his actual trek, what would the largest deviation be?
You were on norwegian national news yesterday if you didn't know!
Is there a media center of the news station that reported it that is accessible outside of Norway? I've been learning Norwegian for two years, so I SHOULD be able to at least understand some of it...
NRK has at least some of their programm accessible, right?
@@wohlhabendermanager Most of NRK's content is only accessible in Norway I think, but with a VPN you should be able to access all of it.
Californication
Hææ? Seriøst, hvordan glapp jeg det?
Someone should upload that to UA-cam
I don't think the line being incorrect should put a dampner on this run at all. Absolutley incredible what you've done.
Still within gold run standards, so it's definitely not a failure!
@@3seven5seven1nine9 ua-cam.com/video/s40FOtkCPFw/v-deo.html
GeoWizard: *Crosses an entire country in a straight line not even deviating 100 ft from the path*
Also GeoWizard: "The harsh judges of you will say..."
He is still 50km from the coast though, so not really an entire contry. There is more land on the other side of the fjord if he wanted to continue the line.
@@abedidabediali9768 The fjord is part of the coastline. It doesn't matter if there is more land on the other side.
I just watched a man talk about how straight a line is for 30 minutes and I could not be happier, love how you're so passionate about sticking to the line exactly. Can't wait for the next one.
Also GeoguessR released a Battle Royale mode, yep 2020 is a wild year. Quite fun though, looking forward to that video.
I’m loving the battle royale
Scuse me?
Ik it’s fascinating
You have 344 million views on a video. 😩
How much money have you made from your videos? I’m interested if you’ve made it in life
Cross NZ in a straight line- very doable on the North Island, incredible scenery
How is he meant to get here when we are only letting NZ citizens in?
@@Minotaur-cd9ch doesn’t have to be right now- just sometime in the future!
Would just cutting across Auckland count?
that'd be one expensive youtube video to film, this is his job so i don't know if he could justify 2 or 4 plane tickets (depening in if its solo) accross the globe
@@fisheatsyourhead He says he loves travel and he's travelled all around the world, so the straight line mission wouldn't have to be the whole trip- most of it could be a normal vacation
You'll always be platinum in our hearts!
Considering this heavy GPS topic, I'd really wanna hear it from Garmin themselves. Maybe they have a special solution for future missions, they are the specialists afterall. Who knows, might even get random sponsorship :D
Well done tho!
This
yeah he's earned that sponsorship
It's nearly impossible to get accurate. Altitude, rate of change the curve of the earth all affects the line that is ultimately mapped. The original one doesn't show the curvature of the earth, the distance from the poles etc.
Get a us military one. They dont realy get more accurate
Not to sound like a know it all....but the earth isn't flat... This sounds obvious after you hear it but think about it for a second.
Matching up a line on a flat map to the sphere of earth isn't going to be easy.
I'm pretty sure that's why your two lines don't match up in the middle but do at the ends.
It's off because you put a straight line on a flat map. Since the world is round, the actual path is going to bend slightly. It's more pronounced the closer to the poles you get, since flat maps get distorted more at the poles.
That was my first thought aswel during the intro, but it doesn't explain the sudden several meter jump after rebooting at 8:30. He also stated it happened in random points on the Wales route, instead of a steady progression with the peak being in the middle - the offset doesn't seem to progress smoothly along the route like it should if it's due to curvature.
I'm clueless, but I'm reasonably sure its an issue with the gps device, or gps technology in general, with earth's curvature being a negligible deviation from the line considering the fairly short route length.
The error was probably also not made during planning (using different maps, one being curved while the other is flat etc), as that wouldn't explain the sudden jumps and the camera footage of the gps tracker, it would be a consistant deviation throughout (which may well also be in the mix, but doesn't seem to be the main issue).
You have a point but localized projections exist. It depends on what he used.
Maybe Google Earth. You're approaching the limitations of several datasets doing things like this. If it were 15 years ago I'd say SA lol
Check mate flat earthers
@@Die__Ene Could it be his altitude-offset is wrong, or barometric pressure sensor (if it has that) is blocked by dirt.
Imagine most of the sattelites he receives are in the south it is like the line from the sattelite to "him" passes through a line about a couple meters above the programmed line and thus he is north of the line.
He should do a trip in a straight line from south to north and see if he has the same problem.
im norwegian and yesterday i came over a newsarticle about you and your mission across Norway, from NRK. it really surprised me, but it was awesome to see them promoting you!
From Wikipedia: NRK (an abbreviation of the Norwegian: Norsk rikskringkasting AS, generally expressed in English as the Norwegian Broadcasting Corporation) is the Norwegian government-owned radio and television public broadcasting company, and the largest media organisation in Norway.
This is for me, no matter what you think, a platinum run for sure.
It’s objectively not though. It’s soo damn close but it’s not
@@astronemir think again!!!!
