Computer Graphics HAND BOOK 2013

MLR Institute of Technology

Laxma Reddy Avenue, Dundigal, Quthbullapur (M), Hyderabad – 500 043Phone Nos: 08418 – 204066 / 204088, Fax : 08418 – 204088

COURSE DESCRIPTION

Course No :Course Title : Computer Graphics

Course Overview

The subject computer graphics is aimed at learning the details of picture generation,

simulation, animation, modeling and rendering 3-D objects, in order to create objects

that look and behave as realistically as possible.

The course progresses through a designed set of units, starting with simple, general

applicable fundamentals and ending with more complex and specialized subjects.

This course also provides a strong base for image processing research for the students

COMPUTER GRAPHICS JNTUH SYLLABUS

UNIT -I Introduction, Application areas of Computer Graphics overview of graphics systems, video-display devices raster-scan systems, random scan systems graphics monitors and work stations and input device.

UNIT – IIOutput primitives : Points and lines, line drawing algorithms, mid-point circle and ellipse algorithms. Filled area primitives: Scan line polygon fill algorithm, boundary-fill and flood-fill algorithms

UNIT –III2-D geometrical transforms: Translation, scaling, rotation, reflection and shear transformations, matrix representations and homogeneous coordinates composite transforms transformations between coordinate systems.

UNIT – IV2-D viewing: The viewing pipeline, viewing coordinate reference frame, window to view-port coordinate transformation, viewing functions, Cohen-Sutherland and Cyrus-beck line clipping algorithms, Sutherland-Hodgeman polygon clipping algorithm.

UNIT – V3-D Object representation: Polygon surfaces, quadric surface, spline representation, Hermite curve, Bezier curve and B-Spline curves, Bezier and B-Spline surfaces. Basic illumination models, polygon rendering methods.

UNIT – VI 3-D Geometric transformations: Translation, rotation scaling, reflection and shear transforms composite transformations.3-D Viewing: viewing pipeline, viewing coordinates, view volume and general projection transforms and clipping.

UNIT – VIIVisible surface detection methods: Classification, back-face detection, depth-buffer, scan-line depth sorting, BSP-tree methods, area sub-division and octree methods.

UNIT – VIIIComputer animation: Design of animation sequence, general computer animation functions, raster animation, computer animation languages, key frame systems, motion specifications.

SUGGESTED BOOKS:T1: “Computer Graphics C version”, Donald Hearn & M. Pauline Baker, Pearson Education.T2: “Computer Graphics - Principles & Practice”, Second edition in C, Foley, Vandam, Friner, Hughes, Pearson Education.

REFERENCES:R1: “Computer Graphics”, Second edition, Donald Hearn & M. Pauline Baker, PHI/ Pearson EducationR2:”Computer Graphics Second edition”, Zhigand xiang, Roy plastock, Schaum’s outlines Tata Mc Graw hill educationR3: Procedural Elements for Computer Graphics, David F Rogers, Mc-GrawHill International, II Edition

Marri Laxman Reddy Institutions –COMPUTER GRAPHICS HAND BOOK– 2013 1

MLR Institute of TechnologyLaxma Reddy Avenue, Dundigal, Quthbullapur (M), Hyderabad – 500 043

Phone Nos: 08418 – 204066 / 204088, Fax : 08418 – 204088

SESSION PLANNER


UNIT WISE SESSION PLANNER

Academic Year: 2013-2014Semester: IV/I

Branch & Year: CSE-B & IV

UNIT NO: I Expected date of completion:

LectureNo.

Date Planned

Subject Topics / Sub-Topics

References Text Books Journals Websites

L0Introduction to Computer Graphics

T1,T2

L1Application areas of Computer Graphics

T1,T2

L2Overview of graphics systems video-display devices

T1,T2

L3 video-display devices T1,T2



L6Raster-scan systemsRandom scan systems

T1,T2

L7Graphics monitors and work stations Input devices

T1,T2

T1,T2

Total No. of Periods 08

Signature of Faculty Signature of HODDate: Date:



Phone Nos: 08418 – 204066 / 204088, Fax : 08418 – 204088

SESSION PLANNER

Branch & Year: CSE-A & IV

UNIT NO: II Expected date of completion:

LectureNo.

Date Planned


References Text Books Journals

Websites

L1Points and lines Line drawing algorithm

T1,T2

L2 Line drawing algorithms T1,T2

L3 Line drawing algorithms T1,T2

L4 Mid-point circle T1,T2

L5Mid-point circle

T1,T2

L6Ellipse algorithms

T1,T2

L7Ellipse algorithms

T1,T2

L8Filled area primitivesScan line polygon fill algorithm T1,T2

L9 Scan line polygon fill algorithm T1,T2

L10Boundary-fill and flood-fill algorithms

T1,T2






Phone Nos: 08418 – 204066 / 204088, Fax : 08418 – 204088

SESSION PLANNER


UNIT NO: III Expected date of completion:

LectureNo.

Date Planned



Websites

L1Introduction to 2D geometrical transforms, Translation T1

L2Scaling , rotation transformations

T1

L3 Reflection transformations T1

L4Shear transformations

T1

L5matrix representations and homogeneous coordinates T1

L6 Composite transforms T1

L7Transformations between coordinate systems

T1






Phone Nos: 08418 – 204066 / 204088, Fax : 08418 – 204088

SESSION PLANNER


UNIT NO: IV Expected date of completion:

LectureNo.

Date Planned



Websites

L1The viewing pipeline, viewing coordinate reference frame T1

L2Window to view-port coordinate transformation Viewing functions T1

L3Cohen-Sutherland line clipping algorithm

T1

L4Cohen-Sutherland line clipping algorithm

T1

L5 Cyrus-beck line clipping algorithms T1

L6Sutherland –Hodgeman polygon clipping algorithm

T1

L7Sutherland –Hodgeman polygon clipping algorithm

T1






Phone Nos: 08418 – 204066 / 204088, Fax : 08418 – 204088

SESSION PLANNER


UNIT NO: V Expected date of completion:

LectureNo.

Date Planned



Websites

L1 Introduction to 3D, Polygon surfaces T1

L2 quadric surfaces T1

L3 spline representation T1

L4Hermite curve

T1

L5Bezier curve

T1

L6 Bezier surfaces T1

L7B-Spline curves

T1

L8B-Spline surfaces

T1

L9Basic illumination models, polygon rendering methods

T1






Phone Nos: 08418 – 204066 / 204088, Fax : 08418 – 204088

SESSION PLANNER


UNIT NO: VI Expected date of completion:

LectureNo.

