How not to trample the tracks in the park

Reflections on the movement, or why lawns suffer

This article is an invitation to the discussion. I am sure that there are professionals in this field and they can say something interesting. I give my view on the problem from the point of view of an amateur and my main goal is to remind readers that many aspects of the human psyche implicitly influence the world around us.

So, let's begin. I’m sure everyone has repeatedly noticed such a phenomenon as trodden paths that do not coincide with the sidewalks? And have you ever wondered why they are trodden so and not otherwise? And why are they being dragged when there are many wonderful sidewalks and other comfortable surfaces around?

Let's deal with this.

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To begin with, we define that a person is always moving towards a goal.

Since the goal is a broad concept, we introduce the concept of a goal as an object to which a person physically approaches.

How does a person move to a goal through a flat field without obstacles? Very simple - in a straight line. A person always tries to minimize his time and distance. However, in real life in a straight line we rarely move, what prevents us from this?

Comfort as a feeling of safety and convenience of overcoming obstacles . It may not be associated with time (we walk along the sidewalk as fast as we go along the road), but it may be associated with objective or subjective safety, including the established rules (it is safe to walk on the lawn, but it is impossible, but you can slow and uncomfortable, on the road quickly, but dangerous). A sense of security is also influenced by an overview of the area. The bigger it is, the more comfortable we feel. Therefore, people always bypass corners , and do not move along the shortest path.

Thus, comfort is determined directly by the type of surface and the aggressiveness of the environment, the viewing angle. And no less important is the distance to the nearest “comfortable” points. An uncomfortable point on the border with a comfortable one seems much more attractive to a person than a point of average comfort at a great distance from a comfortable place.
Perhaps this is an instinctive desire to be able to escape from danger.

Everyday experience tells us that if each point of the plane is assigned a comfort indicator, then the route of movement of a person from A to B will be constructed so as to pass it in the shortest possible time with maximum comfort . In the general case, this will be a family of curves depending on the conditional parameters “haste” and “resilience”, which, of course, are different for each person.

Hurried and resistant will go right through, slow and unstable will go on the longest and safest / most comfortable way, and between them there will be all possible options. But the idea of ​​the essence of the phenomenon can also be obtained from the averaged curve.

What will happen if a person gets in the way of an obstacle?

He needs to get around. And do it with maximum comfort and the fastest way. Difficult task, especially we do not know how to determine comfort. But in fact, all this can be described by a fairly simple model.

We all saw maps of surface temperatures obtained from a thermal imager. But such a map almost perfectly models our situation - there is an area of ​​points, each of which not only has its own characteristics, but also contributes to the overall picture, having the most effect on neighboring points (remember, subjective comfort also depends on the environment). On the ground, you can build the same maps of comfort, where each point along with its own values ​​will affect the surrounding.

I think there are algorithms on this score and I hope someone will bring them in the comments, but we are interested in the result. And the result will tell us that the results of such constructions will have a gradient view with peaks and dips, and their appearance will resemble a temperature map, with the same smoothing of small irregularities and amplification of large ones.

Let's look at the illustration.

We need to get to the goal, passing two evil dogs

Let's build a discomfort card for them.



Let's lead the way.



It looks like the truth, is not it?
After we build a similar map of comfort for the area, it will be more understandable how the person actually behaves in this or that situation.

He will try to keep as far as possible from less comfortable places, moving accordingly to the most comfortable. The greater its durability, the less will be its requirements for the minimum acceptable comfort. Also, the greater the discomfort, the greater the speed of movement of a person and the greater the angle to the line to the target, he will overcome the terrain - minimizing the distance traveled along the uncomfortable part.

Need to cross the road.

Due to the attraction of comfortable points of the edge of the road, they subjectively seem to be safer (although this is not the case), as a result, the trajectory of movement becomes s-shaped. A person walks longer on the edge of the road than on its center, although logically it seems silly, does it really matter where the car kills you? Apparently not.





Well, a little practice .

Why are corners cut off?

Remember - the farther from the comfort point, the less comfortable it seems to us. This rule has a consequence - an uncomfortable point on the border of comfort seems to us quite acceptable. When approaching the top of the corner, the edges of the corner are geometrically approached, making the interior more and more comfortable. The result - the corners are always cut , some more, some less. Lawn trampled down, dirt spreads, and a bunch of minor troubles.



How to deal with it? First of all, fight with direct compounds. Under conditions of variable discomfort, a person moves along curves of different radius and only under ideal conditions do they approach straight lines in their form. At the intersections of the tracks, it should be possible to go to any branch of the intersection by smoothly changing the motion vector, rather than doing it all at once.

I think that it is quite possible to calculate the optimal shape and width of the aisles for places of mass gathering of people simply on the basis of statistical characteristics, taking some variation on our virtual indicators “tolerance” and “haste”.

Strangely enough, these rules are best followed by road designers during the construction of autobahns, although on the sidewalks people behave in the same way.

So think about how you walk, maybe now you will do it more meaningfully :)

PS I thought to write before the New Year, but a few delayed. On the first working day is also normal. I hope this topic helped you a bit to relax and unwind in the middle of the day.