Design a Mathematical function

Hello,

I would like to design on grasshopper the curve of a perfect stadium stand wich is given by this function :

N(k) = ((R+C) x (D+T) / D) - R

With :

R = R0 + sum(R(k-1))

D = D0 + (k-1) x T

With this variable R0 : D0 ; T ; C

I don't succed in entering the function D in the The N(k) function

Could you please help me ?

Attachments:

2016_06_03_Stadium stand.gh, 16 KB

Replies to This Discussion

Permalink Reply by David Rutten on June 4, 2016 at 11:20am

So k is an integer indicating the row and N(k) is the elevation at that point?

Permalink Reply by David Rutten on June 4, 2016 at 11:21am

And what exactly does sum(R(k-1)) mean?

Permalink Reply by Laurent DELRIEU on June 4, 2016 at 12:30pm

I found this image, sum(R(k-1)) must be sum of N+height of eye or R from row 1 to k-1

http://people.bath.ac.uk/ps281/maths_talk/stadiums/teacher_notes/si...

http://people.bath.ac.uk/ps281/maths_talk/stadiums/teacher_notes/ar...

Permalink Reply by David Rutten on June 4, 2016 at 1:05pm

The problem with this is that it is not a function in the sense of f(x). It's the definition of a sequence where each number depends on the previous value. As such you cannot simply evaluate this.

Unless you can rewrite this sequence to a f(x) = [x] form, you'll probably end up writing a C# or python script which can loop over the sequence and thus grow it one element at a time.

Permalink Reply by Laurent DELRIEU on June 4, 2016 at 1:07pm

I am not much found of football but equation of elevation of row was interesting.

As it is recursive I use Anemone

Hope I didn't do some mistakes

Attachments:

2016_06_03_Stadiumstand_LD.gh, 18 KB

Permalink Reply by yann rouxel on June 6, 2016 at 4:01am

Hello Laurent,

It's exactly that thank's a lot, I didn't know the recursive function Anenome.

Permalink Reply by Mohamed Naeim on June 4, 2016 at 1:36pm

Attachments:

Emirate Stadium.gh, 18 KB

Permalink Reply by Mohamed Naeim on June 4, 2016 at 1:55pm

If it was me, I would always set/constraint N to the multiplies of a step height(riser)

i.e if a riser height is 15 cm then N will be either 45/60/75 etc

but i am not sure, any one?

Permalink Reply by peter fotiadis on June 5, 2016 at 11:35pm

Well ... it's a bit more complex than that since the Z focus of sight has to be considered (a theater and a baseball stadium are not the same) PLUS (a) the max allowed sight distance (b) sight clearance for multi leveled arrangements (c) aisle step design constrains (d) evacuation constrains (e) sight comfort angles ... (z) you name it.

Other than that populating such layouts with something (seats and/or figures) requires - obviously - instance definitions : Imagine 80K seats for example present for some classic master drawing or some photo realistic stuff.