Question Subject:- Computer Graphics Answer both question. Related question not a sub part. How can we compute the depth value Z(x, y) in Z-buffer algorithm? Using incremental calculations find out the depth value Z(x+1, y) and Z(x, y+1).

Z-buffer or depth buffer method is an image space approach toeliminate hidden surfaces. The surface depth is measured from the view plane along z-axis of a viewing system.Eaxh pixel position on the view plane is specified using x and y coordinates, whereas depth information is provided by the z- coordinate value. Part 1 To compute the depth value Z(x,y) in Z-Buffer algorithm, first let's see how the algorithm works. Initialize the Z-Buffer and frame buffer so that for all buffer positions:    Z-buffer(x,y) = 0 and frame-buffer(x,y) = IBackground                                         //i.e Set the buffer values. -    Depth buffer x,y = 0    and   Frame buffer x,y = background colour       During scan conversion process, for each position on each polygon surface, compare depth values to previously stored values in the depth buffer to determine visibility.    Calculate z-value for each(x,y) position on the polygon.    If z > Z-Buffer(x,y),                then                                                                                                                                        set Z-buffer (x,y) = z, frame-buffer(x,y) = ISurface(x,y)                                                                 //i.e Process each polygon one at a time                     //i.e For each projected x,y pixel position of a polygon , calculate depth z. //If Z > Depth buffer x,y ,           //compute surface color ,    set Depth-buffer x,y = z and    Frame buffer x,y = Surface Colour x,y    This is how we compute the depth value Z(x,y) in Z-Buffer algorithm. Part 2 Using Incumental calculations to find out the depth value z(x+1, y) and z(x, y+1) ?Let's denote the depth at point A as Z and at point B as Z^{\prime}\therefore To calculate Z values, we ure the plane equationA x+B y+C z+D=0 \Longrightarrow z=\frac{A x-r y-D}{C}where (x, y, z) is any point on the plane, and the coefficieots A, B, C \& D are constants.Considuing point A,\begin{aligned}& A x+B(y+D+C z+D=0 \\\Rightarrow & Z=(-A x-B(y+1)-D) / C\end{aligned}Considuing point B,\begin{aligned}& A\left(x+D+B(y)+C z^{\prime}+D=0 / C=\frac{-A(x+1)-B y-D}{z^{\prime}}\right. \\\Rightarrow & Z^{\prime}=(-A(x+1)-B y-D) / C-(2)\end{aligned}Hence from eqn (1) and (2), we can calculate that\begin{aligned}& \frac{-A x-B(y+D-D}{Z}=\frac{-A(x+D-B y-D}{Z^{\prime}} \\\Rightarrow & \frac{z^{\prime}}{Z}=\frac{-A(x+1)-B^{\prime}+D-D}{-A x-B(y+D-D} \\\Rightarrow & Z^{\prime}=Z-\frac{A}{C} \text {, where } A \xi C \text { are constants }\end{aligned}         .................................... ...