Date Planned



Websites

L1Introduction to 3-D Geometric transformations, Translation T1

L2 Rotation, scaling T1

L3 Reflection and shear transformations T1

L4 Composite transformations T1

L5 Viewing pipeline, viewing coordinates T1

L6View volume and general projection transforms

T1

L7 Clipping T1






Phone Nos: 08418 – 204066 / 204088, Fax : 08418 – 204088

SESSION PLANNER


UNIT NO: VII Expected date of completion:

LectureNo.

Date Planned



Websites

L1Introduction Visible surface detection methods, Classification T1

L2 Back -face detection T1

L3 Depth -buffer T1

L4 Scan -line T1

L5 Depth sorting T1

L6 BSP-tree methods, area sub-division T1

L7 Octree methods T1






Phone Nos: 08418 – 204066 / 204088

SESSION PLANNER


UNIT NO: VIII Expected date of completion:

LectureNo.

Date Planned



Websites

L1Introduction to Computer animation, Design of animation sequence T2

L2 general computer animation functions T2

L3 Raster animation, T2

L4 computer animation languages T2

L5 Key frame systems T2

L6 Motion specifications T2






SYLLABUS SESSION PLAN(Overall)


Phone Nos: 08418 – 204066 / 204088, Fax : 08418 – 204088

SESSION PLANNER Subject: COMPUTER GRAPHICS

Branch & Year: CSE-A & IV Semester: I Academic Year: 2013-14

Faculty: GOUSE SHEIKH

Unit No.

S.No.

TopicLecture

Number as per the period

Date Planned

Date Conducted

I

UNIT

1 Introduction to Computer Graphics L02 Application areas of Computer

GraphicsL1

3 Overview of graphics systems video-display devices

L2

4 video-display devices L35 video-display devices L46 video-display devices L57 Raster-scan systems Random scan

systemsL6

8 Graphics monitors and work stations & Input devices L7

II

UNIT

9 Points and lines Line drawing algorithm L8

10 Line drawing algorithms L911 Line drawing algorithms L1012 Mid-point circle L1113 Mid-point circle L1214 Ellipse algorithms

L13

15 Ellipse algorithms L1416 Filled area primitives

Scan line polygon fill algorithm L15

17 Scan line polygon fill algorithm L1618 Boundary-fill and flood-fill algorithms L1719 Introduction to 2D geometrical

transforms, TranslationL18


IIIUNIT

20 Scaling , rotation transformations L1921 Reflection transformations L2022 Shear transformations L2123 matrix representations and

homogeneous coordinatesL22

24 Composite transforms L2325 Transformations between coordinate

systemsL24

IVUNIT

26 The viewing pipeline, viewing coordinate reference frame

L25

27 Window to view-port coordinate transformation Viewing functions

L26

28 Cohen-Sutherland L2729 Cohen-Sutherland L2830 Cyrus-beck line clipping algorithms L2931 Sutherland –Hodgeman polygon

clipping algorithmL30

32 Sutherland –Hodgeman polygon clipping algorithm

L31

VUNIT

33 Introduction to 3D, Polygon surfaces L3234 quadric surfaces L3335 spline representation L3436 Hermite curve L3537 Bezier curve L3638 B-Spline curves L3739 Bezier surfaces L3840 B-Spline surfaces L3941 Basic illumination models, polygon

rendering methodsL40

VIUNIT

42 Introduction to 3-D Geometric transformations, Translation

L41

43 Rotation, scaling L4244 Reflection and shear transformations L4345 Composite transformations L4446 Viewing pipeline, viewing coordinates L4547 View volume and general projection

transformsL46

48 Clipping L47VII

UNIT49 Introduction Visible surface detection

methods, ClassificationL48

50 Back -face detection L49


51 Depth -buffer L5052 Scan -line L5153 Depth sorting L52

54 BSP-tree methods, area sub-division L53

55 Octree methods L54VIII

UNIT56 Introduction to Computer animation,

Design of animation sequenceL55

57 general computer animation functions L5658 Raster animation, L57

59 computer animation languages L58

60 Key frame systems L5961 Motion specifications L60

Note: Fortnightly verification by HOD

Signature of Faculty Signature of HOD


QUESTION BANKUNIT-I

DESCRIPTIVE QUESTION 1. Distinguish between the Raster scan system & Random scan system 2. Discuss the Flat-Panel Display devices3. Discuss the operation of Raster scan System with a neat sketch4. Discuss the operation of Random scan System with a neat sketch5. List the different Input devices .What are the application

OBJECTIVE QUESTIONS1. The study of techniques to improve communication between human & machine. [a]

a) computer graphicsb) System controlc) Frame bufferd) none

2. ___________ is the art or science of producing graphics images with the of computer.[a]

a) computer graphicsb) System controlc) Frame bufferd) none

3. The primary output device in graphics system is ____________. [a]a) video monitorb) audio controller c) radio controllerd) none

4. The ________ is the smallest addressable screen element. [b]a) Axis b) Pixel c) Scale d) none

5. A ________ is the contiguous piece of the computer memory. [b]a) Video monitorb) Frame bufferc) Video bufferd) None


6. The process of turning on the pixels for a line segment is called_______ [a]a) Vector generatorb) Audio generator c) Video generatord) none

7. The ___________ makes use of the electrostatic fields to focus & accelerate the electron beam. [c]

a) Video gunb) Magnetic gunc) Electron gund) None

8. The phosphor used in a graphics display are chosen for their color characteristics and _______ [b]

a) Resolution b) Persistencec) Aspect ratiod) All the above

9. Persistence is define as the time taken by the field emitted light from the screen to decay to __________ of its original intensity. [a]

a) one-tenthb) two-tenthc) tenthd) twenty

10. A phosphor with low persistence is useful for ________ [b]a) Art b) Animation c) Coloring d) None

11. The most common type of graphics monitor employing a CRT is the raster-scan display , based on _____________ technology.(TV)

