Find vertices of a Voronoi diagram of convex polygons
$begingroup$
From a set of polygons guaranteed to be :
- Convex
- Full (no holes)
- Non-intersecting (polygons may share edges/points, but not penetrate each other)
How do I find the vertices of the Voronoi diagram where each polygon is a seed?
Precisions :
- Any answer for a Voronoi diagram of lines is also welcomed (I can merge the cells for lines belonging to the same polygon)
- I can work with an approximation of the vertices (within reasonable precision). This is for a simulated pathfinding / navigation system, so exact precision is appreciated but not mandatory.
- My math foundations are rusty, so please do mention anything obvious I should know / look into as an alternative.
I already have a working brute-force discretized approach :
- Draw each polygon in a unique color on an image
- For every blank pixel, find closest polygon and fill the pixel with its color
- List all pixels with adjacent to at least 2 different colors
While it works well enough (given a big enough image resolution) the performance is obviously horrible and it adds quite a few corner cases to handle. So I'd prefer to do without brute-forcing if possible.
geometry convex-geometry voronoi-diagram
edited Jan 11 at 13:28
Bernard
122k741116
asked Jan 11 at 12:45
Milan IrigoyenMilan Irigoyen
11
$endgroup$
add a comment |
$begingroup$
From a set of polygons guaranteed to be :
- Convex
- Full (no holes)
- Non-intersecting (polygons may share edges/points, but not penetrate each other)
How do I find the vertices of the Voronoi diagram where each polygon is a seed?
Precisions :
- Any answer for a Voronoi diagram of lines is also welcomed (I can merge the cells for lines belonging to the same polygon)
- I can work with an approximation of the vertices (within reasonable precision). This is for a simulated pathfinding / navigation system, so exact precision is appreciated but not mandatory.
- My math foundations are rusty, so please do mention anything obvious I should know / look into as an alternative.
I already have a working brute-force discretized approach :
- Draw each polygon in a unique color on an image
- For every blank pixel, find closest polygon and fill the pixel with its color
- List all pixels with adjacent to at least 2 different colors
While it works well enough (given a big enough image resolution) the performance is obviously horrible and it adds quite a few corner cases to handle. So I'd prefer to do without brute-forcing if possible.
geometry convex-geometry voronoi-diagram
edited Jan 11 at 13:28
Bernard
122k741116
asked Jan 11 at 12:45
Milan IrigoyenMilan Irigoyen
11
$endgroup$
add a comment |
$begingroup$
From a set of polygons guaranteed to be :
- Convex
- Full (no holes)
- Non-intersecting (polygons may share edges/points, but not penetrate each other)
How do I find the vertices of the Voronoi diagram where each polygon is a seed?
Precisions :
- Any answer for a Voronoi diagram of lines is also welcomed (I can merge the cells for lines belonging to the same polygon)
- I can work with an approximation of the vertices (within reasonable precision). This is for a simulated pathfinding / navigation system, so exact precision is appreciated but not mandatory.
- My math foundations are rusty, so please do mention anything obvious I should know / look into as an alternative.
I already have a working brute-force discretized approach :
- Draw each polygon in a unique color on an image
- For every blank pixel, find closest polygon and fill the pixel with its color
- List all pixels with adjacent to at least 2 different colors
While it works well enough (given a big enough image resolution) the performance is obviously horrible and it adds quite a few corner cases to handle. So I'd prefer to do without brute-forcing if possible.
geometry convex-geometry voronoi-diagram
edited Jan 11 at 13:28
Bernard
122k741116
asked Jan 11 at 12:45
Milan IrigoyenMilan Irigoyen
11
$endgroup$
From a set of polygons guaranteed to be :
- Convex
- Full (no holes)
- Non-intersecting (polygons may share edges/points, but not penetrate each other)
How do I find the vertices of the Voronoi diagram where each polygon is a seed?
Precisions :
- Any answer for a Voronoi diagram of lines is also welcomed (I can merge the cells for lines belonging to the same polygon)
- I can work with an approximation of the vertices (within reasonable precision). This is for a simulated pathfinding / navigation system, so exact precision is appreciated but not mandatory.
- My math foundations are rusty, so please do mention anything obvious I should know / look into as an alternative.
I already have a working brute-force discretized approach :
- Draw each polygon in a unique color on an image
- For every blank pixel, find closest polygon and fill the pixel with its color
- List all pixels with adjacent to at least 2 different colors
While it works well enough (given a big enough image resolution) the performance is obviously horrible and it adds quite a few corner cases to handle. So I'd prefer to do without brute-forcing if possible.
geometry convex-geometry voronoi-diagram
geometry convex-geometry voronoi-diagram
edited Jan 11 at 13:28
Bernard
122k741116
asked Jan 11 at 12:45
Milan IrigoyenMilan Irigoyen
11
edited Jan 11 at 13:28
Bernard
122k741116
asked Jan 11 at 12:45
Milan IrigoyenMilan Irigoyen
11
edited Jan 11 at 13:28
Bernard
122k741116
edited Jan 11 at 13:28
Bernard
122k741116
edited Jan 11 at 13:28
Bernard
122k741116
122k741116
asked Jan 11 at 12:45
Milan IrigoyenMilan Irigoyen
11
asked Jan 11 at 12:45
Milan IrigoyenMilan Irigoyen
11
asked Jan 11 at 12:45
Milan IrigoyenMilan Irigoyen
11
11
add a comment |
add a comment |
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