Computer Graphics-2

Computer Graphics(Practice questions)

Q1 Write a transformation matrix for a 3-D rotation, in homogenous coordinate system with respect to x,y and z axes respectively.

Q2 What is the limitation of DDA line generation algorithm? How does Bresenham line generation algorithm overcome this limitation?

Q3 Define an "Oblique projection". Derive a general transformation matrix for an oblique projection.

Q4 How can frame buffer be used to put colour and intensity on the screen?

Q5 Explain the term " sweep representation". How can a cylinder be produced by using the concept of sweep representation?

Q6 What is the need of the concept of "shading" in computer graphics? List merits and demerits of Phong shading.

Q7 Explain the terms "Cel animation" and "Sprite animation". Which of the two techniques is better for creating animation? Justify your answer.

Q8 Define the use of following formats:

1) GIF

2)JPEG

3) WPG

4)TIFF

5)MPEG

Q9 Write pseudo code for Bresenham circle generation algorithm. Use this algorithm to produce a circle of radius r=4 units, in the first quadrant from x=0 to x=y.

Q10 Write pseudocode for DDA line drawing algorithm for a line segment with negative slope.

Q11 Differentiate between the following.

a) Drawing and painting

b) CAD and CAM

c) Plotter and Printer

Q11 Determine the final co-ordinates of the perspective projection of an object, when the object is first rotated w.r.t. the Y axis by -30 degree and X-axis by 45 degree and finally it is projected onto Z=0 plane with center of projection at (0,0,-5).

Q12 Find the general transformation matrix for the reflection about the line y=-x.

Q13 " Simultaneous shearing is not the same as shearing in one direction, followed by shearing in another direction. What is the maximum number of objects  that can be handled by Z-buffer algorithm? Give two advantages and two disadvantages of Z-buffer algorithm.

Q14 What is the difference between ray tracing and ray casting? Explain how a ray tracing method can be used to achieve realism in computer graphics.

Q15 What is the problem of aliasing? How does the technique of anti aliasing work to get rid of the problem of aliasing?

Q16 Explain the following

1) Panning

2) Compression in digital video

3) Morphing

4) Scholastic Animation

5) Icon based authoring tools

Q17 Discuss the role of image editing tools in creating and editing multimedia elements. Briefly describe the criteria behind the selection of an image editing tool.

Q18 Define the term intensity interpolation. Explain Gouraud shading.

Q19 Write Z-Buffer algorithm for hidden surface detection. Explain how this algorithm is applied to determine the hidden surfaces.

Q 20 What is image filtering? Why is it required?

Q21 Compute the intermediate points on the line drawn from (0,0) to (5,10) using Bresenham's algorithm.

Q22 What is the difference between parallel and perspective projection? Categorize the various types of parallel projections.

Q23 Explain the concept of window to view port transformation with the help of suitable diagram.

Q24 What is the advantage of using homogenous co-ordinate system? Write the transformation matrix in homogenous co-ordinate system for "xy-shear" about origin.

Q25 Why do we use an authoring tool in the context of multimedia? Explain the features of any two types of authoring tools.

Q26 Explain the following terms with the help of an example/diagram, if needed.

a) Tweening

b) Volume rendering

c) Fractual models

d) Morphing

Q27 Derive a general 2D transformation matrix for rotation about the origin. Perform a 45 degree rotation of a square having vertices A(0,0), B(0,2), C(2,2), D(2,0) about the origin.

Q28 Explain Cyrus Beck parametric line clipping algorithm.

Q29 Derive the 2-D transformation matrix for reflection about the line y=mx, where m is constant. Use the transformation matrix to reflect the triangle A(0,0), B(1,1), C(2,0) about the line y=2x

Q30 Explain pseudocode for Sutherland Hodgeman polygon clipping algorithm. Using this algorithm clip the following polygon against the rectangular window ABCD.

Q31 What are refreshing display devices? Describe the working  principle of CRT displays with the help of suitable diagram. Differentiate between Random and Raster Scan display devices.

Q32 Write the three main properties of Bezier curve. Explain the condition for smoothly joining two bezier curve segments.

Q33 Explain the following terms with the help of suitable diagram/ example if needed.

