Cs602 Collection of Old Papers

• N! colors are used in the image • 2N colors are used in the image • N colors are used in the image • 2*N colors are used in the image

If N bits are required to store a pixel then:

Question No. 4 Marks : 1

Differentiate between quadratic and cubic parametric curves and write equations for cubic parametric curve.


• Vector graphics create more realistic image • Bitmap graphics gives realistic image • Bitmap graphics are scalable • Bitmap graphics have limited colors

Which of the following is valid difference between Bitmap graphics and vector graphics:


V1(X1,Y1,Z1)……. Vn-1(Xn-1,Yn-1,Zn-1), Vn(Xn,Yn,Zn) where n=4.

Write an algorithm that can subdivide faces of tetrahedron (type of polyhedron having 4 faces) to depth level 2 and draw after subdivision. Consider the vertices are


Total Marks: 75 Total Questions: 13

Ф , θ, You can copy the symbols given below if you need them

**WARNING: Please note that Virtual University takes serious note of unfair means. Anyone found involved in cheating will get an `F` grade in this course.

c. Write all steps, missing steps may lead to deduction of marks.

b. If you believe that some essential piece of information is missing, make an appropriate assumption and use it to solve the problem.

a. If you think that there is something wrong with any of the questions, attempt it to the best of your understanding.

2. Do not ask any questions about the contents of this examination from anyone.

1. Please Attempt all the questions. Note that you have to complete the paper in the given period of time so attempt all the questions according to their Marks.

Please read the following instructions carefully before attempting any of the questions:

Time Allowed: 150 Minutes Final Term Examination - February 2005 CS602 Computer Graphics

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Page 1 of 3

• Number of horizontal pixels * Number of Vertical Pixels * Number of colours * Refresh Rate • Number of horizontal pixels * Number of Vertical Pixels * Number of colors • Number of horizontal pixels * Number of Vertical Pixels

What is meant by Resolution:


Explain 'Alpha Blending' and its usage.


• Phong shading does not produce shining spot and flat does that • Flat shading does not produce shining spot and Phong does that • Flat shading uses one color and Phong uses two colors • Flat shading produces smooth shades and Phong does not

The difference between Flat shading and Phong shading is that:


A Quad has vertices A (0.2, 0.2, 1.0), B (0.5, 0.2, 1), C (0.5, 0.5, 1.0), D (0.2, 0.5, 1.0). Calculate surface normal? Given light source has vertex L (0.8, 0.2, 1.0); Taking light factor I=0.5 and surface type=0.5; Calculate light vector and light for vertices A, B, C and D?


c) Diffuse Reflection b) Ambient Light a) Specular Reflection

Define the following in view of Lighting Equation:

Question No. 9 Marks : 12 Write an algorithm to draw N points Bezier curve?


Z'= Z Y'= X * sin (θ) + Y * cos (θ) X'= X * cos (θ) – Y * sin (θ)

Given below is the rotation equation about z-axis use this to derive rotation equations about x-axis and y-axis?


Write down steps required for scan-line filling algorithm?


• A complex polygon can be filled with 8 connected approach • Flood-fill is best for filling of triangle • Both are used for filling of close figure • Both can be implemented as recursive as well as iterative methods

Which of the following statements is not true about flood-fill and boundary-fill algorithms?


Page 2 of 3

• Number of horizontal pixels * Number of Vertical Pixels * Number of colours * Number of Buffers Page 3 of 3

• N! colors are used in the image • 2N colors are used in the image • N colors are used in the image • 2*N colors are used in the image

If N bits are required to store a pixel then:


Differentiate between quadratic and cubic parametric curves and write equations for cubic parametric curve.


• Vector graphics create more realistic image • Bitmap graphics gives realistic image • Bitmap graphics are scalable • Bitmap graphics have limited colors

Which of the following is valid difference between Bitmap graphics and vector graphics:


V1(X1,Y1,Z1)……. Vn-1(Xn-1,Yn-1,Zn-1), Vn(Xn,Yn,Zn) where n=4.

Write an algorithm that can subdivide faces of tetrahedron (type of polyhedron having 4 faces) to depth level 2 and draw after subdivision. Consider the vertices are



Ф , θ, You can copy the symbols given below if you need them


c. Write all steps, missing steps may lead to deduction of marks.




1. Please Attempt all the questions. Note that you have to complete the paper in the given period of time so attempt all the questions according to their Marks.


Time Allowed: 150 Minutes Final Term Examination - February 2005 CS602 Computer Graphics


Page 1 of 3

• Number of horizontal pixels * Number of Vertical Pixels * Number of colours * Refresh Rate • Number of horizontal pixels * Number of Vertical Pixels * Number of colors • Number of horizontal pixels * Number of Vertical Pixels

What is meant by Resolution:


Explain 'Alpha Blending' and its usage.


