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filtration from a direction

indragt@...
 

Hi, is it possible in dionysus to get filtration of a rips complex from any given direction?

Dmitriy Morozov
 

I don't understand the question.


On Thu, Feb 7, 2019 at 6:03 AM <indragt@...> wrote:
Hi, is it possible in dionysus to get filtration of a rips complex from any given direction?

indragt@...
 

Hi Dmitriy, sorry that I was not clear. I have a 3D pointcloud and a rips complex on that. I want to pick a point outside the cloud and a direction towards the cloud and make a filtration of the complex  such that each subcomplex in that filtration is the collection of simplices that are below a particular distance from that chosen point. Is it clear ? 

Dmitriy Morozov
 

I see. You want a lower-star filtration. Generate your Rips complex, then replace the value of each simplex by the maximum of any of its vertices projections onto your chosen direction. Then sort the filtration.

This is kind of sketched in the docs, but without enough detail. (Ignore the Freudenthal triangulation part, that doesn't apply here.) 


On Thu, Feb 7, 2019 at 8:36 AM <indragt@...> wrote:
Hi Dmitriy, sorry that I was not clear. I have a 3D pointcloud and a rips complex on that. I want to pick a point outside the cloud and a direction towards the cloud and make a filtration of the complex  such that each subcomplex in that filtration is the collection of simplices that are below a particular distance from that chosen point. Is it clear ? 

indragt@...
 

On Thu, Feb 7, 2019 at 08:47 AM, Dmitriy Morozov wrote:
l. (Ignore the Freudenthal triangulation part, that doesn't apply he
Thank you so much. I will be looking into that in the evening and will let you know as soon as I am done.