Some Graphics mathematical problems - solutions

1.    What pixels will be marked in drawing a circle center (100,90) and radius 10? using Bresenham's algorithm

Ans:

Take x=0,y=r=10,d=3-2r=3-2*10=-17

Decision variable (d)	x	y	Point with Center (0,0)	Point with Center (100,90)
	0	10	(0,10)	(100,100)
-17	1	10	(1,10)	(101,100)
-11	2	10	(2,10)	(102,100)
-1	3	10	(3,10)	(103,100)
13	4	9	(4,9)	(104,99)
-5	5	9	(5,9)	(105,99)
17	6	8	(6,8)	(106,98)
11	7	7	(7,7)	(107,97)

Scaling in C Language

 
 

Point (X,Y) is to be scaled by amount S_x and S_y to location (X',Y')

X' = S_x * X
Y' = S_y * Y

or P' = S * P where

P' = [X`,Y`]   , P  = [X,Y]  

S  = |  Sx  0  |

     |  0   Sy |

Transformation in C language

 

One of the most common and important tasks in computer graphics is to transform the coordinates (position, orientation, and size) of either objects within the graphical scene or the camera that is viewing the scene. It is also frequently necessary to transform coordinates from one coordinate system to another, (e.g. world coordinates to viewpoint coordinates to screen coordinates.) All of these transformations can be efficiently handled using some simple matrix representations, which are combining multiple transformations into a single composite transform matrix.

bresenham line drawing algorithm in c

 

General idea how Bresenham Line drawing Algorithm works

•Uses only integer calculations

•Uses distance between ideal y-coordinate and the upper and lower pixel (assuming gentle slope)

•Suppose that the line is gently sloping upwards from left to right.

•Start by coloring the left-most pixel.

•Then, for the next column (that is, for each x value), we have to figure out whether we color the same y or y+1.

DDA Line Drawing Algorithm in C

In computer graphics, digital differential analyzer (DDA) is used for drawing a line between a start and end point Consider an interval [(x_start, y_start), (x_end, y_end)] by computing for each x_i the equations x_i = x_i-1+1/m, yi = y_i-1 + m, where dx = x_end − x_start and dy = y_end − y_start and m = dy/dx.

A line is sampled at unit intervals in one coordinate and corresponding integer values nearest the line path are determined for other coordinates.

Do U Know?

1. The minimum time delay between the initiations of two independent memory operations is called

a) access time               b)cycle time    c) transfer time  d) latency time

2.   Which of the following comments are true?
1. It is a register
2. It is a cell in ROM
3. During execution of the current instruction, its content changes
4. None of the above

How to take inputs in Java Describe with 2 simple programs

Prog 1:

………………………

Save as input1.java

………………………

import java.util.Scanner;

class input1

{           public static void main(String args[])

            {

                        Scanner scan = new Scanner(System.in);

DO U KNOW?

1. What will be the output of the following arithmetic expression?

5 + 3 * 2 % 10 – 8 * 6

a) –37              b) –42              c) –32              d) –28

Write a GUI program in Java that will have two buttons viz., RED and GREEN. If user clicks on RED button the background of the GUI will be painted in red or if user clicks on GREEN button the background of the GUI will be painted green

………………………………………………………………………………………….

Save this file as=> ex.java

………………………………………………………………………………………..

import java.awt.*;

import java.awt.event.*;

import java.applet.*;

public class ex extends Applet implements ActionListener

{

            Button b1,b2;

           

            public void init()

Some questions with answers from C Language

Can you write another expression which does the same job as ++*ptr;

Ans: (*ptr++)

Are the expressions *ptr++ and ++*ptr same?

Ans; No. ptr++ increments the pointer and not the value pointed by it, whereas, ++*ptr increments the value being pointed to by ptr.