@@thesearchforproof518 next he's gonna reveal that the kicks he made actually counted as goals using some obscure football rules
@@eonnephilim852 lol
He collected all the trophies so I can see why he was awarded the platinum trophy
We had been going over 10 minutes before we got an "are we recording?" and I was getting worried for a second there. Glad we got one in there eventually though.
Thanks Tom! Hey guys, the link to the process I went through to help Tom is in the description. Its a twitch VOD where I answered a lot of questions from the chat as well :)
Great work
Awesome work man 👌
27:43 Wow, Tom accidentally rediscovers calculus!
Yeah, i was internally screaming ,,try to take the integral of the line (and divide it by the length of the entirely straight line, which he was aiming for)''.
Don't continue if you don't like calculus.
With doing that he could also vary the importance of maximum deviation through applying some sort of function( for example x^2) on the line function. So I would, if technically possibly, calculate the score as follows: score=(1/L)*∫(0 to L) dev(x)^2 dx where x is the distance from the start and dev(x) the deviation at that point x. Maybe ^2 is a bit too much, so maybe ^1.5. But you could experiment with that.
If he can't calculate the deviation at every point, he could approximate the integral with a sum. The formula would change to score=(1/L)*∑(1 to n) dev(x)^2 dx where dx=L/n and where n is the number of points at which you would calculate/meassure the deviation. The distance(dx) between the meassuring points should definetly be set in advance(maybe 1m/5m/10m), it could approach 0 if a computer can do this, which would make it really accurate(comparing it to the real area). Then dev(x) gets calculated at every x=dx*k k=1,2,3,...,n until x=L(which is true when k=n).
I probably annoyed you, if you read that. I just love applying maths to things like that :D
@@Ma7iT you are the best! That's exactly what I thought! I also love to apply math to any problem. :)
@@Ma7iT Yeah thats pretty good, I suppose for cases where there are two outputs (like when he is standing still and the signal is bouncing) you would just sample the further point. Also, we'd need to take abs(dev(x)) but if your squaring than it already takes care of that. One thing that we want out of this scale that Tom pointed out is he really wants a hefty penalty for going off course, and you could also just achieve by having your "weight" function that takes in dev(x) be a piecewise that after a certain threshold is when things get really bad. This would be sort of nice to keep it where there is still the concept of a band you want to stay in. Personally, i'd like to see maybe a 15m "safe zone" where there is no penalty, just to try and give some attempt to not penalize for random GPS jumps.
The delta x in the actual sum needs to be pretty darn small, because if it said 5m then it would allow for you to do deviate arbitrarily far in the y aka dev(x) direction, and as long as you got back to line before moving 5m in the x-direction than your big deviation would go undetected.
@@Ma7iT Well done. I wish I was born that smart so I can apply maths to things like you. Sometimes, I even fail at calculating my own age.
That has actually happened in an academic paper btw, some statistician rediscovered calculus in a medical journal or something.
2020 - Geowizard invents calculus
I was about to say, dude is describing integrals the same way a high school maths teacher does,
Yeah I was trying to think back to A-level maths 30 odd years ago - calculating the area under the graph line before Tom mentioned it. This seems like the obvious standard, maybe with deviation from the mean factored in.
For an integral he would need a function that describes the line, god help him.
Possibly the better way of calculating score for the run would be taking some quickly growing function, like exponent, and then integrating. That way every further meter from the line is weighted higher, so big deviation is punished, even if happened over a short distance.
@@vainbow4632 His solution of taking the distance from the line every meter and adding it up is *essentially* just numerical integration. You don't need a function representation of the curve to get a good estimate.
I think I've seen it suggested a couple of times, but the root mean square error would be a nice scoring metric. I basically entails squaring the deviation for the line at ever measurement point (for example every GPS update), taking the average of all the squared values and taking the route of that average. This still indicates the average deviation from the line, but squaring the errors and taking the root of the average has the beneficial effect of punishing large deviations with respect to small ones. That way you encompass both average deviation and punish large deviations in the same scoring metric. I definitely don't recommend doing this by hand, but a simple Python script or even an excel sheet could do the job, I think.
funny it is now what he uses
Boffin here, I would recommend using root mean square (RMS) of deviation measurements to get the best aggregate measure of success sticking to the line. RMS solves a couple problems you mentioned with the proposed rating systems, and is a good aggregate error method used in my field of electrical engineering and a lot of other fields of statistical analysis and the like. I'd be happy to explain further if you're interested in the technical details, and it wouldn't be that much harder to implement than a simple average of deviation lengths. I will outline some benefits below.
1) Disproportionate weight of larger deviations: Just taking an average of deviation from the line at any meter will, like you said, comparatively downplay the influence of more dramatic deviations over a shorter length. RMS uses the square of error values, so a 20 meter deviation actually has 16 times the weight per distance travelled than a 5 meter deviation. You may still want to set some hard limits on distance deviated, but this method has that built in to some extent.
2) Signed Cancelation: Taking a simple average of deviations could cancel out errors in either direction if you don't use the absolute value. RMS can take data in either direction and it contributes equally to the aggregate error calculation because the square of a positive or negative number is positive.
