Calculus 3

Imagine that you are designing the shading algorithm for a 3D com- puter game. The shading algorithm should be very simple. Imagine that we have a very simple planar triangular surface made by three vertices A(3,0,0), B(0,5,0), C(0,0,6), the surface is painted red but depending on how a source of light is hitting the surface and the posi- tion of the camera, we will see a bright red or a dark red. Suppose the light source is located at the point L(1,1, 10) and the cam- era is located at position P(x, y, z). With this information we can compute the brightness of the surface with respect to the camera as a function of the angle that form the light source with respect to the surface and the angle that form the camera with respect to the surface. Let us analyze this. You will need to compute the angle a that form the light source with respect to the surface. Then you will need to compute the angle B that form the camera with respect to the surface. Then consider the cosine of the difference cos(a - b). So if you an index of 100 will be the brightest red and 0 is the darkest red then, 100cos(a - b) will be the shade of the color with respect to the camera. Find the equation of the shading given the above information as a function of the position of the camera x, y, z