Grasshopper

algorithmic modeling for Rhino

how can ı plot this sphere in the simpliest way by the following parameter

x=(1-s²-t²)/(1+s²+t²)         

y=(2*s)/(1+s²+t²)     

z =(2*t)/(1+s²+t²)

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You have to convert it to a centre point and a radius, then you can draw the sphere. 

Parameters already have  the Radius. My main objective is ploting  by parameters. so I can get different surfaces by manipulating this parameters. thank you very much for your reply.

here is my grasshopper file

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You can create a grid of points (like you did) and evaluate them using your three equations to map (s,t) onto (x,y,z):

However these particular equations require you to sample points all the way to infinity in order to close the sphere, so you'll always end up with a small cross-shaped gap at the pole.... Also the density of the mapping varies greatly from pole to opposite. It may be wise to sample a non uniform grid of point, to even out the differences.

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Hi, mr Rutten I want to draw a dodecohedron ı want to overlap the edge of the pentagon what is the simpliest way of that without using expression?   ı can do that roughly with number slider  but I can't know the exact  overlapping points or vectors. is there any way to make number slider do that? 

if we had seen snap points  or like in autocad parametric there were geometric constraint this is possible.

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