3) Recognized convention: RMS is a well-understood way to analyze problems like this, and when statisticians try to draw a line to interpolate data points, they do so to minimize RMS deviation (called residuals in that field), which seems similar to what you are trying to accomplish, and may lend your measurement standard more credibility and understandability. In electrical engineeting, signals are often recognized with a combination of peak-to-peak amplitude and RMS, which is basically analogous to your proposed standard of looking at both peak deviation and average deviation for an overall rating of the accuracy of the run.
4) Similarity to Average/Intuitiveness: An RMS of deviation is exactly the same as an average in the special case of a constant deviation (e.g. walking 10 meters to the left of the line the whole time) it mainly differs from an average by placing higher weight on bigger deviations. What this means though is you will still get a final number that is intuitively understandable in meters. You could say "my RMS deviation was 10 meters, which is just an average that weights bigger deviations higher" and I think most people unfamiliar with the concept would still understand.
Big agree
You're the most famous person in the world to have said the name "Garmin" more than 10 times. Pretty sure they owe you a freebie at this stage.
He probably shouldn't have mentioned the weirdness in the line then.
I doubt that
That's not a culture anyone should want to be a part of to be honest. Tom is an honest guy and I can't even remember if he has even done any sponsorships on his videos besides the regular UA-cam ads. There's no reason why fame should be an access to a ton of random free stuff for the sole reason of marketing. There are so many people who need it much harder and I reckon Tom thinks the same way about it. Else you would have seen your fair share of skillshare/honey/raid shadow legends on this channel already. I think Tom wants to remain genuine, not some sellout influencer and to be fair, genuinity is kinda his trademark.
Sure, he has tried persuading some people in his "How To Not Travel Europe" videos, but that was part of the challenge really.
Hey, I live in Portugal and I'm pretty sure it is possible to cross Portugal in a straight line, from east to west. If you want to try it, I will help you. I'm even thinking of doing it myself.
Where do you even get a gps machine that you can stick a line on?
ua-cam.com/video/jxxFAfQhJic/v-deo.html
Just below Lisboa/Setubal? Looks doable, but still there is a hundred kilometres. May you pass through gardens in Portugal freely?
@@EWEasternWind by just looking at a map it looks easier in the south because there are less villages
@@jakobusvfb117 There are much more hills in the south
Nah, I’m a firm believer of the pink line.
Clearly a platinum run!
The lake anomaly might have to do with the fact that it's an artificial reservoir whose level changes over time. The software line and the GPS line might have both made different assumptions about the lake level and that placed you on a slightly different part of the geoid than expected.
Combine this with some kind of callibration the GPS performs to cancel out margin-of-error when it's restarted, and you might be onto something here...
This seems by far the most believable ipothesis I've read so far.
It's definitely not due due earth curvature because the change is sudden and coincided with the battery change so it's definitely something related to the device
Do GPS devices (like the handheld GPS, obviously not something for usage in an aircraft) assume you're moving on the ground and then use this assumption in calculating your position? Or do they calculate your position in three spatial dimension, ignoring the ground completely?
@@v0ldy54 Totally agree. There could be problems with curvature, but they don't seem like the problem encountered here. And this makes a lot of sense. Especially if a limited number of satellites are in view, it seems plausible than an expected altitude vs actual altitude could make a difference.
The only problem with this theory is that Tom mentioned this problem occuring in Wales as well. If that's true, it couldn't have just been the artificial reservoir at fault. This could well be an altitude calculation problem though, that still makes sense.
I think it was smart to separate this into a dedicated video. I don't think these details make the mission any less successful, but I understand your desire to figure out exactly what went wrong. I wish you the best of luck with future missions and figuring out all of the crazy maps and GPS stuff! Always a joy to watch.
As you said yourself, if anything, it's your amazing success that makes these minor discrepancies visible at all!
Crossing Switzerland would be nice
But impossible
@@4ever_mo956 i mean... there are parts of switzerland where its actually only a couple hundred meters wide max
He'd need to do it live so we know what happened before he either fell off a cliff or froze to death.
Better idea...
*ANTARCTICA IN A STRAIGHT LINE*
@@asdf-y2c yeah but whats the Point of that 😂
Very interesting thoughts on how to score it.
I'm still interested in the definition of across a country especially in the extreme case of Norway, land of the fjords!
1.Border to 1st fjord (seawater).
2. Full country crossing: if continuing straight line over the sea reaches more mainland of the same country, that too must be crossed (if significant % X of land).
-Straight Line across Monaco
-Straight Line across DPRK
-Straight Line across Sealand
All three of these NEED to be done
Get on it bro
Wouldn't monaco be nearly impossible lol
On one day.
@@ryanschabert2515 yeah lol as it is so built up unless you do a mission on the water surrounding it
@@jamesfletcher1689 I was gonna say lmao you'd have to be climbing buildings and shit which is just illegal
On the front page of NRK.no (Norway's BBC) today! Not bad!
