ray tracing anomolies and light question

point lights are easy. they are isotopic, that is they radiate equally in all directions. imagin a sphere of photons being emmited from a point light. the sphere will increase in surface area as it travels away from the light. the density of photons will therefore decrease with this increase in surface area. the surface area of the sphere is 4pi*r^2 so the photon density is Power/4pi*r^2 this is the power/unit area. now we know the power per unit area when the surface is a distance of r away. we need one more thing, a projection factor to take into account the surface orientation. the formula for the irradiance(ie power/area) on a sruface is

I = (N DOT L)*(Power/4pi*r^2)

where N is the surface normal. L is the unit vector in the direction of the light. I could explain the geometry if I drew something but I'm sure you can find it. this is the cosine law for irradiance. imagin a laser hitting a surface in a perpendicular direction, now imagin the same laser in an obleque direction. one configuration will produce a point another will produce an illongated elipse. this is exactly what the cosine(dot product) takes into account, the decrease of photon density with respect to orientation.

so for a diffuse surface the reflected radiance is simply

R = p*I

where p is the reflectivity. this calculation would have to be done for each component of color r,g,b.

however some choose a slightly less physically correct model. it expands the types of effects a point light can have. instead of enforcing a 1/4pir^2 drop off of intensity. the intensity can be "artistically" picked.

usually you set quadratic, linear and constant terms for a qudratic equation for dropoff ie

dropoff = 1/(quad*r^2 + lin*r + const)

then
I = (N DOT L)*dropoff

and the rest is the same.

note that physically correct drop off is a special case of the above with:
quad = 4pi
lin = const = 0

also I'm not quite sure why your images look the way they do. but if you're implimenting shadow rays, this can be caused by not providing a delta value. when you trace a shadow ray you trace a ray from the surface to the light. but you dont want the surface point to intersect the ray. so instead of tracing from t = 0 you trace from t = .001 or something. another thing that could be wrong is you're not clamping your values in the 0 to 1 range. so high power stuff is coming out white.

Tim