• Phong shading does not produce shining spot and flat does that • Flat shading does not produce shining spot and Phong does that • Flat shading uses one color and Phong uses two colors • Flat shading produces smooth shades and Phong does not

The difference between Flat shading and Phong shading is that:


A Quad has vertices A (0.2, 0.2, 1.0), B (0.5, 0.2, 1), C (0.5, 0.5, 1.0), D (0.2, 0.5, 1.0). Calculate surface normal? Given light source has vertex L (0.8, 0.2, 1.0); Taking light factor I=0.5 and surface type=0.5; Calculate light vector and light for vertices A, B, C and D?


c) Diffuse Reflection b) Ambient Light a) Specular Reflection

Define the following in view of Lighting Equation:

Question No. 9 Marks : 12 Write an algorithm to draw N points Bezier curve?


Z'= Z Y'= X * sin (θ) + Y * cos (θ) X'= X * cos (θ) – Y * sin (θ)

Given below is the rotation equation about z-axis use this to derive rotation equations about x-axis and y-axis?


Write down steps required for scan-line filling algorithm?


• A complex polygon can be filled with 8 connected approach • Flood-fill is best for filling of triangle • Both are used for filling of close figure • Both can be implemented as recursive as well as iterative methods

Which of the following statements is not true about flood-fill and boundary-fill algorithms?


Page 2 of 3

• Number of horizontal pixels * Number of Vertical Pixels * Number of colours * Number of Buffers Page 3 of 3

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FINALTERM EXAMINATION

FALL 2006

CS602 - COMPUTER GRAPHICS

Marks: 60

Time: 120min

StudentID/LoginID: ______________________________

Student Name: ______________________________

Center Name/Code: ______________________________

Exam Date:

Instructions

Please read the following instructions carefully before attempting any questions:

1. This examination is closed book, closed notes, closed neighbors. 2. Answer all questions. 3. Do not ask any questions about the contents of this examination from anyone4. You are allowed to use any Software for Diagrams and Symbols like MS Word

**WARNING: Please note that Virtual University takes serious notice of using involved in cheating will get `F` grade in this course.

For Teacher's use only Question 1 2 3 4 5 6 7 8 9 10 Total

Marks Question 11 12 13

Marks Question No: 1 ( Marks: 10 ) The appearance of a color image depends on the display device. If an identical color image is displayed on two different color monitors, why might the displayed result not be identical? List in point form as many reasons as you can think of, and be as specific as possible. Question No: 2 ( Marks: 10 ) What is the effect of implicit clamping of oversaturated colors in the pipeline? Question No: 3 ( Marks: 10 )

What will be the refractive index of a given material at 750 C if refractive index at 250 C is 1.45? Question No: 4 ( Marks: 10 ) Suppose the earth is to be drawn at the origin and it is to rotate on its axis at a rate of ω degrees per unit time. The axis of rotation is to be the y-axis. Give the OpenGL commands that will set the model view matrix correctly to render the earth at time t. (Hint: Your answer will need to include a rotation through an angle of ωt degrees). Question No: 5 ( Marks: 10 ) Sketch the graphics pipeline and indicate where the following are performed a) clipping b) Gouraud shading c) Z-buffer computations Question No: 6 ( Marks: 2 ) How would you convert view reference coordinates to world coordinates? Question No: 7 ( Marks: 2 ) Why should you make all your polygons triangles? Question No: 8 ( Marks: 1 ) - Please choose one Which of the following is NOT true about quaternions? ►

They are made up of 4 numbers

►

They should always be normalized to length 1

►

They can be used to represent all affine transforms

►

They can be used to define the rotation of an object

Question No: 9 ( Marks: 1 ) - Please choose one This projection technique which has the direction of projection perpendicular to the viewing plane, but the viewing direction is NOT perpendicular to one of the principle faces. ►

Orthographic Parallel Projection

►

Axonometric Parallel Projection

►

Oblique Parallel Projection

Question No: 10 ( Marks: 1 ) - Please choose one In OpenGL, there are several different matrices, we have discussed two of them in lectures, which one of the below would be used in conjunction with a glRotatef

function call? ►

GL_MODELVIEW

►

GL_PROJECTION

Question No: 11 ( Marks: 1 ) - Please choose one When obtaining normals for a triangle, which of the following mathematical constructs is NOT used? ►

Point-Point subtraction

►

Vector dot products

►

Vector cross products

►

Vector normalization

Question No: 12 ( Marks: 1 ) - Please choose one The field of view (FOV) of a pinhole camera depends on the size of the backplane and ►

The distance of the backplane from the pinhole

►

The size of the pinhole

►

The distance to the objects

►

The type of film (or recording device) used

Question No: 13 ( Marks: 1 ) - Please choose one Which form of Fractal requires some randomness and several thousand loop executions to give a result? ►

Non-linear fractals

►

Iterated Function Systems

►

L-Systems

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FINAL TERM EXAMINATION III SEMESTER SPRING 2005

CS602-COMPUTER GRAPHICS

Total Marks:55 Duration:120

Minutes

StudentID/LoginID

Name

PVC Name/Code

Date 25-07-2005

Maximum Time Allowed: (2 Hours)


1. Attempt all questions. Marks are written adjacent to each question.


a. If you think that there is something wrong with any of the questions, attempt it to the best of your understanding. b. If you believe that some essential piece of

information is missing, make an appropriate assumption and use it to solve the problem. c. Write all steps, missing steps may lead to deduction of marks.


