Computer Graphics Hand Book of IV CSE JNTUH 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

UNIT WISE PLANNER FOR ACADEMIC YEAR 2012-2013

S.No. Unit No. DescriptionTOTAL NO. OF

LECTURES

1. IIntroduction &Application areas of Computer Graphics 8

2. II Output primitives 10

3. III 2-D geometrical transforms: 7

4. IV 2-D viewing 7

5. V 3-D Object representation 9

6. VI3-D Geometric transformations: 3-D Viewing

7

7. VII Visible surface detection methods 7

8. VIIIComputer animation

6



SYLLABUS SESSION PLAN(Overall)

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

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

S.No.

Unit No.

Topic

Lecture Number

as per the period

Date Planned

Date Conducted

1

I

UNIT

Introduction L02 Application areas of Computer Graphics L13 Overview of graphics systems video-display devices L24 video-display devices L35 video-display devices L46 Tutorial T17 video-display devices L57 Raster-scan systems Random scan systems L68 Graphics monitors and work stations & Input

devices L7

9 Class Test CT10

II

UNI

T

Points and lines Line drawing algorithm L811 Line drawing algorithms L912 Tutorial T213 Line drawing algorithms L1014 Mid-point circle L1115 Mid-point circle L1216 Ellipse algorithm L1317 Ellipse algorithms L1418 Tutorial T319 Filled area primitives

Scan line polygon fill algorithmL15

20 Scan line polygon fill algorithm L1621 Boundary-fill and flood-fill algorithms L1722 Class Test CT23 Introduction to 2D geometrical transforms, L18


III

UNIT

Translation24 Scaling , rotation transformations L1925 Reflection transformations L20

26 Tutorial T427 Shear transformations L2128 matrix representations and homogeneous

coordinatesL22

29 Composite transforms L2330 Transformations between coordinate systems L2431 Class Test CT32

IVUNIT

The viewing pipeline, viewing coordinate reference frame

L25

33 Tutorial T534 Window to view-port coordinate transformation

Viewing functionsL26

35 Cohen-Sutherland L2736 Cohen-Sutherland L2837 Cyrus-beck line clipping algorithms L2938 Sutherland –Hodgeman polygon clipping algorithm L3039 Tutorial T640 Sutherland –Hodgeman polygon clipping algorithm L3141 Class Test CT42

VUNIT

Introduction to 3D, Polygon surfaces L3243 quadric surfaces L3344 spline representation L3445 Hermite curve L3546 Tutorial T747 Bezier curve L3648 B-Spline curves L3749 Bezier surfaces L3850 B-Spline surfaces L3951 Basic illumination models, polygon rendering

methodsL40

52 Tutorial T853 Class Test CT54

VI

Introduction to 3-D Geometric transformations, Translation

L41

55 Rotation, scaling L4256 Reflection and shear transformations L43


UNIT

57 Composite transformations L4458 Viewing pipeline, viewing coordinates L4559 Tutorial T960 View volume and general projection transforms L4661 Clipping L4762 Class Test CT63

VIIUNIT

Introduction Visible surface detection methods, Classification

L48

64 Back -face detection L4965 Depth -buffer L5067 Tutorial T968 Scan -line L5169 Depth sorting L52

70 BSP-tree methods, area sub-division L53

71 Octree methods L5472 Introduction to Computer animation, Design of

animation sequenceL55

73 Class Test CT74

VIIIUNIT

Tutorial T1075 general computer animation functions L5676 Raster animation, L57

77 computer animation languages L58

78 Key frame systems L5979 Motion specifications L6080 Class Test CT


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 ________ is stored in a memory are called refresh buffer.(picture definition) 7. Random-scan display are also known as ________.(vector display)


8. Shadow mask methods are commonly used in _________.(Raster scan system)9. The ________ behaves like a CRT with a extremely long persistence phosphor. (DVST)10. The ________ gun is used to store the picture pattern in DVST.(primary)

