Re: 2d circular union nav-mesh

You can reduce the tests to a point within smaller circles, as long as 
you also test corridors between each circle.  (Where the width of the 
corridor is the distance between the two points of circle intersection 
minus the character's diameter.)

http://www.osodata.com/stuff/circles.png


[email protected] wrote:
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> Hi guys,
>
> Does anyone have any references or pointers for how to constrain a small 
> character (represented by a circle) within the interior of the union of a 
> set of larger circles?
>
> The background is, the larger circles define regions of land where the 
> small circle can navigate around (like a nav mesh), and the union of the 
> these circles defines the entire nav-mesh. The character is not allowed to 
> leave the interior of the nav-mesh and must remain wholly inside it at all 
> times.
>
> Some diagrams:
>
> The general case, the filled circle represents the character and the 
> hollow circles the land
>
> http://www.pfirth.co.uk/ex1.png
>
> My first attempt was to ensure the character was wholly inside at least 
> one land circle, but that fails in this case:
>
> http://www.pfirth.co.uk/ex2.png
>
> In that example, if the character moves any further up, it will not be 
> wholly contained in either circle and will fail, yet it should be able to 
> navigate between them.
>
> Cheers, Paul.
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