[Radiance-general] Curved Longitude Lines - Raytracing Brain Teaser

[Thomas Bleicher]

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


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?
>
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