spherical projection

[leedude]

hi, this is only electronics-related in that it's useful for a project im doing.

what is the formula/matrix for projecting points from a spherical surface?

for instance, if i had a grid, how could i transform it so that it looked like this:
**broken link removed**

is there a name for this like: sphere transform?(no result from google)

 

[leedude]

ok, i've confused myself here, im gonna start from the top.

i have an arrangement of servos which aim a light at a surface based on a latitude and longitude angle(not azimuth).

i need to calculate these two angles based on the position on the surface the beam is to intersect.

there is some kind of 3d projection formula i need.
can anyone help?

 

[MrAl]

Hi there,

Im not sure if this will help or not, but...

one way of doing something like this would be to use what's sometimes
called a 'perspective transformation', where you specify the view point
in space (x,y,z) and you either enter or generate a set of points in 3d
and feed them to the transformation equation(s) to get the 2d points.
You'll have to look on the web im afraid, as im not sure if i have these
equations around anymore. Maybe search for 'perspective view' or
'perspective transform' or something like that.
Once you obtain the equations, you could probably generalize for your
symmetries and constants, unless of course you could find this work
already done for you somewhere.

Wait a minute...
at first i thought you wanted to draw things, but now it sounds like you
just need the intersection of a line and a solid object? If so, you
have to solve for that using the equation for your surface and
the equation for your line.

 

[duffy]

is there a name for this like: sphere transform?(no result from google)

That one is called a "fisheye transform".