07a50503-computergraphics

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Code No: 07A50503 R07 Set No. 2

III B.Tech I Semester Supplementary Examinations,June 2010COMPUTER GRAPHICS

Common to Information Technology, Electronics And ComputerEngineering, Computer Science And Engineering, Computer Science And

Systems EngineeringTime: 3 hours Max Marks: 80

Answer any FIVE QuestionsAll Questions carry equal marks

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1. (a) Write Bresenham’s algorithm for line generation which is suitable for anyslope.

(b) Using the above algorithm, generate the intermediate points of the line seg-ment, if the two end-points are given as (30,18) and (20,10). [8+8]

2. (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 thetypical range of values for parametric variable. [10+6]

3. (a) How does the z-buffer algorithm determine which surfaces are hidden.

(b) Show how the calculation of the intersection of an edge with a scan line canbe made incremental as opposed to absolute. [8+8]

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

(b) Derive the transformation matrix for rotation about origin. [8+8]

5. Explain the procedure to generate the in-betweens for the key frames. [16]

6. (a) Suppose we have a computer with 32 bits per word and a transfer rate of 1mips (one million instructions per second). How long would it take to fill theframe buffer of a 300 dpi (dots per inch) laser printer with a page size of 81/2inches by 11 inches.

(b) Explain the applications of computer graphics in [10+6]

i. entertainment and

ii. education and training.

7. Find a transformation which aligns the vector V = I + J + K with the vector N =2I-J-K. [16]

8. (a) Explain the approach followed in computing the blending function for non-uniform non-rational B-splines.

(b) Compare the effects of multiple control points and of multiple knots. [8+8]

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1. (a) Write an algorithm to implement scan-line algorithm for displaying visiblesurfaces of a given polyhedron.

(b) Explain how the coherence property is used to evaluate points along and be-tween scan-lines. [8+8]

2. Explain the algorithm for polygon clipping by Sutherland-Hodgeman algorithm.Illustrate with an example. [16]

3. (a) Consider three different raster systems with resolutions of 640 × 480, 1280 ×1024 and 2560 × 2048. What size frame buffer (in bytes) is needed for eachof these systems to store 12 bits per pixel?

(b) Explain the working of plasma panel. [8+8]

4. (a) Define the B-spline geometry vector GBS and B-spline basis matrix MBS.

(b) Compute the B-spline blending functions. [8+8]

5. (a) How can scaling with respect to a point P0(x0, y0, z0) be defined in terms ofscaling with respect to the origin.

(b) Explain the step-wise procedure in aligning an arbitrary plane with one of theprincipal planes. [8+8]

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

(b) Describe linear list notation of animation languages. [16]

7. Show that the transformation matrix for a reflection about the line y=x is equivalentto a reflection relative to the x - axis followed by a counter clockwise rotation of900. [16]

8. (a) Show graphically that an ellipse has four-way symmetry by plotting four pointson the ellipse:x = a cos θ + h, y = b sin θ + k where a =2, b=1, h=0 and k=0.

(b) 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? [8+8]

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1. (a) Describe the transformations used in magnification and reduction with respectto the origin.

(b) Find the new Coordinates of the triangle A(0,0), B(1,1) and C(5,2) after ithas been [8+8]

i. magnified to twice its size and

ii. reduced to half its size.

2. Explain the construction of the following devices with suitable sketches and theiroperating characterstics

(a) Raster- refresh devices

(b) Vector- refresh devices. [8+8]

3. (a) What are the basic rules of animation?

(b) Give a brief note about the following: [8+8]

i. Storey board

ii. In-betweening

iii. Morphing.

4. (a) Suppose point P1 with intensity I1 is on scan line y1 and the point P2 withintensity I2 is on scan line y2. Find an incremental formula to compute inten-sity values I1 for the scan lines between P1 and P2 using linear interpolationin the Y-direction.

(b) What are the advantages and disadvantages of interpolated shading method.[10+6]

5. Explain how the shearing of an object with respect to the three coordinate axes areimplemented. What are the corresponding input values for the shearing parameters.

[16]

6. (a) Write an algorithm to implement the flood-fill algorithm, using the 4-connecteddefinition for region pixels.

(b) Write the steps involved in Bresenham’s method for line generation whoseslope is between 450 and 900. [8+8]

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7. (a) Distinguish between object-space and image-space methods of visible surfacedetection algorithms. Give examples for each.

(b) Given points P1 (1, 2, 0), P2 (3, 6, 20) P3 (2, 4, 6) and a view point C (0, 0, -10),determine which points obscure the others when viewed from C. [8+8]

8. (a) How the 4-bit outcodes are computed which are used in Cohen-Sutherlandalgorithm.

(b) If PEi is a point on the window edge, Ni is the normal vector of the samewindow edge and P0 and P1 are the two end-points of a line segment, determinethe parametric variable ‘t’ which determines the Coordinates of intersectionpoint. [8+8]

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1. (a) What are the steps involved in Bresenham’s line drawing algorithm for |m| > 1,where m is slope of the line.

(b) Generate all intermediate points on the line segment, if the two end-points aregiven as (10,20) and (18,30) using the above algorithm. [8+8]

2. (a) Briefly describe various types of input devices used in computer graphics.

(b) Write short notes on:

i. Stroke writing

ii. Raster scan. [8+4+4]

3. (a) Express as a composite transformation matrix, the transformation which mag-nifies an object about its center C (h,k) by s units in each direction.

(b) Derive the transformation that rotates an object point θo about the origin.Write the matrix representation for their rotation. [8+8]

4. Explain the procedure to convert a perspective projection frustrum to a regularparallelepiped. [16]

5. (a) Explain the possible relationships between polygon surfaces while implement-ing area-subdivision method. How to handle these cases.

(b) Illustrate with an example a scene consisting of three or more planes andexplain how the BSP tree is constructed to represent the scene. [8+8]

6. (a) Explain the approach followed in subdividing the Bezier curve.

(b) Analyse the effect on B-spline of having in sequence four collinear controlpoints. [8+8]

7. (a) Illustrate with suitable examples how the three Categories of lines are pro-cessed using Cohen-Sutherland line clipping algorithm.

(b) What is the significance of dot products in decision making in Cyrun-Beckalgorithm? [8+8]

8. Explain the steps involved in transforming a sphere into a specified polyhedron.[16]

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07a50503-computergraphics

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