For Teacher’s use onlyQuestion Q1 Q2 Q3 Q4 Q5 Q6 Total Marks

Question No: 1 Marks: 10 (2x5) Choose the most appropriate answer

1. Which of following is not the property of Phong shading: a. Phong shading is most realistic b. Phong shading is computationally costly c. Phong shading can produce shinny spots d. Phong shading is computationally least expansive 2. If resolution is 800 x 600 pixels and color intensity is 32bit and refresh rate is 70hz

then the size of buffer will be: (in bits) a. 800 * 600 * 32 *70 b. 800 * 600 * 4 c. 800 * 600 * 4 *70 d. 800 * 600 * 32 3. Which of the following is not true about Bitmap graphics and vector graphics: a. Bitmap graphics are easily convertible to vector graphics b. Vector graphics are realistic c. Vector graphics and Bitmap graphics are same d. All of the above 4. The equation P(u) = au + b Generally represents a: a. Plane b. Line c. 3D curve d. Point 5. Bezier curves may be: a. 2D b. 3D c. All of the above d. None of the above

Question No: 2 Marks: 5 (1x5)

Mark True or False

1. Open GL can handle user inputs and outputs very efficiently

2. All the concave polygons are not the convex polygons. 3. Schlick's simplification may or may not remove the exponential terms from the

specular lighting equations. 4. To specify a Bezier curve of degree n , we need n - 1 control points

5. It is necessary for a line to lie in 3D.

Question No: 3 Marks: 10

I. What is specular light, Give the equation of specular lighting given by Blinn.

II. What is light Attenuation how we can calculate it.

Question No: 4 Marks: 10 I. Suppose we have,

color vector md = [0.3564,0.9678,0.5648] light source diffused color sd = [0.3333,0.3582,0.6584]

The angle between light vector from vertex to the light source and the vertex normal vector is 30o, Calculate the diffuse light intensity id at the vertex. II. Suppose the refractive index of the material is 1.4 calculate its critical angle take refractive index of air as 1. Hint: The critical angle is the angle at which the refracted angle is 90o

Question No: 5 Marks: 10

I. Suppose we want to perform the following 3D transformations using homogenous coordinates in the same order as given below

a. Scaling (Take Sx =7, Sy = 12 , Sz = 14) b. Translation (Take Tx = 13, Ty = 27, Tz = 18)

Find the resultant composite matrix that can perform these tasks using the individual 3D transformation matrices using Homogenous coordinates. II. Given are the three points that lie on a plane,

P1<2.0,1.0,2.0> P2<9.0,9.0,8.0> P3<15.0,13.0,11.0>

Find the equation of a normal to this plane. Question No: 6 Marks: 10

1. Derive the formulae and give matrix for oblique projection. 2. Define hidden surface removal and explain its importance in 3D?


, Λ, Ø, , |, , , an,θ,π ∑

For your convenience we are providing you the following symbols, so that you can copy them & paste wherever they are needed in the respective questions.

NOTE:

4. You are allowed to use any Software for Diagrams and Symbols like MS Word, MathType and Visio etc.




b. You will have to answer correctly all questions in this examination to get the maximum possible marks.

a. There is no choice. 2. Answer all questions. 1. This examination is closed book, closed notes, closed neighbors.

Please read the following instructions carefully before attempting any question:

Instructions

Time Allowed: 90 Minutes Mid Term Examination – February 2005

CS602 Computer Graphics



o Line from this point to any point outside the polygon intersects any edge o Line from an outside point to this point crosses the edges odd number of times o Line from any point to this point crosses the edges odd number of times o Line from an outside point to this point does not cross the edges odd number of times

According to Odd Parity Rule, a point is inside the polygon, if: Question No. 6 Marks : 01

Why is the Bresenham's line drawing algorithm more efficient than the DDA line drawing algorithm? Give precise one line answer.


o A + (B + C) = (A + B) + C o (AT)T = AT o a(A + B) = aA + aB o A + B = B + A

Which of the following is not true about matrices: Question No. 4 Marks : 01

o False o True

UV light is used in Plasma Panel displays to excite phosphor. Question No. 3 Marks : 01

o False o True

The circle and ellipse are symmetric across 8 octants. Question No. 2 Marks : 01

What is Rendering?



Give homogeneous translation matrix for 2D transformation. Question No. 14 Marks : 05

o False o True

The amount of time it takes to illuminate a specific location on phosphor coated screen is called Persistence.

