Comments

• Hey mate, first things first, love a good knight and mathematics enthusiast, great job on the development you did mate. Amazing stuff and thank you for showing how important is to have map of the realms basekit. this add on (and also call to arms in my opinion) are both necessary for the knight, sadly.

  
  

  That being said, let me tell you that even though the math is nice, I have found some issues with your development. First, the speed of expansion is the same for all directions, is just that the center of expansion in going down by the speed of the guard. This leads to an issue with your development, in which in order to be valid, the angle of the distance vector between the guard and the survivor MUST BE CONSTANT, which is clearly not the case in this scenario. This makes some of the results you have shown incorrect.

  
  

  THAT BEING SAID, the best and worse cases that you have shown should be correct, since in these specific scenarios, the angle of the distance vector remains the same throughout the simulation (0 degrees for worst case and 180 degrees for best), so all of that argument makes sense as far as I can tell, any other case is going to be something in between. Therefore, seeing your results, I can say that.

  
  

  1. The best and worse case scenario examples are correct.
  2. The at least 13.4m argument is also correct, since you have the circle expanding 13.4-3.4=10m in the y axis and the survivor making 4*2.5=10m of distance from the guard.
  3. sadly, the limit angle of 55 degrees argument cannot be guaranteed. but considering that the distance angle is diminishing over time, I can tell that the limit angle is going to be higher than this (55 degrees is NOT ENOUGH to catch a survivor in this scenario). Also, I did not do the calculations for this, so I cannot tell if you are considering 8m radius or 12m, can you be a little more specific?
  4. Jailor will always catch a survivor (14m radius) is also correct (edit: actually, not true because his patrol speed is 4.1m/s, this means that he does not catch survivors all the time, but should still catch in most cases and will always catch survivors with map of the realms).
  5. Gritty lump argument is correct, but I do not think will be so impactful in any of these cases, but it will make the distance angle diminish faster, so it will make the limit angle even worse.
  6. Just an observation, your y=(r-cos(a)m)(x-1.5) is only correct for time bigger than 1.5s, I understand the reason why you wrote this way since it will give you the behavior of the distance after the spawn time, but you could make a little observation in this case.

  Once again, good job, if you want to do the simulations considering the angle shifting, you can define the angle of distance by a = arctan(4*sin(a)*x/(4*cos(a)*x+m*(x-1.5))), then you can add three vectors of velocity (guard movement, survivor movement, and radius expansion, and integrate over time, and that should give you a better result. I do not have the time to do all the development, so good luck if you wish to try :)

  
  

  OBS: all of this argument takes in consideration the scenario of the guard dropping on the survivor (best case scenario during a chase), which is super hard and in my opinion should always result in a confirmed chase due to the perfection required from the play

  in Nerdy maths post about Knight and his guard ranges (pls make map base kit) Comment by dede5885 May 31, 2023