1) Oblique Projection

2) Bezier Surfaces

3) Object space approach in Visible-surface detection

4) Specular Reflection

5) GIF File compression

6) Hypermedia

7) Representational Animation

8) Ray tracing

Q34 What are the differences between Gouraud and Phong shading?

Q35 Explain Cohen-Sutherland line clipping algorithm.

Q36 Explain the working principle of plasma panel  displays. Give the advantages and disadvantages.

Q37 Compute  2D transformation matrix for rotating a point (12,6) about the point (3,2) by an angle 30 degree in clockwise direction.

Q38 Compute co-ordinate points of  circle drawn  with centre at (0,0) and radius 5, using mid point circle algorithm.

Q39 Show that the simultaneous shearing Shxy(a,b) is not same as the shearing in x direction, Shx(a) followed by a shearing in y-direction, Shy(b).

Q40 Prove the following properties of Bezier curve.

i) P(u=1)=Pn

ii) P'(0)=n(P1-P0)

Q41 Explain the formation of an image in vector graphics with the help of an example. Explain any two file formats that use vector graphics.

Q42 Write a short note on sound editing tools.

Q43 Explain the scan line polygon filling algorithm with the help of suitable diagram.

Q44 Define the term ray casting. Explain any one method of ray casting.

Q45 Derive a transformation matrix for a perspective projection of point P(x, y, z) onto a x =4 plane as viewed from E(6,0,0).

Q46 Why Bresenham line drawing algorithm is better than DDA algorithm? Draw a line segment joining (4,8) and (8,10) using Bresenham line drawing algorithm.

Q47 Given four control point P0(2,2),P1(3,4), P2(5,4) and P3(4,2) as vertices of Bezier curve. Determine four points on Bezier Curve.

Q48 Explain the differences between the following

i) Multimedia and interactive multimedia

ii) Hypertext and hypermedia

iii)Procedural animation and representational animation

Q49 Explain ambient and diffused reflection. Give general mathematical expression for combined effect of ambient and diffused reflection.

Q50 What is frame buffer? How can you use frame buffer for putting color and controlling intensity on display device?

Q51 What is the advantage of using homogenous co-ordinate system? Consider a square (0,0),(0,2),(2,0),(2,2). Perform composite transformation of the square by using the following steps. (Give the co-ordinates of the square at each intermediate steps)

i) Scale by using Sx=2 and Sy=3

ii)Rotation of 45 degree in the anticlockwise direction.

iii) Translate by using Tx=3 and Ty=5

Q52 Why are hidden surface algorithm needed? Explain scan line method for visible surface determination.

Q53 Derive a 3D-transformation matrix for rotation relation matrices for about Z-axis, X-axis and Y-axis, respectively.

Q54 What are the number of memory bits required for 8-bit plane frame buffer for a 512 x 512 raster? Also calculate the refresh rate for the same raster(512 x 512), if pixels are accessed at the rate of 250 nano seconds.

Q55 Differentiate between Random and Raster Scan display devices.

Q56 Use DDA line generation algorithm to draw a line from (2,2) to (8,6).

Q57 Derive a general transformational matrix for 3-D rotation about x-axis.

Q58 Perform a 45 degree rotation of triangle A(1,1), B(5,1), C(3,5) about an aribitary point (3,3).

Q59 Explain any one method of polygon Representation with the help of an example.

Q60 How many key frames does a 45 seconds animation film sequence with no duplication require if there are four in between frames for each pair of key frames? What will happen if duplication is allowed?

Q61 Why file compression techniques are beneficial in computer graphics?

Q62 Write a procedure to implement the Bresenham line generation algorithm. What are the advantages of this algorithm over the DDA line generation algorithm.

Q63 What are the merits and demerits of Gouraud Shading, constant shading and phong shading?

Q64 Explain all the four cases of Sutherland-Hodgman polygon clipping algorithm.

Q65 Derive the 2-D transformation matrix for reflection about the line y=mx+c, where m and c are constants. Use this transformation matrix to reflect the triangle A(0,0), B(4,0) and C(4,4) about the line y=2x+5.

Q66 Explain the terms window and viewport in the  context of clipping. Derive a general transformation matrix for window to viewport mapping.