12. The ________ is stored in a memory are called refresh buffer.(picture definition) 13. The _______ of a CRT is the number of times per second the image is redrawn.(refresh

rate)14. Random-scan display are also known as ________.(vector display)15. A unique problem with the shadow mask tube is that of ________(convergence)16. Shadow mask methods are commonly used in _________.(Raster scan system)17. The ________ behaves like a CRT with a extremely long persistence phosphor. (DVST)18. The ________ gun is used to store the picture pattern in DVST.(primary)19. The ________gun maintains the picture display in DVST.(Flood)20. _______is an example emissive display.(LED)21. _______ is an example of non-emissive display.(LCD)22. The _____ display is also called gas-discharge displays.(Plasma panels)


23. The plasma panel is an array of ________(Tiny neon tubes)24. The ______ display consists of diodes arranged in the form of rows & columns.(LED)25. The ______ are commonly used in the small systems, such as calculators, laptops

computer.(LCD)26. Joystick is a _______device.(locator)27. A _______ is small hand-held box used to position the screen cursor.(mouse)28. A _______is a ball that can be rotated with me fingers or palm of the hand to produce

screen-cursor movement. (Ans: trackball)29. __________provides six degrees of freedom(Ans: Space ball)30. A_______ consist of a small , vertical lever mounted on a base i.e moved to steer the

screen cursor movement(joystick)31. File animation requires _____ frames for each second in the animation sequence.(24)32. Animation is played black on video monitor ______frames per second are required.(30)33. The _____ is a technique of x-ray photography that allows cross-section views of

physiological system to be displayed. (Tomography).34. On a bit-and- white system with one bit per pixel, the frame buffer is commonly called

a________(bitmap).35. For systems with multiple bits per pixel , the frame buffer is often referred to

as______(pixmap).36. The return to the left of the screen ,after refreshing each scan line, is called the _______

retrace of the electron beam.(horizontal) 37. Colors CRts in graphics systems are designed as _______ monitor(RGB).38. An RGB color system with 24 bits for storage per pixel is generally referred to as

______system (full-color).39. The beam-penetration method for displaying color picture has been used with _____

monitors.(random-scan).40. The ______system in a CRT is needed to force the electron beam to converge into a

small spot as it strikes the phosphor.(focusing)

ASSIGNMENT QUESTIONS1. Draw the cross-sectional diagram of a CRT device. Identify the major components and

discuss their roles.2. List & explain the applications of CG

TUTORIAL QUESTIONS

1. .Assuming that a certain full-color (24-bit per pixel) RGB raster system has a 512 by 512 frame buffer, how many distinct color choices (intensity levels)would be available.


2.How much time is spent in scanning across each row of pixels during screen refresh on a raster system with a resolution of 1280 by 1024 and a refresh rate of 60 frames per second? Assume horizontal and vertical retrace times are negligible

UNIT-II

DESCRIPTIVE QUESTION

1. What is meant by aliasing? Discuss two antialiasing methods. 2. Compute the intermediate points on the straight line using the Bresenham’s algorithm, when the end points are given as input. 3. Show graphically that an ellipse has four-way symmetry by plotting four points on the ellipse: x = a cos θ + h, y = b sin θ + k where a =2, b=1, h=0 and k=04. When 8-way symmetry of circle is used to obtain a full circle from pixel coor-dinates generated from first octant, does overstrike occur? Where? 5. (a) Explain the DDA scan conversion algorithm for generating the points on Line segment, when two end-points are given as input.

(b) Digitize the line with end-points (20,10) and (30,18) using DDA algorithm 6. Explain the steps involved in Bresenham algorithm for line drawing. Demonstrate with an example. Discuss its merits and demerits 7 .(a) Write Bresenham’s algorithm for line generation which is suitable for any slope. (b) Using the above algorithm, generate the intermediate points of the line segment, if the two end-points are given as (30,18) and (20,10).

OBJECTIVE QUESTIONS1. Which of the following is true about the Bresnhams algorithm ANS[c]

a) There is only one division operationb) Rounding operation is performed inside the loopc) There are no intensive computations, except multiplication by 2d) Slope of the line is explicitly computed.

2. Comparing with circle ,ellipse generation requires more computation . this becauseANS[c]

a) Circle is described by an equationb) Shapes of the circle is regularc) Origin centered ellipse is not symmetrical x=y axisd) Aliasing problem is less in circle

3. If an algorithm uses the output of the pervious iteration , the computations of outputs in the current iteration , such algorithms are called as

ANS[b]a) Double-differencing algorithm b) Incremental algorithmc) Successive approximation algorithmd) Scan-line algorithm


4. In circle drawing algorithm ,when the circle is centered at an arbitrary point(x,y,c),how many reflections are required

ANS[a]a) 3b) 2c) 1d) 4

5. Circle is not symmetrical aboutANS[c]

a) x=-yb) y=0c) y=x+1d) x=0

6. to identify the interior regions of an object, which of the following rules is usedANS[c]

a) scan-lineb) convex-concave rulec) odd-even ruled) stack-rule

7. for storing edges coordinates in edge table which sorting algorithm is usedANS[a]

a) bucket-sortb) merge-sortc) heap-sortd) selection-sort

8. using odd parity rule, if the number of polygon edges crossed by a line, from a point P is odd a) P is an interior point

ANS[A]b) P is an exterior pointc) P is on the edge d) Odd parity rule alone is not sufficient to judge

9. Origin centered ellipse is symmetrical aboutANS[d]

a) Only x-axisb) Only y-axisc) X-axis , y-axis and x=-yd) Both x & y axis

10. For the efficient circle generation algorithm , for a raster scan display devices ,point on the periphery of circle are to be generated

ANS[b]a) Full


b) One octant(1/8)c) Halfd) one quadrant(1/4)

11. The _______algorithm for computing the incremental movement involve fractional number arithmetic.(DDA).

12. The Cartesian slope-intercept equation for straight line is __________(y=max+b)13. Bresenham’s algorithm uses only ________ that can be to display circles as other

curves(Incremental integer calculation)14. The initial value of decision parameter circle is _______(p0=5/4-r)

15. The _______is accomplished by calculating intermediate positions along the line path between two specified endpoint positions.(Line drawing)

16. For lines with m=1,∆x=∆y and the horizontal and vertical deflection voltages are_____(equal)

17. ________table contain all the information necessary to process the scan lines efficiently (sorted edges)

18. ________ is simply that the properties of one part of scene are related in some way to other parts of the scène o that the relationship can be used to reduce processing.(coherence)

19. A ________defined as the set of points that are all at a given distance r from a center position(x,y).(circle)

20. An _______ is an elongated circle(ellipse).

ASSIGNMENT QUESTIONS1. What are the steps involved in Bresenham’s line drawing algorithm for |m| > 1, where m is slope of the line. Generate all raster points on the line segments, if the two end-points are given as (10, 20) and (18, 30) using the above algorithm2. a) Explain the steps involved in scan-line polygon-fill algorithm. Illustrate with an example polygon and the corresponding sorted edge table. (b) Explain the steps involved in

i. odd-even rule and ii. Non-zero winding number rule, which are used for and carrying out inside-outside test.