Question No. 1 3 Marks : 01

o x' = y cos(θ) + x sin(θ), y' = y sin(θ) – x cos(θ) o x' = x cos(θ) + y sin(θ), y' = x sin(θ) – y cos(θ) o x' = y cos(θ) – x sin(θ), y' = y sin(θ) + x cos(θ) o x' = x cos(θ) – y sin(θ), y' = x sin(θ) + y cos(θ)

When a point P(x,y) is rotated by θ the coordinates of transformed point P' are given as: Question No. 1 2 Marks : 01

o Any two vertices, intersects some edge of polygon. o A point inside the boundary with any point outside, does not intersect the polygon boundary o Any two points inside the polygon intersects its boundary o Any two points outside the polygon intersects its boundary

A Polygon is complex, if the line connecting: Question No. 1 1 Marks : 01

How is the efficiency of circle drawing algorithms improved? Question No. 1 0 Marks : 05

What is Viewing Frustum? Question No. 9 Marks : 05

Describe the Right Handed Rule for determination of direction of axes. Question No. 8 Marks : 06

o False o True

As opposed to direct memory access method, BIOS routines provide an easier and faster method of drawing pixels on screen.


o equal to each other o intersect each other o orthogonal (perpendicular) to each other. o parallel to each other

When dot product of two vectors equals zero, this implies that the two vectors are: Question No. 20 Marks : 01

o False o True

In Pixmap exactly one bit is used to hold color value of each pixel. Question No. 1 9 Marks : 01

o False o True

Parity Rule is used to determine whether a pixel is inside a polygon or not. Question No. 1 8 Marks : 01

o False o True

In Horizontal retrace, after completion of all the pixels in a scan line, the refreshing continues from the 1st pixel of the next scan line.


o The number of columns of 1st matrix must be the same as the number of rows of the second. o The two matrices must either be row matrices or column matrices o The number of rows of 1st matrix must be the same as the number of columns of the second. o The two matrices must be square

In matrix multiplication: Question No. 16 Marks : 01

o False o True

Incremental line drawing algorithm makes use of the equation of straight line. Question No. 15 Marks : 01

o Must not use recursive approach o May use 4-connected or 8-connected approach o Must use 8-connected approach o Must use 4-connected approach

The Boundary Fill and Flood Fill algorithms: Question No. 22 Marks : 0

What is meant by Trivial Accept?

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Largest Online Community of VU Students MIDTERM EXAMINATION

FALL 2006

CS602 - COMPUTER GRAPHICS

Marks: 35

Time: 60min


Student Name: ______________________________

Center Name/Code: ______________________________

Exam Date:

Instructions


1. This examination is closed book, closed notes, closed neighbors. 2. Answer all questions. 3. Do not ask any questions about the contents of this examination from anyone. 4. You are allowed to use any Software for Diagrams and Symbols like MS Word,

MathType and Visio etc.

**WARNING: Please note that Virtual University takes serious notice of using unfair means. Anyone found involved in cheating will get `F` grade in this course.

For Teacher's use only Question 1 2 3 4 5 Total

Marks Question No: 1 ( Marks: 5 ) What are the two focusing methods in CRT? Explain briefly. Question No: 2 ( Marks: 5 ) What is the relation between triads and shadow mask method? Question No: 3 ( Marks: 5 ) Discuss in brief the pixel drawing methods. Question No: 4 ( Marks: 10 )

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http://forum.vupages.com/

What are the steps involved in performing the boundary fill algorithm, also write the pseudo code for the steps you have mentioned above? Question No: 5 ( Marks: 10 ) How the locality of a point can be defined with respect to a plane?

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MIDTERM EXAMINATION

FALL 2007

CS602 - COMPUTER GRAPHICS (Session - 6 )

Marks: 35

Time: 120min


Student Name: ______________________________

Center Name/Code: ______________________________

Exam Date: Tuesday, November 20, 2007





c. Write all steps, missing steps may lead to deduction of marks. **WARNING: Please note that Virtual University takes serious note of unfair means. Anyone found involved in cheating will get an `F` grade in this course.

For Teacher's use only Question 1 2 3 4 5 6 7 8 Total

Marks Question No: 1 ( Marks: 10 ) Suppose an RGB raster system is to be designed using an 10*8 inch screen with a resolution of 100 pixels per inch in each direction. If we want to store 12 bits in per pixel in the frame buffer, how much storage (in bytes) do we need for the frame buffer? Question No: 2 ( Marks: 10 ) Which algorithm finds the closest integer coordinates to the actual line. Summarize this algorithm and suggest some improvements. Question No: 3 ( Marks: 10 )

What could be the ways to implement area filling on raster systems? Summarize scan line polygon filling algorithm in your own words. Question No: 4 ( Marks: 1 ) - Please choose one Intensity of the electron beam is controlled by setting _________ levels on the control grid, a metal cylinder that fits over the cathode. ►

Amplitude

►

Current

►

Voltage

►

electron

Question No: 5 ( Marks: 1 ) - Please choose one True or false. Using Cohen-Sutherland line clipping, it is impossible for a vertex to be labeled 1111. ►

true

►

false

Question No: 6 ( Marks: 1 ) - Please choose one Shadow mask methods can display a __________ range of colours. ►

Small

►

Wide

►

Random

►

crazy

Question No: 7 ( Marks: 1 ) - Please choose one Which one of the following step is not involved to write pixel using video BIOS services.

►

Setting desired video mode

►

Using bios service to set color of a screen pixel

►

Calling bios interrupt to execute the process of writing pixel.