Q67 Write a short note on diffuse reflection.

Q68 Obtain a transformation matrix for perspective projection for a given object projected onto x=5 plane as viewed from [8,0,0].

Q69 Differentiate between the following.
i) Morphing and panning
ii) Motion specific animation and motion generalized animation.

Q70 Given p0(1,2), P1(2,3),P2(4,3), P3(3,2) as the vertices of  Bezier curve. Determine 5 points on Bezier curve.

Q71 What are the limitations of refreshing display devices? What is refresh rate in  1024 x 1024 raster if pixels are accessed at the rate of 250 nanoseconds?

Q72 Illustrate the Bresenham line generation algorithm by digitizing the line with the  end points(20,5) and (25,10).

Q73 Explain the Cyrus Beck line algorithm to clip a line segment for a non-convex clipping window.

Q74 Define the term projection. Categorise various types of perspective and parallel projections.

Q75 Explain the term anti-aliasing with the help of diagram. How does the technique of anti-aliasing work to get rid of the problem of aliasing?

Q76 Explain the process of simulating positive non-zero acceleration.

Q77 Define the following

a) Virtual reality
b) Icon based authoring tools
c) Frame buffer
d) Bitmap images
e) File Compression
f) 3-D modelling and animation tools

Q78 A square ABCD is given  with vertices A(0,0), B(2,2) and D(0,2). Illustrate the effect of

i)x-shear
ii)y-shear
iii)xy-shear

On the given square when a=3 and b=4, where  a is shearing in x-direction and b is shearing in y-direction.

Q79 Write pseudocode for midpoint circle generation algorithm.

Q80 What is difference between Hypertext and Hypermedia? Briefly describes various links used in Hypermedia.

Q81 Reflect the triangle where vertices are A(-1,0), B(0,2) and C(1,0) about
i) The horizontal line y=2

ii) The vertical line x=1
iii) The line y=x+3

Q82 What are the various types of audio and video formats?

Q83 What is foreshortening factor in the context of parallel projection? How it is related to Isometric, Diametric and Trimetric projection?

Q84 Explain the basic Ray tracing algorithm with the help of suitable diagram.

Q85 Find the transformation matrix for the reflection about the line y=4x.


Q86 Determine the expression of frame spacing which can be used to simulate positive acceleration  in any animation.

Q85 Write a short note on loss less audio formats.

Q86 How Raster scan display devices are different from Random scan display devices? Can we use frame buffers to control picture color and intensity, justify your answer with suitable arguments.

Q87 Explain the terms " Parametric Continuity" and "Geometric Continuity" in Bezier curves.

Q88 Discuss Area Subdivision Method. What are the conditions to be satisfied, in Area Subdivision Method, so that it is finalized that no further surface division is required?

Q89 How many key frames does a 30 seconds animation film sequence with no duplicates require? How the results are affected if five in between frames are inserted between each pair of key frames?

Q90 Differentiate between Bitmap and Vector graphics.

Q91 Find the final coordinates of the triangle ABC, A(-3,0), B(-1,1), C(-1,-1) when it is subjected to clockwise rotation of 45 degree  about  an axis  passing through an arbitrary point P(-1,1). Draw a suitable figure to demonstrate your solution.

Q92 Derive a general perspective transformation matrix with respect to an arbitrary centre of projection C(a,b,c). Obtain the perspective transformation matrix onto Z=-5 plane where the centre of projection is at (0,0,18).

Q93 Prove that two successive rotations are additive

Draw a suitable diagram to demonstrate your solution.

Q94 Perform 45 degree rotation of triangle ABC A(0,2), B(-1,-1), C(1,-1) about the origin.

Q95 What is the utility of tabular representation of polygon surface? Can you implement a polygon surface with just a vertex table  and an edge table? Justify your answers.

Q96 What are the maximum number of  objects that can be handled by Z-buffer algorithm? What will happen if the Z- buffer algorithm is used and it is found  that two polygons have the same z-value?

Q97 Write a short note on Stochastic animation and its area of application.

Q98 Differentiate between calligraphic display device and raster scan display devices.

Q99 Determine the number of memory bits required for a 4 bit plane buffer for a 512 x 512 raster.

