For a surface, how is radiosity defined? For diffusely emitting and reflecting surfaces, how is radiosity related to the intensities of emitted and reflected radiation?

Radiosity is a measure of the total amount of energy leaving a surface per unit area, per unit time. It is the sum of both emitted and reflected energy from the surface, and in mathematical terms, it can be expressed for a surface with emitted and reflected intensities I_e and I_r, respectively, as: \[ B = I_e + I_r \]

A diffusely emitting surface is a surface that emits energy uniformly in all directions. Similarly, a diffusely reflecting surface reflects incoming energy in all directions uniformly. For such surfaces, the relationship between radiosity and radiation intensities holds true as mentioned above.

For diffusely emitting and reflecting surfaces, the radiosity (B) is related to the intensities of emitted (I_e) and reflected (I_r) radiation as follows: \[ B = \rho I_i + I_e \] Where \(B\) is the radiosity, \(\rho\) is the reflectivity of the surface, and \(I_i\) is the intensity of the incident radiation. So, the radiosity is the sum of the emitted intensity and the product of the reflectivity and the incident radiation intensity. To summarize, radiosity is the measure of the total energy leaving a surface per unit area, per unit time, and is the sum of emitted and reflected radiation intensities. For diffusely emitting and reflecting surfaces, radiosity is related to the intensities of emitted and reflected radiation through the equation above.