►

Using OpenGL service to set color of a screen pixel

Question No: 8 ( Marks: 1 ) - Please choose one Each number that makes up a matrix is called an ___________ of the matrix. ►

Element

►

Variable

►

Value

►

component


grade in this course. of unfair means. Anyone found involved in cheating will get an `F` **WARNING: Please note that Virtual University takes serious note

∑ , Λ, Ø, , |, , , an,θ,π

For your convenience we are providing you the following symbols, so that you can copy them & paste wherever they are needed in the respective questions.

4. You are allowed to use any Software for Diagrams and Symbols like MS Word, MathType and Visio etc.

the problem.

b. If you believe that some essential piece of information is missing, make an appropriate assumption and use it to solve



b. You will have to answer correctly all questions in this examination to get the maximum possible marks.

2. Answer all questions. a. There is no choice.

1. This examination is closed book, closed notes, closed neighbors.

NOTE:

Please read the following instructions carefully before attempting any question:

Instructions

Time Allowed: 90 Minutes Mid Term Examination – February 2005 CS602 Computer Graphics

mailto:[email protected]

mailto:[email protected]

o Line from this point to any point outside the polygon intersects any edge o Line from an outside point to this point crosses the edges odd number of times o Line from any point to this point crosses the edges odd number of times o Line from an outside point to this point does not cross the edges odd number of times

According to Odd Parity Rule, a point is inside the polygon, if:

Question No. 6 Marks : 01 algorithm? Give precise one line answer. Why is the Bresenham's line drawing algorithm more efficient than the DDA line drawing


o A + (B + C) = (A + B) + C o (AT)T = AT o a(A + B) = aA + aB o A + B = B + A

Which of the following is not true about matrices:


o False o True

UV light is used in Plasma Panel displays to excite phosphor.


o False o True

The circle and ellipse are symmetric across 8 octants.

Question No. 2 Marks : 01 What is Rendering?



o False o True

called Persistence. The amount of time it takes to illuminate a specific location on phosphor coated screen is


o x' = y cos(θ) + x sin(θ), y' = y sin(θ) – x cos(θ) o x' = x cos(θ) + y sin(θ), y' = x sin(θ) – y cos(θ) o x' = y cos(θ) – x sin(θ), y' = y sin(θ) + x cos(θ) o x' = x cos(θ) – y sin(θ), y' = x sin(θ) + y cos(θ)

When a point P(x,y) is rotated by θ the coordinates of transformed point P' are given as:


o Any two vertices, intersects some edge of polygon. o A point inside the boundary with any point outside, does not intersect the polygon boundary o Any two points inside the polygon intersects its boundary o Any two points outside the polygon intersects its boundary

A Polygon is complex, if the line connecting:


How is the efficiency of circle drawing algorithms improved?


What is Viewing Frustum?


Describe the Right Handed Rule for determination of direction of axes.


o False o True

of drawing pixels on screen. As opposed to direct memory access method, BIOS routines provide an easier and faster method Question No. 7 Marks : 01

o equal to each other o intersect each other o orthogonal (perpendicular) to each other. o parallel to each other

When dot product of two vectors equals zero, this implies that the two vectors are:


o False o True

In Pixmap exactly one bit is used to hold color value of each pixel.


o False o True

Parity Rule is used to determine whether a pixel is inside a polygon or not.


o False o True

continues from the 1st pixel of the next scan line. In Horizontal retrace, after completion of all the pixels in a scan line, the refreshing


o The number of columns of 1st matrix must be the same as the number of rows of the second. o The two matrices must either be row matrices or column matrices o The number of rows of 1st matrix must be the same as the number of columns of the second. o The two matrices must be square

In matrix multiplication:


o False o True

Incremental line drawing algorithm makes use of the equation of straight line.


Give homogeneous translation matrix for 2D transformation.


o Must not use recursive approach o May use 4-connected or 8-connected approach o Must use 8-connected approach o Must use 4-connected approach

The Boundary Fill and Flood Fill algorithms:

Question No. 22 Marks : 0 What is meant by Trivial Accept? Question No. 21 Marks : 04

MID TERM EXAMINATION I SEMESTER Spring 2005

CS602-COMPUTER GRAPHICS Total Marks: 35 Duration:60mins

StudentID/LoginID

Name

PVC Name/Code

Date

Maximum Time Allowed: (1 Hour)




a. If you think that there is something wrong with any of the questions, attempt it to the best of your understanding. b. If you believe that some essential piece of information is

missing, make an appropriate assumption and use it to solve the problem. c. Write all steps, missing steps may lead to deduction of marks.




Question No: 1 Marks: (5) Choose the most appropriate answer 1. To show 256 colours , the no of bits required for each pixel are

a. 8 b. 16 c. 32 d. 64

2. 25 * 80 resolution with 16 colors supports

a. Text mode b. Graphics mode c. Both d. None

3. Two matrices are said to be equal , if they have

a. same order b. same corresponding elements c. Same order and same corresponding elements. d. Different elements.