TUTORIAL QUESTIONS

1.Digitize the line with end-points (20, 10) and (30,18) using DDA algorithm

2.Generate all raster points on the line segment, if the two end points are given as (10,20) and (18,30) using Bresenham’s line drawing algorithm

3.The circle with radius 5, demonstrate midpoint circle algorithm by determining along with radius along the octant in the first quadrant from x=0 to x=y.


4.Show graphically that an ellipse has four way symmetry by plotting four points on the ellipse.X=acosө+hY=bsinө+k. Where a=2,b=1,h=0 and k=0


UNIT-III

DESCRIPTIVE QUESTION 1. (a) List the basic transformation techniques. What are their respective mathe-

matical and matrix representations? (b) Prove or disprove that two successive rotations in 2-D space are

commutative 2. (a) Derive the transformation matrix for rotation about origin. (b) Explain the terms: i. Homogeneous Coordinates ii. Rigid-body transformations iii. Composite transformations. 3. (a) List the basic transformations which cause the physical distortion in the transformed

object. (b) An object point P(x,y) is translated in the direction U = aI + bJ and simultaneously an observer moves in the direction U. Show that there is no apparent motion of the object point from the point of view of obsever.

4.(a) Prove that a uniform scaling (sx = sy) and a rotation form a commutative pair of operations, but that, in general, scaling and rotation are not commutative.

(b)Derive the transformation matrix for rotation about origin.

5. Is it possible to subject the following transformations on the characters, which are generated by a hardware character generator? (a) a rotation (b) a scaling (c) a translation 6.(a) Perform a 45 degree rotation of a triangle A(0,0), B(1,1) and C(5,2) about P(-1,-1).

(b) Magnify the triangle with vertices A(0,0), B(1,1) and C(5,2) to thrice its sizewhile keeping B(1,1) fixed.

7. (a) Describe the transformation that rotates an object point Q(x,y),degrees about a fixed center of rotation p(h,k). (b) Magnify the triangle with vertices A(0,0), B(1,1) and C(5,2) to twice its size,

while keeping C(5,2) fixed.

OBJECTIVE QUESTIONS1. if every point on the object is translated by the same amount ,such transformation is

called asANS[a]

a) rigid-bodyb) transformation with deformationc) deformation in translationd) tightly coupled transformation


2. if the sx and sy , are scaling factors applied in x and y directions respectively , on P(x,y) the output point coordinates after applying scaling operation is

ANS[d]a) x1=1/xsx,y=y.sxb) b)x1=x+sx,y1=y+syc) x1=x.sx,y1=1/y.syd) x1=x.sx,y1=y.sy

3. The transformation that alters the size of an object. [a]a) Scalingb) Translation c) Rotation d) Shearing

4. The transformation that cause the image to slant [d]a) Scalingb) Translation c) Rotation d) Shearing

5. The transformation that applied to an object by repositioning its along a straight-line path from one coordinate location to other

a) Scalingb) Translation c) Rotation d) Shearing

6. The reflection about x-axis is given by matrix [a]a) 1 0 b) -1 0 c) -1 0 d)0 1

0 -1 0 1 0 -1 1 07. The reflection about y-axis is given by matrix [b]

a) 1 0 b) -1 0 c) -1 0 d)0 10 -1 0 1 0 -1 1 0

8. The reflection about origin is given by matrix [c]a) 1 0 b) -1 0 c) -1 0 d)0 1

0 -1 0 1 0 -1 1 09. The reflection about x=y is given by matrix [d]

a) 1 0 b) -1 0 c) -1 0 d)0 10 -1 0 1 0 -1 1 0

10. The reflection about y=x is given by matrix [d]a) 1 0 b) -1 0 c) -1 0 d)0 -1

0 -1 0 1 0 -1 -1 011. The homogenous coordinate transformation matrix for a translation of tx, ty is [a]

a) 1 0 0 b) 1 0 0 c) 0 1 0 d) none0 1 0 1 0 0 0 0 1tx ty 1 tx ty 1 1 tx ty


12. If the scaling factors sx & sy are equal ,then the scaling transformation matrix [a]a) A constant multiplied with unit matrix b) Becomes rotation matrixc) Becomes reflection matrix d) Resembles unit matrix

13. If the rotation about an arbitrary point is to be performed, what is the sequence of operations to achieve the desired effect [d]

a) Translate & rotateb) Rotate , Translate & Rotatec) Rotate , Translate & Scaled) Translate ,Rotate & Translate

14. If the object is to be rotate 30® anticlock wise , keeping the object stationary , the same effect achieved by rotating the coordinate system

[d]a) 60® in anti-clock wiseb) 60® in clock-wisec) 30® in anti-clock wised) 30® in clock-wise

15. The scaling factor in the scaling translation are [b]a) Positive and less than oneb) Always positivec) Either positive or negatived) Positive and greater than one

16. Two successive translation can be represented as[d]a) Difference of two translation matricesb) Addition of two translation matricesc) A combination of translation & scalingd) A single translation matrix

17. Which of the following is a rigid body transformation [a]a) Shearb) Translation c) Rotation d) None

18. Two successive translation is [a]a) Commutativeb) Non-commutativec) Distributived) Commutative only if in both times, the displacement applied is in one

direction 19. The matrix for rotation about the origin when the rotation angle is Θ is given by

[a]


a) cos θ -sin θ b) -cos θ sin θ b) cos θ -sin θd) none

sin θ cos θ sin θ cos θ sin θ cosθ

20. the transformation matrix for x-direction shear relative to the x-axis is [b]a) 1 0 shx b) 1 shx 0 c) 1 0 0 d) 1 0 0

0 1 0 0 1 0 0 1 0 shx 1 00 0 1 0 0 1 0 0 shx 0 0 1

21. the transformation matrix for x-direction shear relative to the x-axis is [d]a) 1 0 shx b) 1 shx 0 c) 1 0 0 d) 1 0 0

0 1 0 0 1 0 0 1 0 shx 1 00 0 1 0 0 1 0 0 shx 0 0 1

ASSIGNMENT QUESTIONS1. Prove that the multiplication matrices for each of the following sequence of operations

is commutative i. Two successive rotations

ii. Two successive translationsiii. Two successive scalings.

