# Path between two points in rolling terrain

• Loren Booda
In summary, it is possible to putt from one point on a frictionless, smooth (albeit curved) terrain to any other point on the terrain.
Loren Booda
Show that there exists at least one trajectory connecting any two points on a frictionless, smooth (albeit curved) terrain.

This actually sounds like more of a mathematics question, a proof even, rather than a physics question. Are you talking about a 2D terrain, a 3D terrain? Is a trajectory a parabola or something? What would constitute a path between two points that is not a trajectory?

I don't understand what you are asking.
A connected set is not necessarily path-connected.

CaptainQuasar

Take for instance an idealized putting green, one without friction or discontinuities, but with any combination of curvatures. Is it always possible to putt from one point on the green so that the ball rolls directly over any other point thereon? I may be overlooking the obvious.

arildno

A connected set is not necessarily path-connected.

Would it be in this case?

arildno,

I now understand what you are saying. You are quite right. I withdraw my question.

Ah, I see. So in this case a trajectory is a path that remains in contact with the surface and behaves like a particle with a gravity-like force applied to it? Is this a particular meaning of “trajectory” or am I ignorant of the real definition of that word?

I don't know if this is an answer or a misunderstanding of the problem, but in your putting example if there were any overhangs the golf ball would leave the surface, so in that sort of curved surface there would definitely be points which the golf ball could not roll over.

I'm not making some sort of objection to the problem, as arildno may think, I'm really not understanding it.

I think this is the most rigorous way to state the question:

Given some simply-connected, smooth, 2-dimensional metric space M and a point P on M, does every point of M have a geodesic that also passes through P?

Ah, so as I suspected, this is essentially a topology problem that would require a proof as an answer? I've never studied topology so even if this is a trivial problem I'd have some learning to do to answer it but it looks interesting. Just looking up the words you used was very helpful, Ben. But that's basically what I meant by saying it looks like a math problem instead of a physics problem.

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## 1. How do you calculate the shortest path between two points in rolling terrain?

The shortest path between two points in rolling terrain can be calculated using a variety of methods, including Dijkstra's algorithm or A* search algorithm. These algorithms take into account the elevation changes in the terrain to determine the most efficient path between the two points.

## 2. What factors affect the path between two points in rolling terrain?

The path between two points in rolling terrain can be affected by various factors such as the steepness of the terrain, the type of terrain (e.g. grassland, forest, etc.), and any obstacles such as rocks or bodies of water. These factors can impact the difficulty and length of the path.

## 3. How accurate are the paths calculated in rolling terrain?

The accuracy of the paths calculated in rolling terrain depends on the method used and the quality of the terrain data. In general, more complex algorithms and higher quality terrain data can result in more accurate paths. However, some level of error is expected due to the unpredictable nature of terrain and potential errors in data collection.

## 4. Can the path between two points in rolling terrain be affected by weather conditions?

Yes, weather conditions can affect the path between two points in rolling terrain. For example, heavy rain or snow can cause changes in the terrain, making certain paths more difficult to traverse. Additionally, extreme weather conditions may make certain paths unsafe or impassable.

## 5. Are there any tools or software available to help with calculating paths in rolling terrain?

Yes, there are various tools and software available for calculating paths in rolling terrain. Some examples include GIS software, online mapping tools, and specialized routing software for hikers or cyclists. These tools use different algorithms and data sources to provide path calculations and may vary in accuracy and features.

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