4. Two points are said to be collinear, if they lie on the

a. same line b. different but parallel lines c. either on the same plane or two parallel planes d. different plane

5. A Polygon is convex, if the line connecting:

a. Any two points outside the polygon intersects its boundary b. Any two points inside the polygon don’t intersect any edges of the polygon. c. A point inside the boundary with any point outside, does not intersect the polygon

boundary d. Any two vertices, intersects some edge of polygon.

Question No: 2 Marks: 7Write the pseudo code to draw a Circle and an Ellipse simultaneously (using their polar coordinate equation and the angle that the points lying on them make with x axis) suppose both are located at the same center (xc,yc) , take radius of the circle as ‘r’, semi major radius of ellipse as ‘a’ and semi minor radius as ‘b’.

CircleAndEllipse (xc, yc, r , a, b) For θ = 0 to θ = π/2 step = 1/radius x_circle = r * cos θ y_circle = r * sin θ x_ellipse= a * cos θ y_ellipse= b * sin θ

DrawSymmetricPoints (xc, yc, x_circle, y_circle,x_ellipse,y_ellipse) DrawSymmeticPoints (xc, yc, x_circle, y_circle,x_ellipse,y_ellipse) { /*For Circle*/ DrawPixel ( x_circle + xc, y_circle + yc ) [First Quadrant] DrawPixel ( -x_circle + xc, y_circle + yc) [Second Quadrant] DrawPixel ( -x_circle + xc, -y_circle + yc) [Third Quadrant] DrawPixel ( x_circle + xc, -y_circle + yc ) [Fourth Quadrant] /*For Ellipse*/ DrawPixel ( x_ellipse + xc, y_ellipse + yc ) [First Quadrant] DrawPixel ( -x_ellipse + xc, y_ellipse + yc) [Second Quadrant] DrawPixel ( -x_ellipse + xc, -y_ellipse + yc) [Third Quadrant]

DrawPixel ( x_ellipse + xc, -y_ellipse + yc ) [Fourth Quadrant] } Where semi_major_ radius = a semi_minor_ radius = b radius = r Question No: 3 Marks 7

a. Find in which quadrant the point (-2, 3) lies in 2D plane. b. Consider these 3-D vectors:

A = [9,8,7] B = [4,7,3] C = [2,9,6]

Compute: i) A.BxC ii) AxB.C

c. What is the main difference between i) Orthographic projection ii) Oblique projection

a) 2nd quadrant b) BxC =[7x6 - 3x9 , 3x2 - 4x6 , 4x9 – 7x2] =[15,-18,22]

A.BxC =9x15 +8x(-18)+7x22= 135-144+154=145

AxB =[8x3 - 7x7 , 7x4 - 9x3 , 9x7 – 8x4] =[-25,1,31]

AxB.C =-25x2+1x9+31x6 = -50 + 9+186=145

Orthographic Projection

If the direction of projection is perpendicular to the projection plane then it is an orthographic projection.

Oblique Projection

If the direction of projection is not perpendicular to the projection plane then it is an oblique projection.

Question No: 4 Marks: 4a) Suppose we want to perform 3D scaling using homogenous coordinates with respect to a point Q (x1,y1,z1) Derive the matrix we should use for this purpose. take (Sx = 6, Sy = 4 , Sz = 7) b) Suppose we want to perform 3D Rotation of 180 degrees about Y-Axis using homogenous coordinates using Reflection, Give the matrix that can do this task.

Scaling with respect to a selected fixed position: Scaling with respect to a selected fixed position (x1,y1,z1) can be represented with the following transformation sequence:

1. Translate the fixed point to the origin. 2. Scale the object relative to the coordinate origin 3. Translate the fixed point back to its original position

The reflection transformation operation is equivalent to rotation of 180 degrees so we can use the following transformation matrix using homogenous coordinates to perform the rotation of 180 degrees about y axis, Question No: 5 Marks: 7 Suppose we want to perform the following operations in 2D using homogenous coordinates in the order as given below:

a. Reflection about Y axis b. Rotation of + 30 Degrees c. Reflection about X axis

Find the resultant composite matrix that can perform this task using the individual 2D transformation matrices using Homogenous coordinates. You can use the table: Angle (Degrees) Sin Cos 30o

Solution:

−

1000010000100001

1 0 0 1 0 0 0 1 0 0 10 1 0 1 0 0 0 0 1 0 1

. .0 0 1 1 0 0 0 0 0 1 10 0 0 1 0 0 0 1 0 0 0 1

x Sx xy Sy yz Sz z

− − −

We can produce Reflection about Y-Axis by matrix

1 0 00 1 00 0 1

−

We can produce Rotation of 30 degrees by matrix

cos sin 0sin cos 0

0 0 1

θ θθ θ

−

= cos30 sin 30 0sin 30 cos30 0

0 0 1

−

We can produce Reflection about X-axis by matrix

=1 0 00 1 00 0 1

−

cos30 sin 30 0sin 30 cos30 0

0 0 1

−

1 0 00 1 00 0 1

−

=1 0 00 1 00 0 1

−

3 / 2 1/ 2 0

1/ 2 3 / 2 00 0 1

−

1 0 00 1 00 0 1

−

=

1 0 00 1 00 0 1

−

3 / 2 1/ 2 0

1/ 2 3 / 2 00 0 1

− − −

=

3 / 2 1/ 2 0

1/ 2 3 / 2 00 0 1

− −

−

Final Matrix Question No: 6 Marks: 5

−

100010001

Clearly Explain the Following: a. Why in Scan Line Filling Algorithm we don’t put the edges having 1/m = 0 in

active edge table. b. In matrix multiplication the number of columns of first matrix should be

equal to number of rows of second matrix. a. In Scan line filling algorithm we don’t put the edges having 1/m in active edge table because

we treat it as special a case. If this edge is at the minimum y value for all edges, it is drawn. Otherwise, if the edge is at the maximum y value for any edge, we do not draw it.