2. (a) Show that the composition of two rotations is additive by concatenating the matrix representations for

R (θ1) R (θ2) = R (θ1 + θ2)(b) Give a brief note about the following transformations.

i) Reflection ii) Shear3. Scale the given triangle to twice and rotate it by 90 .The triangle ABC Coordinates are A(2,2,),B(2,8),C(4,4).Implement the above transformations with respect to point B

TUTORIAL QUESTIONS

1.Show the transformation matrix for reflection about line y=-x is equivalent to reflection relative to the y-axis followed by a counter clockwise rotation of 900

2.Perform a 45 degree rotation of a triangle A(0,0), B(1,1) and C(0,1) about P(-1,-1).Magnify the triangle with vertices A(0,0), B(1,1) and C(5,2) to twice its size while keeping C(5,2) fixed

3.Given 3x3 homogeneous coordinate transformation matrix which will have the same effect ae each of the following transformation techniques.a) scale the image to be twice as large and then translate it 1 unit to the left.b) rotate counter-clockwise by 900 and then scale the x-direction to be on-half as large

4.Prove that a uniform scaling (sx = sy) and a rotation form a commutative pair of operationsObtain the reflection of the point A(10,10) about y=x+2


UNIT-IV


1. (a) what are the stages involved in two-dimensional viewing transformation Pipeline. Explain briefly about each stage.

(b) What is parametric representation of a line? What is its form? What are the Typical range of values for parametric variable.

2. (a) What are the stages involved in Window-to-viewport coordinate transforma-tion. Explain about each stage. (b) What is the procedure followed in point clipping with respect to a

rectangular window. 3. (a) Write procedure copy-segment (old-segment, new-segment) which copies Old segment to new segment. (b) Distinguish between window and view port. 4. Find the normalization transformation that maps a window whose lower left corner is at

(1,1) and upper right corner is at (3,5) onto (a) a view port that is the entire normalized device screen and (b) a view port that has the lower left corner at (0,0) and upper right corner at (1/2,1/2)

5. Explain the following terms with reference to 2-D displays:a. Viewing transformationb. Windows and view port

6. Compute the transformation matrix that maps a window with (wxmin,wxmax)=(2,2)and (wxmax,wymax) =(4,6) onto a normalize device coordinated which has lower left corner at (0,0) and upper right corner at (1,1)

7. Let R be a rectangular window whose lower left corner is at L (-3,1) and upper right- hand corner is at R(2,6). If the line segment is defined with two end points with A (-4,2) and B (-1,7).

(a) The region codes of the two end points,(b) Its clipping catezory and(c) Stages in the clipping operations using Cohen-Sutherland algorithm.

6. Explain the algorithm for line clipping by Cohen-Sutherland algorithm. Demon-strate with an example all the three cases of lines

(a) Find the general form of the transformation N which maps a rectangular window with x extent xwmin to xwmax in the x-direction and y extent ywmin to ymax in the y-direction on to a rectangular view port with x extent xvmax to xvmax and y extent yvmin to yvmax. (b) Distinguish between Cohen-Sutherland outcode and Sutherland-Hodgeman al-gorithm.

9. (a) List the algorithms which are suitable for line clipping when the clippingpolygon is non-rectangular window. (b) Explain about the following categories of lines with respect to rectangularclipping window.


i. Completely visibleii. Clipping-candidate

iii. Completely invisible. 10 . Explain the Cohen-Sutherland algorithm for finding the category of a line segment.Show clearly how each category is handled by the algorithm

OBJECTIVE QUESTIONS1. A rectangular area with its edges parallel to the axis of NDCS is used to specify a

sub-region of the display area that embodies the image. This rectangular areas is called as [c]

b) Normalized device

c) Physical device

d) View-port

e) Window

2. Which of the following bits (from right) is set to 1 in cohen-sutherland algorithm if Y<Ymin

a) bit 3 b) bit 1 c) bit 4 d) bit 2 [a]3. The logical AND operation performed on the 4-bit codes correspond to the end-

points of the line segment consists same non-zeros, then the line segment is.[b]

a) Partially visible or completely invisible

b) Completely invisible

c) Partially visible

d) Completely visible

4. The dot product of two vectors is positive then the angle between those two vectors is defined in the range of [c]

a) 0<Θ<90

b) 90< Θ<270

c) 0<Θ<90 & 90< Θ<270

d) 0< Θ<180

5. The dimensions of normalized space in viewing transformation are[d]


a) 640 x 480

b) Xmax x Ymax

c) Workstation dependent

d) 1 x 1

6. If the clipping polygon (window ) consists of n edges, how may iterations are to be performed in outermost loop [a]

a) n b) n-1 c) window dependent d) 1

7. The second bit from right, in four bit code of Cohen Sutherland algorithm indicates the [b]

a) Above region b) Right region c) below regiond)left region

8. The equation for finding the coordinate value at the intersection point for the line segment (x1,y1) to (x2,y2) with x=xmax window edge is

a) Y=(wxmax-y1)*m+x1

b) Y=(wxmax-x1)*m+y1

c) Y=(wxmax-y1)*m+x2

d) Y=(wxmax-x1)*m+x2

9. If a point is within the clipping rectangle, four bit code of the point according to cohen-sutherland algorithm is ]a]

a) 0 0 0 0 b) 1 0 0 0 c) 1 1 1 1 d)010010. Which of the following 4 bit codes cannot be assigned to any region in cohen-

sutherland algorithm [a]

a) 0011 b)0100 c) 0000 d)011011. The method for selecting and enlarging portions of a drawing is______[a]a) windowing b) clipping c) viewport d) none12. The ______ defines where is to be displayed [c]a) Windowing b) clipping c) view port d) none13. The ____ defines what to be viewed. [b]a) windowing b) window c) view port d) none14. ______algorithm is used for polygon clipping. [c]a) cohen-sutherland b) sutherland Hodgemman c) Both a & b d) none15. ______ polygons are correctly clipped by the sutherland Hodgemman. [b]a) Window b) convex c) view port d) none


16. By varying the size of _______ , we change the size & proportions of displayed object [c]a) Windowing b) window c) view port d) none17. the method that can be used to test lines for total clipping is to perform the logical ____ operation with both region [b]a) OR b) AND c) NOR d) none18. the region which an object is clipped is called a) window b) clip window c) viewport d)none19. a __ area selected for display is called a window [a]a) world-coordinate b) view port c) origin d) none20. any procedure that identifies those portions of a picture that are either inside or outside of a specified region of space is referred to as a_______ algorithm [b]a) Window b) clipping c) view port d) none

ASSIGNMENT QUESTIONS1. (a) What are the stages involved in Window-to-viewport coordinate transformation.

