CS 184: COMPUTER GRAPHICS

Working with the Lighting/Shading equations.

Given a directional white light source (sun) sending 3 trillion photons per second per mm²

shining at an angle of 60 degrees (measured against the normal vector) onto a cyan-colored, lacquered surface

with those specifications: color = (0.2 1.0 0.7), k_a = k_d = 0.2, k_s = 0.8, k_sp = 75, k_sm = 0.6;

the surface is in an environment of yellow ambient light: color = (1.0 1.0 0.0), I = 0.4*10¹² photons / s / mm².

Calculate the intensities of the (r,g,b) components sent towards an eye located in direction of the ideally reflected rays.

I_{eye, r} = _____ ; I_{eye, g} = _____ ; I_{eye, b} = _____ .

Calculate the diffusely reflected components:

I'_d   = ( I_a + I_d*cos(inc.angle) ) * k_d * (r,g,b):
I'_dR = ( 0.2   + 1 * 0.5   )    *   0.2 * (0.2) = 0.028 *10¹² photons / s / mm².
I'_dG = ( 0.2   + 1 * 0.5   )    * 0.2    * (1.0) = 0.14 *10¹² photons / s / mm².
I'_dB = ( 0.0 + 1 * 0.5   )    *   0.2 * (0.7) = 0.07    *10¹² photons / s / mm².

Calculate the speculalrly reflected component:

I'_s = I_d * k_s * (Phong.Factor) * (adjusted color):
I'_sR = 1 * 0.8 *       (1.0)          * (0.6*0.2 + 0.4*1.0) = 0.416 *10¹² photons / s / mm².
I'_sG = 1 * 0.8 *       (1.0)          * (0.6*1.0 + 0.4*1.0) = 0.8      *10¹² photons / s / mm².
I'_sB = 1 * 0.8 *       (1.0)          * (0.6*0.7 + 0.4*1.0) = 0.656 *10¹² photons / s / mm².

Sum up the components:

I'_totalR = 0.444 *10¹² photons / s / mm².
I'_totalG = 0.94 *10¹² photons / s / mm².
I'_totalB = 0.663 *10¹² photons / s / mm².

This kind of computation has to be done by your raytracer every time it hits a surface !

Page Editor: Carlo H. Séquin