Q100 Determine the final coordinates of a polygon ABCD A(1,4), B(-4,1), C(-1,-1), D(2,-2) when it is scaled upto twice its size with respect to an arbitary point P(1,1).

Compuer Graphics(Numericals)- 1

Computer Graphics 

Numericals Questions

Q1 Compute co-ordinate points of circle drawn with center at (0,0) and radius 5, using mid-point circle.

Q2 Draw line segment from point (2,4) to (9,9) using DDA algorithm.

Q3 Using DDA algorithm draw line segments from point (1,1) to (9,7).

Q4 What steps are required to plot a line whose slope is between 0 degree to 45 degree using Bresenham's line generation method? Draw a line joining(5,4) and (11,15) using the Bresenham's line generation algorithm.

Q5 Write a C program to implement DDA line drawing algorithm.

Q6 Using any of the line clipping algorithm obtain the visible position of the following line segment

1) P1=(0.5,0.4)  P2=(1.6,0.7)

2) P1=(0.4,-1.6) P2=(0.4,2.7)

3) P1=(0.4,-1.6) P2=(0.8,-2.7)

4) P1=(-2,-3)   P2=(3.5)

Q7 Find the new co-ordinate of a triangle A(0,0), B(1,1), C(5,2) after it has been

a) Magnified to twice its size

b) Reduced to half its size

Q8 Perform a 45 degree rotation of a triangle A(0,0), B(1,1), C(5,2) about the 

origin.

Q9 Translate a square ABCD with the coordinates A(0,0), B(5,0), C(5,5), D(0,5) by 

2 units in x-direction and 3 units in y direction.

Q10 Perform a 45 degree rotation of triangle A(0,0), B(1,1), C(5,2) about 

an arbitary point P(-1,-1)

Q11 Perform a rotation of triangle A(1,2), B(2,4), C(1,1) about P(-1,-2) in anti-clockwise direction by 60 degree.

Q12 Reflect the diamond-shaped polygon whose  vertices are A(-1,0), B(0,-2), C(0,0) and D (0,2) about

a) The horizontal line y=2

b) The vertical line x=2

c) the line y=x+2

Q13 Consider a given triangle ABC where A(1,0), B(0,1), C(1,1) and apply the following transformation as below

1) Rotate around the origin and then translate in the direction of vector(1,0) 

2) Translate first in the direction of vector (1,0) and then rotate by 45 degree.

Q14 Obtain the mirror reflection of the triangle formed by the vertices A(0,3), B(2,0) and C(3,2) about the line passing through the points (1,3) and (-1,-1)

Q15 Show that Sa,b.Sc,d=Sa,b.Sa,b=Sac,Sbd

Q16 Find the isometric view of a cuboid. The size of cuboid is 10 x 8 x 6, which is lying at the origin.

Q17 Obtain a transformation matrix for perspective projection for a given object projected onto x=4 plane as viewed from (6,0,0)

Q18 Consider the line segment AB parallel to z axis with end points A(3,2,4) and 

B(3,2,8). Perform a perspective projection onto the z=0 plane from the center of projection at E(0,0,-2). Also find out the vanishing point.

Q19 Obtain the perspective transformation onto z=-2 plane where the center of projection is at (0,0,18)

Q20 Find equation of plance which passes through point P(0,0,0) and the normal

to the plane is given by N(1,0,-1)

Q21 Calculate the equation of plane for a quadrilateral planar polygon described by the four vertices V1(1,0,1) , V2(1,1,0) , V3(0,1,1) nd V4(1,1,1)

Q22 Given P0(1,1);P1(2,3);P2(4,3);P3(3,1) as vertices of Beizer curve. Determine

three points on Bezier curve.

Q23 To prove P(u=0)=P0

Q24 To prove P(1)=Pn

Q25 Based on the Bezier curve definition derive the equation of 3 points Bezier curve defined by the following control point (-1,0),(0,2) & (1,0)

Q26 What is an image aspect ratio, if an image has a height of 2 inches and aspect ratio of 1.5, What is its width?

Grade 8 Squares and square roots

Squares and square roots 

Beginners level

Q1) Find the squares of first 10 natural numbers.