Ya got the name of the article? Only getting the ones for today (obviously)
Nevermind, I found it! 👌
www.nrk.no/nordland/youtuber-tom-geowizard-davies-ville-krysse-norge-i-en-rett-linje-i-rana_-var-ikke-godt-nok-forberedt-1.15293567
@@GrumpySalmon I love how they say "he could have chosen an easier route if he went to the Finnmark instead" and the guy from Visit Norway also seems quite happy about the publicity. At least, that's what I get from the article with my limited Norwegian skills. :)
Surprised you only used one GPS in case one broke or anything plus you can then cross reference the reading from the second one. Bloody impressive still, great series
That GPS is worth around £400 if I am not mistaken... He fund raised for the gear.
Why would you want to carry another GPS when you could use those grams to carry a couple packets of Jelly Babies
@@bricksburger5409 or rancid beef jerky...
Telephone gps as back-up
Thought the same, I take two phones anytime I'm making wild rides or runs for redundancy. GPS or software error happends rarely but it happends.
I'm getting hyped for Scotland, and it's just before midge season too! Remember to get wrapped up though, February/March can be real cold up here with all the wind, rain & snow. I usually go skiing at that time of the year in Glencoe.
This series is one of the most enjoyable I've watched
I have a cabin on that mountain you walked past, there are two or three hundred cabins there. That lake is regulated and it's still quite low.
The software you are looking for is known as Excel ;-))
Also the two suggestions you have made are kind of the same. The surface method is just a higher resolution version of your first suggestion.
Using the length of the line is bad idea, because a more accurate calculation will always result in a worse score. It's the same paradox of measuring the circumference of a country.
But you have a similar Problem when you use the "integral" of the line; everytime you calculate something with the entirety of the line it depends on it's resolution. You could get around that with setting a resolution to calculate, ie you connect every 1m mark with a straight line (or some curvature function, idk).
@@maxkr8285 integral does not cause the coastline paradox, interestingly (hence why it's the coastline that causes a problem not the area of the problem). This is a good video that touches on the topic (and finds there IS a similar paradox when it comes to surface area when you introduce topography, it's basically when the "number of dimensions" is off)
ua-cam.com/video/PtKhbbcc1Rc/v-deo.html
Exactly and I think 'method 2' is a bit overkill not really worth having a higher resolution than the accuracy of the GPS
Method 2 won't work. What happens if you walk perpendicular to the line for 100m and go back the same way ? The integral (area between the staight line and your path) would be zero although you were 100m away from the line. Method 1 is the best calculation imo.
@Mum Blinc I agree with you the two methods mentioned at the end are basicly the same, with the difference that one time you multiply the average distance with the length of the line. So I think for better comparison between different missions I would use the average distance.
However I think the max deviation is also an important factor for "judging the success of a mission".
So I would use these two variable to compare missions.
Came from NRK. You made the news!
You should make sure you're measuring your deviations at a perfect 90° angle, if you do that your 26 might actually be a 25
Damn, I had to like the comment so Tom might see it, but there were 90 likes before I pressed the button.
These type of content creators is what UA-cam was made for
It might be decimal precision differences. Like on the PC you planned it used 5 decimal points so 14.43245 but the gps is only precise to 4 so it read as 14.4325
That would actually explain the line changing right during the mission, because the GPS suddenly starts rounding up the coordinates instead of down, or vice-versa. Makes a lot of sense to me
@@finnluis1409 I’m not to sure how it would explain the line being right in the first part of the journey then getting displaced when he changes the batteries at 8:30, then correcting itself at 20:55. You could probably get away with saying that the first displacement is caused by the batteries being changed but how does the pink line go back into the original line at 20:55 without anything occurring. Doesn’t add up to me 🤔🤔
@@platyguy maybe the was calculating the line at battery changing with the current location and the point where the lines meet again, which was looking like the middle between battery changing and the end. But that's a pretty wild theorie, some others probably make more sense
Edit: was there a bend in the new line or why do they meet up again and then stay on top? Ok now I'm totally confused
All the answers I've seen are really good ones. You have some point on decimal precision, however I think it is a lesser factor and the rounding error is more likely to come in with some of the other calculations. Strictly, for these calculations you shouldn't be computationally using decimal, or floating point numbers ;) if the gps does that would be a factor certainly.
ua-cam.com/video/s40FOtkCPFw/v-deo.html
Thoroughly enjoyed your Norway expedition Tom. Feel I need to remind you of the most important bit though - you made it across! Like Bruce Lee said, It's like the finger pointing away at the moon. Concentrate on the finger for too long you miss all that heavenly glory ;-)
Just the fact that you did this trip is unbelievable
GARMIN should sponsor you with the most high-tech equipment they have!
"I've only got myself to blame, partly". Story of my life right there.
I might be a bit late, but this is what I came up with (i'll mail this to Tom as well).
