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I've posted the same question at GameDev Stack Exchange, but unfortunately I am not getting any response. So I am going to post ( and reword) it here. Hopefully I can get an answer!

I have a terrain ( in the form of mesh/element), and I want to indicate how the water flows in the terrain, subjected to gravity force and the terrain condition ( of course).

A crude way of doing this is to take every single mesh element, then draw the water flow direction from the highest point to the lowest, but I think this will result in a lot of ugly arrows that although can roughly point towards the correct directions, but really don't look nice when view as a whole.

Is there an algorithm, or even better, an existing code implementation ( in the form of well-documented APIs with Windows DLLs, or open source soure code), that allows me to generate the water "flow map" in an elegant, intuitive, look-nice way?

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This is a well-studied problem in geomorphological and hydrological modeling, as well as the fields of geomorphometry and terrain analysis.

For visualization, flow accumulation is usually calculated. If every element of your terrain is taken as contributing a value of 1 to the flow, then flow accumulation is the sum of all the flow that passes through a given element. A depiction of this for a landscape might look like this:

Flow accumulation

There are several different flow routing methods. The one you describe is known as D8. A few additional ones are depicted below.

Different flow routing methods

Algorithms for performing the above, along with citations to appropriate references, are available in my library, RichDEM.

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  • $\begingroup$ Looks impressive, but what does the legend actually stand for? $\endgroup$
    – Graviton
    May 18, 2018 at 3:39
  • $\begingroup$ In this case, number of upstream cells or portion thereof. $\endgroup$
    – Richard
    May 18, 2018 at 3:42
  • $\begingroup$ So it would appear that the RED area is the lower ground and BLUE is the upper ground, based on the legend ( shouldn't it be the other way round to conform to the normal topography legend usage)? $\endgroup$
    – Graviton
    May 18, 2018 at 4:36
  • $\begingroup$ That's correct. Red has a higher flow accumulation (more upstream cells) so its value is higher. $\endgroup$
    – Richard
    May 18, 2018 at 4:50
  • $\begingroup$ Interesting! Gotta check it out! $\endgroup$
    – Graviton
    May 18, 2018 at 6:46
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There is one program, called IBER, that fits into your request: http://www.iberaula.es/space/53/modules

You can download it for free here: http://www.iberaula.es/space/54/downloads

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  • $\begingroup$ Any specific module that I can use? Also, there seems to be no source code, nor a DLL that I can call? $\endgroup$
    – Graviton
    May 16, 2018 at 6:39
  • $\begingroup$ I have never used this code before... Only I kew about its existence. You can also programm the Shallow Waters equations by your own... $\endgroup$
    – HBR
    May 16, 2018 at 7:22

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