Q2) Find the square root of the following

a) 4 b) 9 c) 16 d) 25) e) 121

Q3 Find the square root of the following by prime factorisation

441, 2500, 625,1225,3025

Q4 Find the square roots  by long division method

144, 169, 225, 256, 361,4225,7225,1521,1089,2401

Grade 8 Maths

Simple equations

Practice 

Q1 Solve for x(integers)

a) x + 2=3

b) 2 + x=3

c) -x - 2=3

d)-2 - x=3

e) -x +2=3

f)  x - 2=3

g) -2 + x=3

h) -2x=3

i) -2x + 1=3

j) x + 2= -3

k) 2 + x= -3

l) -x - 2= -3

m)-2 - x= -3

n) -x +2= -3

o)  x - 2= -3

p) -2 + x=-3

q) -2x= 3

r) -2x + 1=-3

Q2 Solve for x(Fractions)

a) x/2 + 2=3

b) 2 + x/2=3

c) -x/2 - 2=3

d)-2 - x/2=3

e) -x/2 +2=3

f)  x/2 - 2=3

g) -2 + x/2=3

h) -2x/3=3

i) -2x/3 + 1=3

j) x/2 + 2= -3

k) 2 + x/2= -3

l) -x/2- 2= -3

m)-2 - x/2= -3

n) -x/2 +2= -3

o)  x/2 - 2= -3

p) -2 + x/2=-3

q) -2x/3= 3

r) -2x/5 + 1=-3

Grade 7 Maths Set 2

Grade 7 CBSE

Simple equations

Practice Set 2

Q1 Solve the following

a) 13x-5=60

b) 5m + 12=32

c) -3(x+2)=6

d) 5 -5(t+1)=20

e)1.5(x+1)=0.5

Q2 Anjani thinks of number, if she adds 8 to it  and divide the sum by 2, she will get 4.

Q3 Virat scored twice as many runs as Gautam. Together, their runs fell 2 short of 

double century. How many runs did each one score?

Q4 In a isosceles triangle ,the base angles are equal, the vertex angle is 30 degree. Calculate the base angles of the triangle.

  

Q5 Iqbal says  that he has 8 toffees more than 5 times the toffees Tinu has. If Iqbal has 37 toffees. How many toffees does Tinu has?

 Q6 Solve the following

a) -25 x 2 +3 x 25
b) -20 x 76 + 20 x 152 + 20 x 34
c) 0.2 x 1.4
d) 1.4/0.2

Exponents and Radicals

Grade 8 

Basic Level

 Set 2

Exponents and Radicals

Q1 Express the following in exponential form

 

Q2 Express the following as radicals

 

 

Q3 Find the value of the following

 

 

Q4 Express each of the following with positive exponent.

 

 



Q5 Simplify

 

 

Grade 7 Maths Set 1

Grade 7

Practice Test 

(Fractions and decimals, integers, simple equation and data handling)

Level Basic Set 1

Q1 The temperature at 12 noon was 10°C above zero. If it decreases at the rate of 2°C per hour until midnight, at what time would the temperature be 8°C below zero? What would be the temperature at mid-night?

Q2 Find each of the following products

a) 3 x (-1) + 4
b) 225 + 15 x 95
c) -3(2x +2)=12

Q3 Vidya and pratap went for a picnic, their mother gave them a water bottle that contained 5 ltr. vidya consumed 2/5 of the water, pratap consumed the remaining water
(1) how much water did vidya drink?
(2) what fraction of the total quantity of water did pratap drink?

Q4 Lipika reads a book for 1 3/4hours every day.she reads the entire book in 6 days.how many hours in all were required by her to read the book?

Q5 Dinesh went from place A to place B and from there to place C. A is 7.5 km from B and B is 12.7 km from C. Ayub went from place A to place D and from there to place C. D is 9.3 km from A and C is 11.8 km from D. Who travelled more and by how much?

Q6 Find

a) 0.12 x 1.2
b)0.5 x 0.05
c) 1.2 /0.12
d) 7.75 / 0.25

Q7 Find the median and mode of 14,25,14,28,18,17,18,14,23,22,14,18

Q8 Kimi subtracts thrice the number of notebooks he has from 50, he finds result to
be 8. Form a equation.

