**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).

Community Answer

Honor CodeSolved 1 Answer

See More Answers for FREE

Enhance your learning with StudyX

Receive support from our dedicated community users and experts

See up to 20 answers per week for free

Experience reliable customer service

Get Started

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}         .................................... ...