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#1 2012-02-17 03:48:48
- probiner
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- Registered: 2011-05-08
- Posts: 11
[Help] Genus: Having difficulty to fully understand it.
Hi
I'm having trouble to fully understand the concept of Genus: https://en.wikipedia.org/wiki/Genus_(mathematics)
Those examples are preety simple to me Genus = number of handles/holes. But what the wikipedia doesn't cover (at least visually) is when these handles or holes share space like in the last 3 examples of the image link below:
TopMod is a modeling program that has a display that shows how many Genus the present mesh has.
I was expecting different numbers honestly...
I cant get a rational grasp to understand the rules of these numbers.
It seems that it's the number of possible exits there is when going through a hole of the mesh.
So the Single Y shape has Genus 2 because when I go through Hole-number-1 I can exit on Hole-number-2 or Hole-number-3, so 2 possibilities.
The Double Y shape has Genus 4 because it's the previous situation but independent and doubled.
Is this it?
Cheers
Last edited by probiner (2012-02-17 03:50:50)
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#2 2012-02-17 05:18:07
- probiner
- Member
- Registered: 2011-05-08
- Posts: 11
Re: [Help] Genus: Having difficulty to fully understand it.
Got it, it's the number of cuts not holes/handles 
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#3 2012-02-17 08:48:29
- probiner
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- Registered: 2011-05-08
- Posts: 11
Re: [Help] Genus: Having difficulty to fully understand it.
Oh and here is the homeomorph
Last edited by probiner (2012-02-17 08:48:39)
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