b. Because we multiply the rows of first matrix by the column of second matrix so if we don’t have the number of corresponding elements equal, we would not be able to multiply the matrices.

MID TERM EXAMINATION II SEMESTER Spring 2005

CS602-COMPUTER GRAPHICS Total Marks: 35 Duration:60mins

StudentID/LoginID

Name

PVC Name/Code

Date

Maximum Time Allowed: (1 Hour)




a. If you think that there is something wrong with any of the questions, attempt it to the best of your understanding. b. If you believe that some essential piece of information is

missing, make an appropriate assumption and use it to solve the problem. c. Write all steps, missing steps may lead to deduction of marks.




Question No 1 Marks 5 Choose the most appropriate answer 1. A Polygon is complex, if the line connecting:

a. Any two points outside the polygon intersects its boundary. b. Any two points inside the polygon intersects its boundary. c. A point inside the boundary with any point outside does not intersect the polygon

boundary. d. Any two vertices, intersects some edge of polygon.

2. The equation of hyperbola centered at origin (if the transverse axis is along x -axis) can be given as:

a. x2 b2+ y2 a2–1 = 0 b. x2 b2+ y2 a2+1 = 0 c. x2 a2– y2 b2–1 = 0 d. x2 b2 – y2 a2–1 = 0

3. Which of the following statements is not true about flood-fill and boundary-fill algorithms?

a. Both are used for filling of close figure b. Both can be implemented as recursive as well as iterative methods c. Flood-fill is best for filling of triangle d. A complex polygon can be filled with 8 connected approach

4. Which one is not valid out code to perform trivial accept / reject test in line clipping:

a. 1101 b. 1001 c. 0101 d. 0110

5. Which one of the following is not the graphics library is use:

a. FastGL b. OpenGL c. DirectX d. EasyGL

Question No 2 Marks: 5 Write the pseudo code to draw an ellipse located at the center (xc, yc) (using its polar equations and the angle that the points lying on it make with x axis) such that the length of its semi minor radius is equal to half of its semi major radius take semi major radius of the ellipse as ‘a’. Solution:

Ellipse (xc, yc, a) For θ = 0 to θ = π/2 step = 1/a x_ellipse= a * cos θ y_ellipse= a/2 * sin θ DrawSymmetricPoints (xc, yc,x_ellipse,y_ellipse) DrawSymmeticPoints (xc, yc,x_ellipse,y_ellipse) { DrawPixel ( x_ellipse + xc, y_ellipse + yc ) [First Quadrant] DrawPixel ( -x_ellipse + xc, y_ellipse + yc) [Second Quadrant] DrawPixel ( -x_ellipse + xc, -y_ellipse + yc) [Third Quadrant] DrawPixel ( x_ellipse + xc, -y_ellipse + yc ) [Fourth Quadrant] } Where semi_major_ radius = a semi_minor_ radius = a/2 Question No 3 Marks: 4+2

1. Suppose a man is standing at the point P= (-3,2,3) and it is looking along the vector V = [4,9,11] Determine whether the man would be able to see a point P’ (1, 0, 1) or not. 2. Find the distance between the points (-2,3) and (-6,6)

Solution: First we will find Test vector T as follows: T = [(-3-1),(2-0),(3-1)] So, T= [-4,2,2] Now Finding T.V = -16+ 18 + 22 = +24 As T.V > 0

Question No 4 Marks: 6 + 2

I. Differentiate between the following:

a. Concave and convex polygons. b. Complex and concave polygons. c. Filled and Unfilled Polygons.

II. Give the short answers to the following:

a. How we can find that whether a point lies inside a polygon or not? b. Describe any case in which Boundary fill algorithm may fail.

Difference between concave and convex polygons If a straight line connecting any two points that are inside the polygon intersects any edges of the polygon, then this polygon is called Concave polygons, otherwise it will be convex one. Difference between Complex and Convex polygons In complex polygons the vertices intersect some edge of the polygon whereas in convex polygons they can not. Difference between Filled and Unfilled Polygon In an unfilled polygon, only the points on the perimeter of the polygon are drawn. Whereas, in filled polygons all the interior points of the polygon must be filled. This means that all of the pixels within the boundaries of the polygon must be set to the specified color or pattern. II

a) How we can find that whether a point lies inside a polygon or not? To test it, draw a line segment from any point that lies outside the polygon to a point P that we wish to determine whether it is inside or outside of the polygon. Count the number of edges that the line crosses. If the number of polygon edges crossed is odd, then P lies within the polygon. Similarly, if the number of edges is even, then P lies outside of the polygon.

b) The boundary fill algorithm may fail in the case of Complex Polygons. Question No 5 Marks: 5+2

Give the resultant point when we apply 2D scaling using homogenous coordinates on the point P(9,3), about the point P(7,7) Take Sx = 2,Sy = 3.