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 are the steps involve in Midpoint Circle algorithm 2. Write an algorithm for line generation using DAA approach .Analysis its time & space3. Explain the steps involved in Scan-line algorithm for polygon filling4. Write an algorithm for line generating the intermediate points by using algorithm

Bresenhams when two endpoints are given as inputs5. Explain the role of stack in Flood-Fill Algorithm

OBJECTIVE QUESTIONS

1. 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 about ANS[c]a) x=-yb) y=0c) y=x+1d) x=0


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

7. Bresenham’s algorithm uses only ________ that can be to display circles as other curves(Incremental integer calculation)

8. The initial value of decision parameter circle is _______(p0=5/4-r)9. A ________defined as the set of points that are all at a given distance r from a center

position(x,y).(circle)10. An _______ is an elongated circle(ellipse).

ASSIGNMENT QUESTIONS1. What are the steps involve in mid point ellipse algorithm2. By using Bresenham’s line drawing , generate the intermediate points of lnes if the two

end-points are given as (20,10) and (30, 18) using the above algorithm

TUTORIAL QUESTIONS

1. 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.

2. The circle with radius 10, demonstrate midpoint circle algorithm by determining along with radius along the octant in the first quadrant from x=0 to x=y.


UNIT-III

DESCRIPTIVE QUESTION 1. List the basic transformation techniques. What are their respective mathematical and

matrix representations?2. 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 commutative3. Show that the transformation matrix for a reflection about the line y=x is equivalent to

reflection relative to the x axis followed by a counter clockwise rotation of 90 degrees

4. Show that the transformation matrix for a reflection about the line y = -x is equivalent to a reflection relative to the y-axis followed by a counter clockwise rotationof 90 degrees.

5. Perform a 45 degree rotation of a triangle A(0,0), B(1,1) and C(5,2) about P(-1,-1).Magnify the triangle with vertices A(0,0), B(1,1) and C(5,2) to thrice its sizewhile keeping B(1,1) 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. The transformation that alters the size of an object. [a]

a) Scalingb) Translation c) Rotation d) Shearing

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

4. 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 05. 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


6. If the rotation about an arbitrary point is to be performed, what is the sequence of operations to achieve the desired effect ___________(Translate ,Rotate & Translate)

7. If the object is to be rotate 30® anticlock wise , keeping the object stationary , the same effect achieved by rotating the coordinate system__________(30® in clock-wise)

8. The scaling factor in the scaling translation are ____________(Always positive)9. Two successive translation can be represented as________(A single translation

matrix)10. Two successive translation is____________(Commutative)

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) Shear

TUTORIAL QUESTIONS 1. Perform a 45 degree rotation of a triangle A(0,0), B(1,1) and C(0,1) about P(-1,-1).2. Obtain the reflection of the point A(10,10) about y=x+2


UNIT-IV


1. What are the stages involved in two-dimensional viewing transformation Pipeline. Explain briefly about each stage.

2. Draw the flow diagram or a brief step-wise procedure for implementing Sutherland-Hodgeman algorithm

3. Explain the algorithm for line clipping by Cohen-Sutherland algorithm. Demonstrate an example all the three cases of lines.

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

5. 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)

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]

a) Normalized deviceb) Physical devicec) View-portd) Window

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

a) bit 3 b) bit 1 c) bit 4 d) bit 2

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 invisibleb) Completely invisiblec) Partially visibled) Completely visiblee)

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<90b) 90< Θ<270c) 0<Θ<90 & 90< Θ<270d) 0< Θ<180


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

a) 640 x 480b) Xmax x Ymaxc) Workstation dependentd) 1 x 1

6. The method for selecting and enlarging portions of a drawing is______ (windowing)

7. The ______ defines where is to be displayed ( view port )

8. The ____ defines what to be viewed. ( window )

9. ______algorithm is used for polygon clipping.( cohen-sutherland & sutherland Hodgemman)

10. ______ polygons are correctly clipped by the sutherland Hodgemman. ( convex) none

ASSIGNMENT QUESTIONS1. What are the stages involved in Window-to-viewport coordinate transformation. Explain about each stage.2. 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).(a) The region codes of the two end points,(b) Its clipping categoryStages in the clipping operations using Cohen-Sutherland algorithm.