-Get the .gpx data (this gives your postions in ??°N ??°E ??? meters altitude)
-Rotate/move all the .gpx points so that the start point is now on 0°N 0°E
-Rotate all these points again so that the end point is on 0°E (so that all your deviations are now in the north-south direction)
-Convert these degree-values (polar coordinates) into meters (cartesian coordinates) so you now have simple XY-data, where X tells you how far along the path you are and Y tells you how far away you are from the ideal path (fyi, the ideal path is an arc on the ball-shaped surface of the earth.)
-At this point you could output this data to excel and work from there (or keep it in software, your choise)
-You could calculate the best fitting straight line and use that as baseline to calcutate your deviation (you need to do another transformation on the data but no biggie)
-Sort all positions according to the X-values from smallest to biggest
-Take the X value of each coordinate, subtract the X-value of the next coordinate and multiply with the average Y-value of both coordinates (ie, calculate the surface area between the line and the x-axis)
-Add all the calculated values up and you get the surface area between the best path and the one you took
-Divide the area by the total length and you get a nice numerical score.
This is all very doable in any programming language of choise.
Also, the twitch-stream videos of Noah are already deleted so I dont know how he did it, but if the LIDAR data is publicly availible, you could automatically calculate all the gradients, say how steep they are and in what direction they are going (you need to go up? down? or is the gradient sideways and your just walking on a the same hight)
So basically an average from the best fitting line?
This is exactly the kind of math problem my math prof at university was dreaming of
That moment in the bog was reeeeally scary. Terrifying actually.
I'm so glad you're okay.
I look forward to next week's episode where Tom and Numberfile team up to teach us about computational integration...
Want to say that as well as the fact that the mission was very impressive, complements to the quality editing and voiceover for the videos
I'm more excited at the prospect of your Scotland mission and smaller missions than I am of any film, series or game announcement, and that's saying something.. Well done mate, you've created a new exciting concept and your videos are made and edited wonderfully.
Your channel is gonna be huge by the end of 2021, fair play and good luck. 👍
Tom - I just found your channel and I'm loving the videos! Keep up the great work, I'm looking forward to more adventures!
You should watch “How not to travel Europe”. It was one of the best series I have ever watched.
@@travismakoto agreed
@@travismakoto Binged that already! :)
In the field of statistics there is a way to measure how well data points fit on a line called the *mean squared error*. To calculate it: for each data point take the length of the line segment from the data point perpendicular to the golden line and square it. The average of these squared lengths will be your score. This has two advantages: 1. straying far from the line a few times will be penalized harder than having many small deviations (due to the squaring). 2. staying still, going backwards, experiencing bad signal reception or other small anomalies will not change the result significantly (due to the mean).
the 10-meter error is probably because the data is planed/imported/recorded in the wrong coordinate datum. like recorded in WGS 72 but imported as WGS 84 (or any other datums). Another theory that can result in a consistent error like this is that the GPS and the mapping software are configured with a different coordinate system that on the surface is interchangeable, but uses different reference ellipsoids (for localization purposes), like NAD83 and WGS84.
Hey there, I tried to keep everything the same coordinate system so all my data was generated in the UTM Zone that Norway uses for their geospatial data.
Possible, but it doesn't explain why the error only seemed to appear when he rebooted the GPS device.
Maybe it started in a Swedish coordinate system, then when rebooted it changed to a Norwegian coordinate system?
I'm in awe watching this, if that was the amount of error that you are aiming for then you are undoubtedly a perfectionist. The fact that you were able get that close to the line all the way is mind blowing to me
How about dividing the entire line into 100 equal sections. Each section is 1% of the total 100% points available. You pick the widest point in that section and that is your deciding factor. The widest point in a section under 20 meters is a point and anything over that number is 0 points. Platinum could be 95% or higher, gold is 90%, silver is 85% etc.
Doesn't solve the problem of deviating any distance. It's a good idea but you could potentially deviate 500m off and only lose one percentage point.
@@jakebrennan7685 I know nothing about what causes the deviation or how to fix it. This was just a suggestion on how to score the attempt without automatically losing the platinum from one instance of deviating too far from the line. I'm sure smarter people will come up with better solutions for the other stuff
@@RecBr0wn Might not have been clear. Your system allows for him to deviate massively for one of the sections and only penalised 1 percentage point. Maybe a deviation scale could be put in for set amounts but that's kinda just moving the problem. It's a good starting point though.
@@jakebrennan7685 you could integrate all the deveation over the total length of the line. then divide that over the line length. that way, you can compare different runs more easily. going off by 500m would then punish you harder
I think the easier thing would say platinum for staying within 15m with 1 exception per 20 miles or something, gold is within 25m with maybe just 1 exception overall, silver within 35 or 40m, with 1 exception overall. Bronze within 100m with 0 exceptions, go farther outside then 100m its not even bronze
I think the reason for the deviation from the yellow line is due to being close to the north pole. At the poles the earth's curvature has a more significant impact on we would consider straight lines across the globe and what could be considered the shortest route. If choose two waypoints on a map and draw a line between them, then use a compass to work out which direction would will go, this will give you a Rhumb line, which is the line of constant bearing from north. However your GPS has probably worked out the shortest route between those two points, which as we're on a globe will always bow slightly towards the nearest pole - Called a Great Circle.