AS the matrix for scaling with respect to point P(x,y) is

So the result would be

When we apply it on point P(9,3), we get the result as follows

So our resultant point would be P’(11,-5)

Question No 6 Marks: 4 Clearly Explain the Following:

a. How can we tackle edges meeting at a vertex and for both edges the vertex is the minimum point in scan line filling algorithm.

b. In which of planes given below the Point P(2,0,3) lies i) xy plane ii) yz plane iii) zx plane

c. Why the Cohen-Sutherland Line-Clipping Algorithm involves much more calculations than the other line clipping algorithms.

0 (1 )0 (1 )0 0 1

Sx Sx xSy Sy y

− −

2 0 ( 1)70 3 ( 2)70 0 1

− −

2 0 ( 1)7 90 3 ( 2)7 30 0 1 1

18 0 ( 7)0 9 ( 14)0 0 1

115

1

− = −

+ + − = + + − + + = −

a. We tackle the edges meeting at a vertex in scan line by incrementing the parity

in scan line algorithm twice and filling the point at the vertex. b. ZX plane.

c. We need much more calculations in Cohen Stherland line clipping Algorithm

because we have to perform trivial accept / Reject test for every point on the line this consumes a lot of computational power and time.

Connecting VU Students

FINALTERM EXAMINATION SPRING 2006

CS602 - COMPUTER GRAPHICS (Session - 1 )

Marks: 80

Time: 120min


Student Name: ______________________________

Center Name/Code: ______________________________

Exam Date: Thursday, August 17, 2006

Instructions


1. This examination is closed book, closed notes, closed neighbors. 2. Answer all questions. 3. Do not ask any questions about the contents of this examination

from anyone. 4. You are allowed to use any Software for Diagrams and Symbols like

MS Word, MathType and Visio etc.

**WARNING: Please note that Virtual University takes serious noticeof using unfair means. Anyone found involved in cheating will get`F` grade in this course.

For Teacher's use only Question 1 2 3 4 5 6 7 8 9 10 Total

Marks Question 11 12 13 14 15 16 17

Marks Question

Marks Question No: 1 ( Marks: 1 ) - Please choose one A Bezier curve is a scalar-valued function of one variable.


►

True

►

False

Question No: 2 ( Marks: 1 ) - Please choose one The transformation process to produce the desired scene for viewing is analogous to taking a photograph with a camera. ►

True

►

False

Question No: 3 ( Marks: 1 ) - Please choose one There's always a trade-off between the display speed and the quality of the image. ►

True

►

False

Question No: 4 ( Marks: 1 ) - Please choose one A space curve is confined to a plane. ►

True

►

False

Question No: 5 ( Marks: 1 ) - Please choose one As a software interface for graphics hardware, OpenGL renders multidimensional objects into a frame buffer. ►

True

►

False

Question No: 6 ( Marks: 1 ) - Please choose one The index of refraction for most materials is not a function of the wavelength of the light. ►

True


►

False

Question No: 7 ( Marks: 1 ) - Please choose one Ambient light is the light that comes from one direction. ►

True

►

False

Question No: 8 ( Marks: 1 ) - Please choose one As opposed to parallel projection, perspective projection gives a more realistic view of the objects in the scene. ►

True

►

False

Question No: 9 ( Marks: 1 ) - Please choose one Spotlights have three angles associated with them. ►

True

►

False

Question No: 10 ( Marks: 1 ) - Please choose one Phong shading is the most realistic shading model. ►

True

►

False

Question No: 11 ( Marks: 10 ) Each line drawing algorithm has advantages and disadvantages. What you suggest to improve the performance of line drawing algorithm. Question No: 12 ( Marks: 10 ) Calculate the magnitude and direction of vector V whose x, y, and z components are 10, 6, and 4 respectively.


Question No: 13 ( Marks: 10 ) In solid fill triangle rendering, what are the changes to be made to the DDA algorithm when the vertex coordinates do not fall on integer bound. Question No: 14 ( Marks: 10 ) During a graphics application development there is a need to use specular light in a scene. What technique you will use; Phong’s equation or Blinn’s version of Phong’s equation and why? Explain. Question No: 15 ( Marks: 10 ) How parametric functions, that are second degree polynomials, can be used to define plane curves? Question No: 16 ( Marks: 10 ) While designing an animated scene one of your team member is confused about the timing in animation and seeks your help. Will you help your team member by explaining “What is good timing”? Question No: 17 ( Marks: 10 ) What are the characteristics of Bezier curve? Does MS Windows Paintbrush facilitate to draw Bezier curve?

Documents

Cs602 Collection of Old Papers