UNIT-V

DESCRIPTIVE QUESTION 1. Distinguish between boundary representation and space-partitioning representation of

solid object representation schemes2. What is the blending function used in Bezier’s method for curve generation?3. What are the steps involved in rendering a polygon surface mesh using Gouraud shading4. Describe the phong illumination model. Explain the parameters used in phong’s model.5. Explain B-Spline curves.

OBJECTIVE QUESTIONS1. ________ 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. the range of parametric variable ‘t’ used in Bezier curve is________( 0,1 )

7. _____ light has no spatial or directional characteristics______( ambient)


8. the _____ model ,sets the intensity of specular reflection proportional to cosns0 [b]_______(phong)9. the range of values for the reflection coefficients followed in illumination model is_______(0 to 1)10. ____ draw back is observed in Gouraud shading_______(mach bands)

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.Give a brief account on three-dimensional rotations.2. Discuss about 3-dimensional viewing pipe line3. Prove that the multiplication of three-dimensional transformation matrices for eachof the following sequence of operations is commutative.

i. Any two successive translationsii. Any two successive saling operations

iii. Any two successive rotations about any one of the coordinate axes.4.Classify the projections. Explain the properties of each. Distinguish the parallel projection and Perspective Projection view volumes. Give suitable examples5. 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 the main diagonal from (0, 0, 0) to (1, 1, 1) in the counter clock-wise direction when looking along the diagonal toward the origin.

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. ____ means of technique of projecting 3D object to 2D screen_____ (projection)7 a parallel projection preserves ______ of object.(relative projection)8. When the projection are perpendicular to the view plane then it is called_______(Orthographic projection) 9. ortho graphics projections are often used to produce the front,side and ___ of an object ( top view )10. a top orthographic projection is called a ______(Plainview )


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.TUTORIAL QUESTIONS

1. Find the transformation matrix which align the vector V=i+j+k with the vector N=2i-j-k.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 passing through point C(0, 1, 0). Find the coordinates of rotated figure

UNIT-VII

DESCRIPTIVE QUESTION 1. Distinguish between object-space and image space methods of visible surface detection

algorithms. Give examples for each.2. Explain the depth-buffer (z-buffer) algorithm for hidden surface removal.3. Explain how the BSP-tree method is implemented for visible surface detection. 4. 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-buffer5. 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.

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 algorithm


c) 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 _____ (Z-Buffer)

7. In which of the following algorithm the polygons in the scene are grouped into cluster_______( BSP tree algorithm)8.In which of the following algorithm, is well suited when the view point changes____

(BSP tree algorithm)

9.The correct priority order polygon list can be obtained using ____in BSP tree( in order tree walk)

10. How many buffers are used in Z-Buffer algorithm ___(2)

ASSIGNMENT QUESTIONS1. Outline the z-buffer algorithm. List the advantages and disadvantages of the z-buffer2. Explain about the octree method for visible surface detection.

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. 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.3. List the general-purpose animation languages. Explain the characteristics any are language4. Discuss about the following graphical animation languages.

(a)P-curve(b) DIAL

5. Discuss about the techniques to achieve the simple animation effects.

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) Orientation6. In the films , graphics terminals are refreshed at the rate of ____ frames per second

(30 to 60)7. A single-arm robot has ___degrees of freedom (6) 8. Morphing methods can be applied to any motion or transition involving a change in

_______ (Shape)9. ____ forces affects object motion ( Magnetic,Gravitational &fraction)

10. _______requires the specification of the forces that produce the velocities & accelerations (Dynamics)


ASSIGNMENT QUESTIONS1.Discuss about the techniques to achieve the simple animation effects. What are the various types of interpolation used in animation?2.What are the steps in design of animation sequence? .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


Documents

Computer Graphics Hand Book of IV CSE JNTUH 2013