Q9 Find a number, such that one-fourth of the number is 3 more than 7.

Q10 The heights of 10 girls were measured in centimetre and the results are as follows 135, 150, 139, 128, 151, 132, 146, 149, 143, 141

i)what is the height of the tallest girl?
(ii)what is the height of the shortest girl?
(iii)What is the mean height of the girls?
(iv)How many girls have more than the mean height?
(v) What is the range of data?

Rational numbers, square roots and cube roots Set 2

Grade 8  Practice Test
(blog.infate.in)

(Rational numbers, square roots and cube roots)

Q1 Solve the following

 

Q2 Find the square root of the following

 
 
 
 
 

Q3 Estimate the value of following  to the nearest one decimal place

 
 

Q4 Find the five rational numbers between
 

Q5 Which of the following triplets are Pythagorean?

a)(3,4,5)
b)(6,7,8)

Q6 Find the least number which must be subtracted from 2509 to make it a perfect
square.

Q7 Find the least square number which is exactly divisible by each of the numbers 6,9,15 and 20.

Q8 Find the cube of the following

a)-2  b)0.4  c)1.2

Q9 Find the cube root of the following

 
 

Q10 Find the cube root of the following numbers through estimation

1) 10648
2) 91125

Simple equations

Grade 7 CBSE

Simple equations
Practice Set

Q1 Solve the following

a) 3x=18

b) 5m + 12=10

c) -2(x+2)=6

d) 5 -5(t+3)=10 

e)0.5(x+1)=0.5

Q2 Virat scored twice as many runs as Gautam. Together, their runs fell 4 short of 

double century. How many runs did each one score?

Q3 In a isosceles triangle ,the base angles are equal, the vertex angle is 50 degree. Calculate the base angles of the triangle.

Q4 Mamta thinks of number, if she adds 4 to it  and divide the sum by 2, she will get 4.

Q5 Chintan says  that he has 7 toffees more than 5 times the toffees Tinu has. If Chintan has 37 toffees. How many toffees does Tinu has?

Square roots and cube roots

Grade 8

(www.infate.in)

Practice Set :Square roots and Cube roots

Q1 Find the square root of the following by long division method.

1)0.0064

2)0.0004

3)7.29

4)150.0625

5) 1.69

Q2) Find the cube root of the following

1) -8

2) -64

3) 3375

4)-2274

5) -1

Q3 Find the cube root of the following numbers through estimation

1) 13824

2) 166375

Q4 By which smallest number must 7200 be multiplied to make it a perfect

cube?

Q5 Evaluate

Data handling and simple equations

Grade 7 CBSE

Practice Set 1 for data handling and simple equation

Q 1 A cricketer scores the following runs in eight innings: 58, 76, 40, 35, 46, 45, 0, 100 Find the mean score.

Q2 The marks (out of 100) obtained by a group of students in a science test are 85, 76, 90, 85, 39, 48, 56, 95, 81 and 75. Find the:
(i) The highest and the lowest marks obtained by the students.
(ii) Range of the marks obtained.
(iii) Mean marks obtained by the group

Q3The weight ( in kg) of 15 students of a class are:
38,42,35,37,45,50,32,43,43,40,36,38,43,38,47
1) find the mode and median of this data.
2) is there more than one mode?

Q4The performance of a student in 1st term and 2nd term is given. Draw a double bar graph choosing appropriate scale and answer the following

subject                        English  Hindi   Maths    Science    S.Science
1st term  (MM. 100)    67           72         88            81              73
2nd term  (MM (100)  70           65         95            85              55

Q5 Solve

1. 5x +3=13
2. 812x-312=12

Q6 Solve the following equation

a)-4(2+x)=8
b) 16=4 + 5(t+1)

Q7 Set up a equation: One fifth of a number minus 4 gives 3

Rational numbers

           Grade 8 

Practice Questions 

(Rational numbers and square roots)

Set 1

Q1 Solve the following
a)  

b)  

c)   

d)   

e) 

Q2 What number should be added to  to get -3?
Q3 Find 5 rational numbers between  and  .
Q4 Find the  least square number divisible by each one of 8,9 and 10
Q5 Find the Pythagorean triplet whose smallest number is 8.