The most obvious example of this is if you look at the routes of long haul aircraft. For example if you look at a map (let's choose a Mercator projection) and draw a line between Seoul, South Korea and New York, USA, you'd assume the best route would be out over Japan, past Hawaii and then across the USA in almost an exact west to east direction. However this route turns out to be 15,800 miles, compared to the much shorter route of 12,700 miles if you travel almost directly north from Seoul and up over the north pole.
At the end of the day, both of these routes are straight lines on a sphere, but depending on the map projection you use can appear to bend.
"length of the line" division measurements is bit of a "coastline paradox", the "wiggles" make it potentially infinate! You could do "length of the line" if you did a standard sample distance every 1m along the line etc, similar to the area of land.
In the coastline case the measured number gets bigger and bigger and in this case it would get closer and closer to an finite number. It is converging.
@@flachlappen why is it converging?
You still stuck to your line mate, well done. Even thought it may not have been the original plan, you still did it!
Me, 30 seconds in: "it's cos the earth ain't flat mate innit"
As far as I see, if you still committed to staying as close to a line as possible (without changing the line on purpose) then it’s just as good as the “actual” line.
Loving your content!
Keep up the great work!
I am going to ask my dad what he thinks about that problem. He is working for the bkg in germany (those are the people google buys their maps from). I am pretty sure he will find the solution, i will write an update tomorrow.
Keep us posted!
Im investing here
I'm curious about what he'll say
interested to hear what he says!!
following!
Reset GPS - new starting point and old finish point. Fully explains the video for me. Yellow one - calculated before walk, so predictions calculated are right. Pink - after reset, that is what he was looking onto during walk.
Do a calibration pattern/movement every time you restart the system, or at random distance intervals during the trek. It will make the line correlation post mission easier and accurate.
If you need a new measurement for your runs how about this:
You look at the total distance of your line and just simply calculate the percentage of track outside of the 25 meter radius. If 99% of your track is within this limit you get platinum, 97.5% is gold 95% silver and 90% bronze.
the problem with this is going around an obstacle by 25m to 50m my reward you more than zig zagging 10m to 15m away from the line as it is longer
That would be extremely easy
This is a good way if none of the more complicated standard deviation or calculus-based methods are possible
Mate u got a platinum! The pink line is the true line!
We are all proud of your legendary achievement. We knew you would make it. Never give up, never surrender!
Get a life, bro
Can confirm, in the closing minutes Tom has reinvented the Trapezium Rule. Nice!
Really great suggestions for the ranking system, funnily the area between the drawn and the actual line divided by the line length is roughly the same concept as calculating the average of the distances calculated after every meter. You can think of the area concept as calculating the distance infinitely many times (the same way Riemann integral calculation is taught), basically you would get the same result both ways.
Was thinking the same thing, he stumbled onto calculus there
Hi Tom!
My name is Cam, from Ontario Canada.
Made some friends from UK, playing video games.
Found out we both watched your videos.
Spent a long time watching your videos together on discord, what a blast.
Absolutely love your content.
LEGEND.
* Shout out to Vagas :) *
"Are we recording?"
Funny how he edits the video at several spots but doesn’t edit that out. I guess it’s a meme at this point.
@@Jeff321 Yes, I love it. Does also make you think how many times he has been 12 minutes into a recording and it WASNT recording!! lol, makes me laugh.
Technically you can't really cross any country in a straight line because of the Earth's curvature... :)
But basically what I wanna say is - don't worry about it so much. You might not have followed THE line, but you followed A line and you did a great job. It's your own challenge with your own rules anyways. You did your best, you succeeded at least on 99% in my eyes (and I believe most of your subscribers think the same), and you had a great trip and a nice adventure. So, well done, you're still a winner! Keep doing what you're doing.
"Straight line" here is an informal term for "geodesic curve".
This was a wonderful series! Thank you very much. I'm sure someone has suggested this before - but Finland might actually be pretty doable due to the relative flatness of the landscape. The country is actually quite thin between the Russian border and Oulu on the western coast - around 200 km. There's one big lake to be crossed, but other than that I think you could draw a line with just a few smaller puddles remaining in the way. Anyways, cheers and thanks again for the content!
Truly a legend. Keep it up Tom, I've been enjoying these adventures/missions and what goes on behind them a lot!
I think the best way to measure success would be to do a linear regression. Take all of the points (lat, long). The closer the r2 is to 1 the better. And would account for any error in the gps
This is what I’m thinking too. There are a couple of complications here.
1. The earth is not a plane. It more closely resembles a sphere. So we’d be fitting the points to an arc on a sphere, not a line on a plane.
