BE Computer Engineering (Pokhara University) Computer Graphics (PU, CMP 234) Question Paper 2078

(a) With the help of a neat block diagram, explain the architecture of a raster-scan display system. Differentiate between raster-scan and random-scan (vector) display systems on the basis of refresh mechanism, image quality, and suitability for solid-area scenes. (8)

(b) A raster system is designed using a resolution of 1280 × 1024 with a color depth of 24 bits per pixel. Calculate the total size of the frame buffer required in megabytes. If the display refreshes at 60 Hz, determine the access (read) rate per pixel in nanoseconds. (4)

(c) Define aspect ratio and persistence of a phosphor. Why is persistence an important parameter in the design of a CRT display? (3)

(a) Derive the decision parameter for the Bresenham's line drawing algorithm for a line with slope 0 < m < 1, clearly stating the assumptions made and the incremental update of the decision variable for both possible pixel choices. (8)

(b) Using the midpoint circle drawing algorithm, plot the pixel positions for a circle of radius r = 8 centred at the origin. Show the calculation of the decision parameter for the first octant in tabular form, and explain how the eight-way symmetry is used to obtain the remaining pixels. (7)

(a) Distinguish between parallel projection and perspective projection. Explain, with diagrams, oblique and orthographic parallel projections, and define the terms centre of projection, vanishing point, and view plane. (8)

(b) Derive the 4 × 4 homogeneous transformation matrix for a perspective projection onto the z = 0 plane with the centre of projection located at a distance d along the negative z-axis. (4)

(c) Why are homogeneous coordinates used in 3D transformations? Explain how a single composite matrix can represent a sequence of rotation, scaling, and translation operations. (3)

(a) Explain the Cohen–Sutherland line clipping algorithm. Describe the assignment of region (outcodes) to the endpoints and the use of logical AND/OR operations to trivially accept or reject a line segment. (7)

(b) A clipping window is defined by the corners (x_min, y_min) = (1, 1) and (x_max, y_max) = (9, 8). Using the Cohen–Sutherland algorithm, clip the line segment with endpoints P1(0, 3) and P2(11, 6). Show the outcodes and compute the coordinates of the clipped (visible) segment. (8)

A triangle is defined by the vertices A(2, 2), B(6, 2), and C(4, 6). Perform a reflection of the triangle about the line y = x, and write down the new coordinates of the vertices. Show the transformation matrix used and verify one vertex by hand calculation.

Obtain the composite transformation matrix to rotate an object by an angle θ about an arbitrary pivot point (x_p, y_p) in 2D. List the sequence of basic transformations involved and explain why the order of matrix multiplication matters.

Define a Bézier curve. Write the blending (Bernstein) functions for a cubic Bézier curve with four control points P0, P1, P2, P3, and state the key geometric properties of Bézier curves (endpoint interpolation, convex hull, and tangent conditions).

Differentiate between interpolation and approximation splines. Explain the meaning of parametric continuity (C0, C1, C2) and geometric continuity (G0, G1) at the join point of two curve segments.

Explain the Z-buffer (depth-buffer) algorithm for hidden surface removal. Write the algorithm in steps, state the two buffers required, and discuss its main advantages and limitations compared to the painter's (depth-sort) algorithm.

What is back-face detection? Given a polygon surface with outward normal N = (A, B, C) and a viewing direction along the positive z-axis, state the condition under which the polygon is identified as a back face and can be culled.

Compare Gouraud shading and Phong shading with respect to the quantity interpolated across the polygon, computational cost, and quality of specular highlights produced. Explain why Phong shading renders highlights more accurately.

State the Phong illumination model and write its equation including the ambient, diffuse, and specular components. Define each term and explain the role of the shininess (specular reflection) coefficient.

Explain the Sutherland–Hodgeman polygon clipping algorithm. Describe the four possible cases that arise when an edge of the polygon is processed against a single clip boundary, and state one limitation of this algorithm for concave polygons.

Write short notes on any two of the following:

(a) Boundary-fill and flood-fill algorithms for area filling

(b) Aliasing and anti-aliasing techniques

(c) Scan-line polygon fill algorithm