Explain about each stage.(b) What is the procedure followed in point clipping with respect to a rectangular window

2. a) Find the normalization transformation that maps a window whose lower left corner is at (1,1) and upper right corner is at (3,5) onto (a) a view port that is the entire normalized device screen (b) a view port that has the lower left corner at (0,0) and upper right corner at (1/2,1/2) 3. Explain the algorithm for line clipping by Cohen-Sutherland algorithm & Sutherland- Hodgeman algorithm.

TUTORIAL QUESTIONS

1.Find the normalization transformation that maps a window whose lower left corner is at (1,1) and upper right corner is at (3,5) onto

(a) a view port that is the entire normalized device screen and (b) a view port that has the lower left corner at (0,0) and upper right corner at(1/2,1/2)

2.Let R be a rectangular window whose lower left corner is at L (-3,1) and upper right- hand corner is at R(2,6). If the line segment is defined with two end points with A (1,-2) and B (3,3).(d) The region codes of the two end points,(e) Its clipping category(f) Stages in the clipping operations using Cohen-Sutherland algorithm.

3.Find the normalization transformation N that uses the rectangle A(1,1), B(5,3), C(4,5) and D(0,3) as a window and the normalized device screen as a viewport


UNIT-V


1. (a) Distinguish between boundary representation and space-partitioning representation of solid object representation schemes. (b)List and describe the polygon tables representation for polygon surfaces of a 3-D object. Give an example. 2.(a) Explain about different representation of polygon meshes in surface modeling. (b) What are the characteristics of parametric cubic curves? What are its advantages?

3. (a) Determine the blending functions for uniform periodic B-spine curve for d=6.(b) Write the equation for the basic illumination model using a single point light source and constant surface shading for the faces of a specified polyhedron.

4. (a) What is the blending function used in Bezier’s method for curve generation?

Explain the terms involved in it? (b) What are the properties of Bezier curve?

5. (a) Distinguish zero-order, first-order and second-order continuity. (b) What is the organization of control points followed in Bezier’s method to ensure second order continuity?

(c) What are the properties of Bezier’s curve? 6. Explain the procedure to design two-dimensional, cubic Bezier curve shapes that have

first order piece-wise continuity.

7. (a) What are the advantages of B-splines over Bezier Curves?(b) Differentiate between interpolation and approximation in spline representations. (c) Give the applications of raster scan graphics.

8.(a)State the blending function suitable for Bezier surface and explain the terms involved In it

(b)Demonstrate that Bezier curve is axis independent.

9.(a)Determinetheblending functions for uniform periodic B-spine curve for d=5. (b) Give a note about Phong specular-reflection model.

10. (a) Represent a cube using an explicit edge listing method. (b) Show that the nth degree B-spline basis function Bc,n(x) satisfying Bc,n(x) =

0 if x < ti or x > ti+n+1.

OBJECTIVE QUESTIONS


1. ________ is the polynomial with maximum power 3 [a]

a) Cubic polynomialb) Quadric polynomialc) Binomial polynomiald) Acute polynomial

2. A polynomial curve using a parameter called as [a]

a) Parametric polynomial curveb) Cubic polynomial curvec) Quadric polynomial curved) Solid polynomial curve

3. A set connected polygon ally bounded planar surface is called as[a]

a) polygon meshb) solid objectc)3D objectd) Mesh-cube

4. ____ is not a common represented of 3D surface [d]

a) polygon surfaceb) parametric surfacec) quadratic surfaced) neural surface

5. _______surfaces are defined on a plane, then the lanes normal is computed as.[c]

a)cubic surface b) Bi-cubic surfacec) quadratic surfaced) binomial surface

6. _____surface are generated by cubic polynomial in both u and v parameter [b]

a) cubic b) Bi-cubic c) Quadratic d) Binomial

7. Of Q(t) is a cubic polynomial , then the tangent vector of the curve is [b]

a)[Q(t)2 b) Q’(t) c)1/Q(t) d) Q2(t)

8. The number of coefficient in a cubic polynomial [b]

a) 3 b) 4 c) any number d) 19. _____ is the basis matrix of Hermites curve [a]


a)2 -2 1 1 b)2 -2 1 1 c)1 0 0 0 d) none -3 3 -2 -1 3 3 -2 -1 0 0 1 0 0 0 1 0 0 0 1 0 3 3 -2 -1 1 0 0 0 1 0 0 0 2 -2 1 1

10. The Horner’s rule for factoring polynomial f(t)=at3+bt2+ct+d is [b]

a)((t+1)a+b)+c)+db) ((at+)t+c)t+dc) ((at+1)t+c)t+dd)((a+1)t+b)+c)+d

11. In the following curves, _______curves require, for its definition two end points & two end point tangent vectors [a]

a) Hermit curveb) Bezier curvec) B-splined) none

12. in the B-splines algorithm , the B stands for [a]a) Basis b) black c) bold d) none13. the range of parametric variable ‘t’ used in Bezier curve is [c]a)1,1 b)1,0 c) 0,1 d) none14. _____ light has no spatial or directional characteristics [a]a) ambient b) ray light c) illuminationd) none15. the _____ model ,sets the intensity of specular reflection proportional to cosns0

[b]a) increase b) phong c) song d) none16. the range of values for the reflection coefficients followed in illumination model isa) 1 to 2 b)0 to 1 c) -1 to 1 d) 0 to a [b]17. ____ draw back is observed in Gouraud shading [a]a) mach bands b) intensity c) density d) none18. ___ is the principle of Gouraud shading [b]a) vector b) intensity interpolation c)surface d) none19. _____ is the principle of constant intensity shading [c] a) vector b) intensity interpolation c) single intensity d) none20. surfaces that are shiny and the light sources create highlight or bright spots called

[a]a) specular reflection b)Distributed reflection c)diffuse d) ambient

ASSIGNMENT QUESTIONS1. What is the blending function used in Hermite curve method generation? Explain the

terms involved in it? What are the properties of Hermite curve?2. (a) Describe the properties of B spline approximations.

