BE Computer Engineering (Pokhara University) Computer Graphics (PU, CMP 234) Question Paper 2079

(a) Derive the decision parameters for Bresenham's line drawing algorithm for a line with slope $0 < m < 1$, clearly stating the initial decision parameter and the incremental updates. (8)

(b) Using the Bresenham line algorithm, digitize the line from $(20, 10)$ to $(30, 18)$ and tabulate the pixel positions plotted. (6)

(a) Explain why homogeneous coordinates are used to represent two-dimensional transformations, and write the matrix representations for translation, rotation and scaling. (6)

(b) A triangle is defined by the vertices $A(2,2)$, $B(6,2)$ and $C(4,6)$. Obtain the composite transformation matrix to rotate the triangle by $90^\circ$ counter-clockwise about the vertex $A$, and compute the coordinates of the transformed triangle. (6)

(a) Distinguish between parallel projection and perspective projection, and classify parallel projections with the help of suitable diagrams. (6)

(b) Derive the transformation matrix for an oblique parallel projection onto the $xy$-plane, and show how the cavalier and cabinet projections are obtained as special cases of it. (8)

(a) State the Cohen-Sutherland line clipping algorithm and explain the significance of the 4-bit region (out) codes. (6)

(b) Given a clipping window with corners $(x_{min}, y_{min}) = (10,10)$ and $(x_{max}, y_{max}) = (40,40)$, clip the line segment from $P_1(5,5)$ to $P_2(45,35)$ using the Cohen-Sutherland algorithm. Show the region codes and the computed intersection points. (6)

Compare raster scan and random (vector) scan display systems with respect to working principle, image quality, memory requirement and suitability. Define resolution, aspect ratio and frame buffer.

Explain the midpoint circle drawing algorithm and the use of the eight-way symmetry of a circle. Using it, determine the pixel positions for the first octant of a circle of radius $r = 8$ centred at the origin.

Define a Bezier curve. Write the parametric equation of a cubic Bezier curve in terms of its Bernstein blending functions and four control points, and list the important properties of Bezier curves.

Differentiate between object-space and image-space methods of hidden surface removal. Explain the Z-buffer (depth-buffer) algorithm and state one advantage and one disadvantage of it.

Compare Gouraud shading and Phong shading in terms of the quantity interpolated, computational cost and quality of the rendered surface (in particular the appearance of specular highlights).

Explain the Sutherland-Hodgeman polygon clipping algorithm with a neat diagram. What is the major limitation of this algorithm when clipping concave polygons?

Write the homogeneous transformation matrices for 3D rotation about the $x$, $y$ and $z$ axes. Obtain the matrix that reflects a 3D object about the plane $z = 0$.

Write short notes on any two of the following:

(a) Anti-aliasing techniques (b) Boundary-fill vs. flood-fill algorithms (c) Color models (RGB and CMY)