2. Is that we don’t have a perfect arc on a sphere either, we have elevation to contend with. e.g imagine an arc A being the true line, which goes over a large hill. Next the path B goes around the large hill. You can calculate the distance from a point a on A and a point b on B using spherical geometry, but it will not take elevation into account. Spherical geometry will assume the sphere has constant radius. Therefore we need to use geographical data for our distance function in the regression.
Hey Tom, im a researcher in the states. I specialize in meteorology but I have a method we use to compute forecasting errors that might be applicable to your mission. Consider Root Mean Squared Error. If you look it up online its fairly self explanatory but I wanted to mention a few caveats. For your "actual location minus optimal location" it is just the distance from the line, perpendicular. You will of course need some weighting. We will weight each point based on midpoint distance between the 2 surrounding points... for example if you travel 10 meters before a point and 20 meters after a point, that point is weighted 15 meters. Look for the largest midpoint distance in your journey. Divide all your midpoint distances by that distance. This will have them all be a fraction between 0 and 1. Thus, large lines are weighted alot... small distances (like when still) are weighted a little. The metric is calculated for the whole journey since it is a summation in the numerator and denominator. The output is a single number that represents your mean error in meters. Using this you could set your platinum, gold, silver. Feel free to reach out if you care. Additionally, if you see this could you like so it gets to tom!
Cheers,
Colton
My review:
You got a line on the GPS in the field and followed it. I would say that is a success, even if the line on the computer is in another place.
As a selfish norwegian, I'd love to see an attempt #2 next year :)
Herjadalen to Bergen next time😂
I think after all this practice it’s about time you took on the equator. 😅 loving your videos. Really good to see some outside world during this pandemic. Keep up the great work you absolute legend!
Watching youtube while not doing calculus homework and I end up being asked to solve a deviation problem anyways
Still feel of regardless of how you decide to evaluate your run, you can either find ways to game it, or find ways to feel worst about it. These videos were a lot of fun to watch. Thank you.
Great work!
A possible explanation for the deviation in the GPS path and the yellow line may relate to different S2 projections between GIS systems (such as WGS84 vs. Mercator, etc., and the computer's maps vs. GPS device schemas)?
Another possibility is that straight lines from an S2 projection translate to curved geodesics on S2 in the real world? This was likely handled in the planning GIS phase, but add in elevation, terrain, and location of the path on the Earth can compound to a systematic error (ie, point-to-point bowing) you've experienced. Google 'wgs84 straight line projection' to see some articles on the subject.
If you make the raw data captures available for public download, someone with better GIS knowledge could be able to help further, idk, hope that all helps!
Yeah, this seems plausible to me. It is just a bit weird that the problems suddenly occurs when he restarts his GPS device. The only explanation I can come up with is that the device switched projection when he restarted it, this could be plausible since Garmin apparently has some specific projection options for Sweden, but only the global MGRS for Norway (support.garmin.com/en-US/?faq=lvWzTYlPsx6BvUDTyKfqC8). Maybe the device started out with one of the Swedish projections because of the proximity, but switched to one of the other. IDK total speculation though, really weird.
Yes, but why would it jump back and fourth then?
I think that line is a brilliant achievement, regardless of the vagaries from the gps.
As far as measuring the straightness, I think your original approach of looking at maximum deviation is fine. I would just imagine the line more as a strip of tape on the map, rather than as a mathematical line with no thickness. Set a width for the line (maybe 5-10m) that you can freely move within without that counting as deviation. This should allow for the slight randomness of the gps and of yourself. Then, measure only deviation from that narrow zone, and set maximum deviation for platinum, gold etc, as you did.
Also, look at getting sponsored by Garmin! They'd love this, it's fantastic!
I feel like there's always gonna be some sort of inaccuracy when measuring the line. I had this too with my mission and some of it is just inevitable (standing still, forests, gps doing weird things sometimes, etc).
Subscribed, lol!
@@dashingdave2665 thanks man!
Bottom line, you were still within ~40 meters? That's still insane. The physical achievement alone is laudable. It's definitely curious as to why there is this variation. But if I were you I'd take it as an academic issue rather than one of credibility or honesty. You put all your cards on the table; So long as you don't hide things people will understand just about anything and support you the whole way. Really amazing achievement mate. Outstanding work. Hope you find the cause of the issue and post a video about it. Good luck with your future endeavors.
I feel in a general sense that for any attempt when thinking about the line it's totally fine to just redraw it after the fact, and see the one you planned as a guide. So long as it's still a straight line I don't really see how you'd be able to game that and it would account for any weirdness like this
Dude your straight line videos are epic but I have to say none of them have been as good as the first! I loved the first one especially when you’re trying to stick to your plans doing 8-9 hours a day pushing on to your next camp spot! I didn’t enjoy the Norway one as much as there wasn’t as much epic content like camping and also bumping into people and running through dodgy places! Honestly though a credit to you especially all that rowing near the start! Please keep doing them!
Imo his best series was Europe w Welsh Greg
A better score would be to calculate the Mean Squared Error between the target line and the travelled route. Another option is to calculate the Linear Regression of the travelled route and compare it to the target line (can't remember a good method for it right now).