(b)What is the difference between Bezier curve and B-spline curve?

TUTORIAL QUESTIONS 1.What is the blending function used in Bezier’s method for curve generation?Explain the terms involved in it?What are the properties of Bezier curve?


2.Different types of B-Spline curves


UNIT-VI


1. Prove that the multiplication of three-dimensional transformation matrices for eachof the following sequence of operations is commutative.(a) Any two successive translations(b) Any two successive saling operations(c) Any two successive rotations about any one of the coordinate axes.

2. A pyramid defined by the coordinates A(0, 0, 0), B(1, 0, 0), C(0, 1, 0) and D(0,

0, 1) is rotated 450 about the line L that has the direction V=J+K and passingthrough point C(0, 1, 0). Find the coordinates of rotated figure.

3. Explain the Procedure to clip three-dimensional planes against a regular parallelepiped by extending Sutherland-Hodgeman algorithm for polygon clipping.

4. (a) Derive the quaternion rotation matrix for rotation about an arbitrary axis inthree-dimensional domain.(b) Classify the perspective projections and explain about each.

5. Given a unit cube with one corner at (0, 0, 0) and the opposite corner at (1, 1,1), derive the transformations necessary to rotate the cube by θ degrees about themain diagonal (from (0, 0, 0) to (1, 1, 1) in the counter clock-wise direction whenlooking along the diagonal toward the origin.

6. (a) Give a brief account on three-dimensional rotations.(b) Show the sequence of transformations for rotating an object about an axisthat is parallel to the x axis

7. Derive transformation matrix for rotation about an arbitrary axis

8.(a)Write 3 dimensional homogeneous matrix to rotate by degrees about the line passing through the point (0,0,0) and (1,0,1)

(b)Write a note on smooth shading. 9.Consider a line from the origin of a right-handed coordinate system to the point P(x,

y, z). Find the transformation matrix needed to rotate the line in to the positivez-axis. Follow the below mentioned sequence to achieve the desired transformationmatrix:(a) Rotate about the z-axis into the (x, z) plane,(b) Then rotate about the y-axis in to the z-axis.

10. (a) What is the procedure for reflecting an about an arbitrarily selected plane.(b) What are the characterstics of perspective projections?


OBJECTIVE QUESTIONS1. In 3D scaling transformation for transition with a unit along x-axis & b units along y-

axis & c units along z-axis is [b]

a)1 0 0 0 b)1 0 0 0 c) a b c 1 d) none 0 1 0 0 0 1 0 0 0 0 0 1 0 0 1 0 0 0 1 0 0 0 1 0 -a b 0 1 a b c 1 1 1 1 1

2. If the axis of rotation is X ,then the direction of positive rotation is [a]

a)y to z b) z to x c) x to y d) y to x3. If the axis of rotation is Y ,then the direction of positive rotation is [b]

a)y to z b) z to x c) x to y d) y to x 4. If the axis of rotation is Z ,then the direction of positive rotation is [c]

a)y to z b) z to x c) x to y d) y to x 5. In 3D space rotation of an object is done about [b]

a) a point b) an axis c) a plane d) a hyper plain6. In 3D scaling , all the three scaling parameters. [b]

a) must be positive & greater than oneb)must be positivec) either positive or negatived)n one

7. The x-shear maintains the coordinates of which of the following directions constant[d]

a) x b) y c) z d)y and z8. The y-shear maintains the coordinates of which of the following directions constant

[c]

a) x b) y c) x and z d)z9. The x-shear maintains the coordinates of which of the following directions constant

[b]

a) x b) x and y c) z d)y and z10. If an object is reflected about xy plane , ten the coordinates of which axis do not

change [d]

a)x b) y c) z d) x and y11. If an object is reflected about xy plane , ten the coordinates of which axis do change

[c]

a)x b) y c) z d) x and y12. ____ means of technique of projecting 3D object to 2D screen [a]


a) projection b)elevation c) display d) none13. _____ show the true image ,size & shape of the object [b]a) relative projection b)parallel Projection c) display d) none14. a parallel projection preserves ______ of object [a]a) relative projection b)parallel Projection c) display d) none15. when the projection are perpendicular to the view plane then it is called [c]a) relative projection b)parallel Projection c) orthographics projection d) none16. ortho graphics projections are often used to produce the front,side and ___ of an object [c]a)side view b) bottom view c) top view d) none17. a toportho graphic projection is called a _______ [a]a) Plainview b) bottom view c) top view d) none

ASSIGNMENT QUESTIONS1. Consider a line from the origin of a right-handed coordinate system to the point P(x, y, z). Find the transformation matrix needed to rotate the line in to the positive z-axis. Follow the below mentioned sequence to achieve the desired transformation matrix:

(a) Rotate about the z-axis into the (x, z) plane,(b) Then rotate about the y-axis in to the z-axis.

2. Classify the projections. Explain the properties of each. Distinguish the parallel projection and Perspective Projection view volumes. Give suitable examples

3. The pyramid defined by the coordinates A(0,0,0), B(1,0,0), C(0,1,0) and D(0,0,1) is rotated 15 deg. About the line L that has the direction V=J+K and passing through the piont C(0,1,0). Find the coordinates of the rotated pyramid.TUTORIAL QUESTIONS

1.Find the transformation matrix which align the vector V=i+j+k with the vector N=2i-j-k.Prove that the multiplication of 3D transformation matrices for each of the following sequence of operation is commutative.

2.a) Any two successive translations.b) Any two successive scaling operation c)any two successive rotations about any one of the coordinate axes

3.A pyramid defined by the coordinates A(0, 0, 0), B(1, 0, 0), C(0, 1, 0) and D(0, 0, 1) is rotated 450 about the line L that has the direction V=J+K and passing through point C(0, 1, 0). Find the coordinates of rotated figure


UNIT-VII

DESCRIPTIVE QUESTION 1.(a) Distinguish between object-space and image space methods of visible surface

detection algorithms. Give examples for each.(b) Given points P (1, 2, 0), P (3, 6, 20) P (2, 4, 6) and a view point C (0, 0, -10),determine which points obscure the others when viewed from C.

2. (a) Explain the depth-buffer (z-buffer) algorithm for hidden surface removal.

(b) Explain the procedure to compute the z-values in two successive locations ina scan-line and intersection positions on two successive scan lines.

