Assume we have the following:

a planar patch with endpoints $(2,2,4),(0,2,0),(8,4,2)$ and $(6,0,2).$

a viewer at $(0,0,6)$

a white light source at $(3,6,1),$ with maximum diffuse and specular components and ambient components set at $0\mathrm{.}1.$

We want to determine the shading at the center point on the planar patch $($where the center point is the average of the four vertices$).$

$($a$)$ Using the information above the location of the center of the patch determine the four vectors used in the Phong model.

$($b$)$ Use the Phong mode to determine the amount of red, green and blue light the user sees coming from the center of the patch, assuming the planar patch uses the parameter for listed below $($which are the parameters for a copper$-$ish surface$).$ Be sure to show your work.

ka kd ks $\backslash$alpha

red $0\mathrm{.}191250\mathrm{.}70380\mathrm{.}25677712\mathrm{.}8$

green $0\mathrm{.}07350\mathrm{.}270480\mathrm{.}137622$

blue $0\mathrm{.}02250\mathrm{.}08280\mathrm{.}086014$