But for that, like every other calculation method involving calculations with the line as a function, you'd have to use the line with a given resolution, because you can't calculate that with infinite points, what the line currently is. And with that I think there are better ways like just the integral. But none of those methods really are perfect, but I can't think of anything better
@@maxkr8285 The GPS-provided points should be enough. He doesn't have any more data whatever method is used.
Yep, he could regress the actual line traveled on his hypothetically perfect line, calculate the R^2 and he has a measure of fit. Ofcourse to account for forrests and deviations when stood still, he would have to 'clean' the data from the GPS, but that shouldn't be that difficult.
@@TommyHoare I think the fluctuations of standing still should cancel out. And yeah, R^2 was the measure I was trying to remember.
You would still have to manually delete point where you stand still or go slower, because those will skew a regression to the side.
This is awesome. Love the rundown of the line after the actual trip.
I think the score should be calculated through average deviation instead of maximum deviation
or better, average maximum deviation. For example walking for 10m while deviated by 30m is worse than only 1m by 30m
If we're being technical, you could do something like root-mean-square.
i somewhat maybe kinda disagree
both as he explained. Otherwise you can deviate once by a far bit, then keep close to the line. Depending on the length of the route that could mean you could briefly deviate miles from the line.
I have an idea to tackle the measurements regarding medal selection: Lets just divide the medals into two categories: Highest Deviation & Persistence Deviation.
Essentially in case of highest deviation, you can work with the tools you already have established: 25m Platinum, 50m Gold, etc. In case of persistence deviation rewarding the idea of sticking as close to the line as possible and overcoming obstacles, you can compute the area under the straight line (like when you say you deviated by 10m at some place, just compute the area of that triangle of 10m vertex meaning for a small 10m deviation you'd be penalised low but for 10m deviation across long distance, area would be higher and hence high penalty). Its very easy to calculate these area using programming by feeding it logs files.
In case of standing still or walking back (GPS inconsistencies) just add a rule in program to eliminate those coordinates and have manual inspection to ensure you only take GPS ones and not actual mistakes (trust and honesty). And now finally about GPS moving 2-5m zig zag when you are under tree-cover: Compute the area under straight-line from a 3-5m pathway meaning anytime you deviate more than 3-5m on any direction, the area of the deviation will be added to your deviated path.
Medals of persistence deviation could be: 5% Deviated Area Platinum, 10% Gold, etc.
Hence, even if you at one point deviated more than 25m and fell below Platinum category of Highest Deviation, you would still have the Platinum of Persistence Deviation to fight for!
Now final medal can have categories like Pure Platinum (Platinum of HD AND Platinum of PD), Impure Platinum (Platinum of either HD or PD AND Gold of other), Pure Gold, Impure Gold, etc.
---
Lastly on the yellow and pink line deviation - its the result of Great Circle and Thumb line projections (orthodrome and loxodrome) inconsistency where your map is working on one projection while GPS being on another - such that they take separate paths but have the same starting and ending point.
I think a better way to determine how close you were to the target line is to turn your line into a series of sampled points. Then find the best fit line for those series of points. Then determine the translation (in distance and angle) between this best fit line and your target line. Then give distance and angle a weight to determine if it was a platinum, gold, or silver run. A*x + B*phi = GWLM (GeoWizard Line Metric). Where A and B are the weights (0 to 1), x is the translation distance, and phi is the translation angle. Based on the GWLM, determine if it was a platinum, gold, or silver.
Loved the series by the way. I don't think your GPS error makes it any less epic.
11:50 in......"Are we recording?" LMAO - classic Tom.
Dont usually comment but really enjoy these and wanted to give the algorithm a push. Thanks, mate!
“I’ve only got myself to blame....partly” 😂😂
I´d like to say, that for my part... it is not an issue you deviated from the Yellow line. If you followed your own line from start to finish, it is still a straight line. Doesn´t matter if its not the one you calculated beforehand. Your explainations and motivations to make sure you have the ´perfect´ line, are really commendable though. Ofcourse if you can improve the whole GPS issue on your next adventure, i´d be great. But for this one, I´d say you did a really nice job!
Love the content, it is really something special and I hope you keep it coming!. Greetings from a fan from the Netherlands ;)
ps. A straight line through the Netherlands is always something i'd be looking forward to. Don't worry about steep hill/slope 1, it wont come. Might be a little bit overcrowded though!
27:50 lol you essentially stumbled across integral calculus here 😅
I feel that "how straight is this line" is something mathematicians can almost certainly help you answer.
Very hyped for all the videos you're gonna come out with in 2021. Those mini missions have peaked my interest
1:55 Mission across Scotland confirmed? ;D
I think he mentions in the Norway series an upcoming Scotland trip with Welsh Greg. I think it was why he had such a short window for the Norway trip because he had to squeeze it in before that trip
Don't forget the mission across Jaw too, so excited!
Straight line across Australia?