# Creating a Raster Map with a 2-Variable Distance Equation

Discussion created by thetennesseefireman on Nov 22, 2013
Latest reply on Nov 22, 2013 by curtvprice
Hello, everyone. I'm a student currently working on a project that correlates crime and ground illumination from streetlights, and I've found myself at a bit of a loss for what tool and/or Python script to use.

I'm modeling the streetlight illumination based on this formula: E[SUB]h[/SUB] = [I(Theta) * N * cos[SUP]3[/SUP](Theta)] / H[SUP]2[/SUP], where Eh is the illumination at a point on the ground, H is the constant height of each streetlight, N is the constant lamp lumen output, Theta is the angle of radiation perpendicular to the horizontal plane, and I(Theta) is luminous intensity as a function of Theta. As height and lumen output are constant, the only variables are Theta and Eh.

By measuring E[SUB]h[/SUB] at Theta=0 with a light meter, I was able to solve for I(Theta) at that point, and as theta is directly related to the constant height, I can use basic trig to convert Theta into distance from the streetlight. Therefore, if I have a two-variable equation with one being distance and the other being illumination, I feel I should have a tool at my disposal to create a raster map; however, I can't find anything as of yet. My end goal is to produce a raster layer of illumination values on the ground defined by these formulas. My questions therefore are twofold:

1) Do I need to model other points on the ground in order to make this into a equation that can be projected? (This is more a math question than anything else. I can use a theodolite and light meter to take new measurements without too much trouble.)
2) Are there any tools I can use for creating this raster based on a two-variable equation with one of them being distance, or am I doomed?