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A

Section A: Long Answer Questions

Attempt all / any as specified.

4 questions
1long12 marks

(a) Derive the decision parameter for Bresenham's line drawing algorithm for a line with slope 0 < m < 1, and state how the algorithm is generalized to handle lines of arbitrary slope. [7]

(b) Using the midpoint circle drawing algorithm, compute and tabulate the pixel positions in the first octant for a circle of radius r = 8 centred at the origin. [5]

line-drawingcircle-drawingscan-conversion
2long12 marks

(a) Explain why homogeneous coordinates are used in computer graphics. Obtain the composite transformation matrix required to reflect an object about the line y = x + 2, clearly stating each elementary transformation in order. [8]

(b) A triangle has vertices A(2, 2), B(6, 2) and C(4, 6). Find the coordinates of the triangle after it is rotated 90° anticlockwise about the point (4, 2). [4]

2d-transformationshomogeneous-coordinates
3long12 marks

(a) Distinguish between parallel and perspective projection. Derive the perspective projection transformation matrix for a centre of projection located at a distance d from the projection plane along the z-axis, and explain the effect of vanishing points. [8]

(b) Write down the transformation matrix to rotate a 3D object about an axis parallel to the z-axis passing through the point (x0, y0, 0) by an angle θ. [4]

3d-transformationsprojections
4long12 marks

(a) Describe the Cohen-Sutherland line clipping algorithm. Explain the significance of region (outcodes) and the conditions for trivial acceptance and trivial rejection. [7]

(b) Using the Cohen-Sutherland algorithm, clip the line segment from P1(−10, 30) to P2(40, 5) against a rectangular clipping window with corners (xmin, ymin) = (0, 0) and (xmax, ymax) = (30, 30). Show the intersection calculations. [5]

clippingcohen-sutherland
B

Section B: Short Answer Questions

Attempt all / any as specified.

8 questions
5short8 marks

Explain the Z-buffer (depth-buffer) algorithm for hidden surface removal. Compare it with the back-face detection method, stating one advantage and one disadvantage of each.

hidden-surface-removalz-buffer
6short8 marks

State the Phong illumination model and write its equation including ambient, diffuse and specular components. Differentiate between Gouraud shading and Phong shading.

illuminationshading
7short8 marks

What are Bezier curves? List the important properties of a Bezier curve. A cubic Bezier curve is defined by control points P0(1, 1), P1(2, 4), P2(5, 4) and P3(6, 1); compute the point on the curve at parameter u = 0.5.

curves-surfacesbezier
8short8 marks

Explain the scan-line polygon fill algorithm. Describe the role of the edge table and the active edge list, and how the algorithm handles vertices that are local minima or maxima.

scan-conversionpolygon-filling
9short6 marks

Describe the Sutherland-Hodgeman polygon clipping algorithm. Explain, with the help of a diagram, the four possible cases that arise when an edge is clipped against a single window boundary.

clippingsutherland-hodgeman
10short6 marks

Differentiate between raster scan and random (vector) scan display systems. What is meant by aspect ratio and frame buffer of a raster display?

output-primitivesdisplay-devices
11short6 marks

What is a B-spline curve? Explain how B-spline curves provide local control over the curve shape and state two advantages of B-spline curves over Bezier curves.

curves-surfacesb-spline
12short6 marks

Explain the depth-sorting (Painter's) algorithm for visible surface determination. Under what circumstances does the simple depth ordering fail, and how can such cases be resolved?

hidden-surface-removalpainters-algorithm