# Curved Longitude Lines - Raytracing Brain Teaser

Hi David,

I did not really get what you really want to achieve. What kind of a sky coordinate grid are you refering to? It looks like you want to create a projection of the longitudonal lines of a hemisphere, right? What projection do you refer to when saying hemispherical view? What I see on the image looks a lot like a parralel proction of the dome, so the lines's coordinated could be calculated from spherical coordinates, obtained from the horizontal and vertical angle and radius, and ignoring the third coordinate (for the image you just need the two dimensions), transfered into cartesian coordinates. If you write down the formulas for this, you should be able to combine to something much simpler describing the parabolic curves. But I am not sure if I really got your intention yet.

So do you want a parallel projection of a hemisphere with longitudonal lines?

Lars.

David.

For a parallel projection all you have to do is take
the circle equation (x^2 + y^2 = r^2) for the outmost
line (+/-90 deg long, stays a circle) and 'squeeze' it
with the sin of the longitude. I assume that 0 deg long
is in the centre of the image.

A perspective projection is not as simple because
you have to take distance from centre and z-value
into account. It's still a linear equation, though.

Regards,
Thomas

ยทยทยท

On 19 Feb 2009, at 05:59, Lars O. Grobe wrote:

Hi David,

I did not really get what you really want to achieve. What kind of a sky coordinate grid are you refering to? It looks like you want to create a projection of the longitudonal lines of a hemisphere, right? What projection do you refer to when saying hemispherical view? What I see on the image looks a lot like a parralel proction of the dome, so the lines's coordinated could be calculated from spherical coordinates, obtained from the horizontal and vertical angle and radius, and ignoring the third coordinate (for the image you just need the two dimensions), transfered into cartesian coordinates. If you write down the formulas for this, you should be able to combine to something much simpler describing the parabolic curves. But I am not sure if I really got your intention yet.

So do you want a parallel projection of a hemisphere with longitudonal lines?

Lars.<lars_grobe.vcf>_______________________________________________