3. (a) Assuming that one allows 224 depth value levels to be used, how much memory would a 1024 × 768 pixel display requires to store the z-buffer. (b) How can the amount of computation required by the scan-line method be reduced?

4. (a) Write an algorithm to that would test a given plane surface against a rectangular area to decide whether it is a surrounding, overlapping, inside or outside surface.

(b) Distinguish depth-sort and z-buffer algorithms.

5. (a) Explain how the depth values are computed in scan-lines?(b) What are the merits and demerits of z-buffer?

6. Implement the depth-buffer method to display the visible surfaces of a given poly-hedron. How can the storage requirements for the depth buffer be determined fromthe definition of the objects to be displayed?

7. Outline the z-buffer algorithm. List the advantages and disadvantages of the z- buffer algorithm.

8. (a) Discuss about the scan line method for visible surface detection. (b) Compare and contrast depth-buffer and depth-sort methods.

9 .(a) Illustrate the procedure for implementing area-sub division method.

(b) Explain how the BSP-tree method is implemented for visible surface detection.

10. (a) Explain about the octree method for visible surface detection. (b) Write an algorithm for back-face detection using a perspective projection to view visible faces of a convex polyhedron.

OBJECTIVE QUESTIONS1. Coherence methods are used to take advantage of [a]

a)Regularities in a scene


b) irregularities in a scenec)Computational power of computerd) Precision of image capturing

2. Coherence property is used un visible surface detection algorithms to [a]a) speed-up the processb) increase the precisionc) Speed-up the process& increase the precisiond) none

3. The equation of polygon surface is Ax+By+Cz+D=0. Examining of which coefficient is sufficient to determine the visibility of polygon surface [c]a) A b) B c) C d) D

4. Another name for depth-buffer method for visible surface [a]a) z-buffer algorithm b) Depth-sorting algorithmc) scan-line algorithmd) Painters algorithm

5. In Z-Buffer algorithm , the Z-Buffer stores the value of [b]a) Depthb) Intensityc) Depth & Intensityd) Intensity & interaction number

6. In which of the following algorithm , the object surfaces need not be polygon [a]

a) Z-Bufferb) List-priority c) Depth-Sortd) Binary space algorithm

7. In which of the following algorithm the polygons in the scene are grouped into cluster [b]a)List priority algorithmb) BSP tree algorithmc) Scan-line algorithmd)Z-Buffer algorithm

8. In which of the following algorithm, is well suited when the view point changes[b]a)List priority algorithmb) BSP tree algorithmc) Scan-line algorithmd)Z-Buffer algorithm

9. The correct priority order polygon list can be obtained using ____in BSP tree [a]a) in order tree walkb) Pre-order tree walkc) Post-Order tree walkd) BFS tree walk

10. How many buffers are used in Z-Buffer algorithm [b]a) 1 b) 2 c)3 d) 4


ASSIGNMENT QUESTIONS1. a)Outline the z-buffer algorithm. List the advantages and disadvantages of the z-buffer

algorithm.b)Explain Painter’s Algorithm

2. (a)What are the advantages of mini max test in z-buffer algorithm (b)A polygon has a plan equation ax + by + cz + d = 0. Suppose that we know the value of ‘z’ at a point (x,y). What is the easiest way to calculate the value of z at (x + 1,y) and at (x,y +1)?

TUTORIAL QUESTIONS

1. Given points P (1, 2, 0), P (3, 6, 20) P (2, 4, 6) and a view point C (0, 0, -10), determine which points obscure the others when viewed from C.2. Assuming that one allows 256 depth value levels to be used, approximately how much memory would a 512 × 512 pixel display require to store the Z-buffer?


UNIT-VIII

DESCRIPTIVE QUESTION 1.What are the steps in design of animation sequence? Describe about each step briefly.2. (a) List and explain about the steps of animation. (b) What are the various types of interpolation used in animation. 3. Discuss about the problems peculiar to animation and propose suitable solutions. 4. What are the steps in design of animation sequence? Describe about each step brief (a)What is raster animation? Describe it. (b)List the typical tasks for which the animation functions are defined in animation anguages. 5. What are the issues involved in design of a story board layout with accompanying key Frames for an animation of a single polyhedron. List the categories of animation Languages. Briefly explain the characteristics of each of these languages.

6. Discuss about the techniques to achieve the simple animation effects. 7. How the morphing effects are implemented in key frame system bared animation languages?

8.What are the issues involved in design of a story board layout with accompanying key frames for an animation of a single polyhedron.

9. List the general-purpose animation languages. Explain the characteristics any are language.

10. (a) Explain how the linear interpolation is implemented when the key-frame positions of an object are given.

(b) Describe linear list notation of animation languages

OBJECTIVE QUESTIONS1. Application of computer-generated animation are [d]

a)Advertisingb) Scientificc) Trainingd) All the above

2. Many applications of computer animation require _____display [c]a) Random b) Regularc) Realisticd) Motive

3. ____define the motion sequence as a set of basic events that are to take place [b]a) Action b) Storyboard c) Frame d) none

4. Films requires ____frames per second [b]a) 34 b) 24 c)23 d) 25

5. Within each frame, each object is positioned according to the ___for that frame[a]

a) time b) Shape c)Size d) Orientation


6. In the films , graphics terminals are refreshed at the rate of ____ frames per second[c]

a) 30 to 80 b) 60 to 80 c)30 to 60 d)30 to 1207. A single-arm robot has ___degrees of freedom [b]

a)two b) six c) ten d) twenty 8. Morphing methods can be applied to any motion or transition involving a change in

[d]a) size B)Color c)Texture d)Shape

9. ____ forces affects object motion [d]a) Magneticb) Gravitationalc) fractiond) all the above

10. _______requires the specification of the forces that produce the velocities & accelerations [a]a)Dynamicsb)Kinematicsc) Inverse dynamicsd) none

ASSIGNMENT QUESTIONS1. (a) Discuss about the techniques to achieve the simple animation effects.

(b) What are the various types of interpolation used in animation?2. What are the steps in design of animation sequence? Describe about each step brief (a)What is raster animation? Describe it.

(b)List the typical tasks for which the animation functions are defined in animation languages.TUTORIAL QUESTIONS

1.What are the various types of interpolation used in animation2.The typical tasks for which the animation function are defined in animation languages


Computer Graphics HAND BOOK 2013

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Transcript of Computer Graphics HAND BOOK 2013