BE Computer Engineering (IOE, TU) Computer Graphics (IOE, CT 605 / ENCT 201) Question Paper 2079

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

(b) Using Bresenham's line drawing algorithm, trace and tabulate all the intermediate pixel positions for a line segment from point A(2, 3) to point B(9, 8). [4]

(a) A triangle is defined by the vertices $A(1, 1)$, $B(4, 1)$ and $C(2, 3)$. Perform a rotation of $90^\circ$ counter-clockwise about the point $P(2, 2)$ and find the coordinates of the transformed vertices using homogeneous coordinate matrices. Show the composite transformation matrix. [8]

(b) Explain why homogeneous coordinates are used to represent 2D transformations, and show how translation can be expressed in matrix form using them. [4]

(a) Distinguish between parallel projection and perspective projection. Derive the transformation matrix for a perspective projection of a 3D point onto the $z = 0$ plane with the centre of projection at distance $d$ along the negative z-axis. [8]

(b) Write the $4\times 4$ homogeneous transformation matrix for scaling about an arbitrary fixed point $(x_f, y_f, z_f)$ in 3D. [4]

(a) Explain the Cohen–Sutherland line clipping algorithm using region (outcode) codes. With the help of the algorithm, clip the line segment from $P_1(40, 15)$ to $P_2(75, 45)$ against a rectangular clipping window with corners $(x_{min}, y_{min}) = (50, 10)$ and $(x_{max}, y_{max}) = (80, 40)$. [8]

(b) State the limitation of the Sutherland–Hodgeman polygon clipping algorithm when clipping a concave polygon. [4]

Explain the midpoint circle drawing algorithm, deriving its decision parameter. Using the eight-way symmetry property, list the pixel positions generated in the first octant for a circle of radius $r = 8$ centred at the origin.

Define a Bézier curve. Write the blending (Bernstein basis) function for a cubic Bézier curve, and list any three important properties of Bézier curves.

Describe the Z-buffer (depth-buffer) algorithm for hidden surface removal. State its main advantages and disadvantages compared to a scan-line method.

Explain the Phong illumination model, clearly describing the ambient, diffuse and specular components and the role of each term in the lighting equation.

Differentiate between Gouraud shading and Phong shading. State which technique correctly renders specular highlights and explain why.

Explain boundary-fill and flood-fill area-filling algorithms. Distinguish between 4-connected and 8-connected approaches with the help of suitable diagrams.

(a) Describe the Sutherland–Hodgeman polygon clipping algorithm and the four possible vertex-edge cases it handles. [4]

(b) Briefly explain the strategies used for text clipping. [2]

What is meant by local control of a curve? Compare B-spline curves with Bézier curves with respect to local control and continuity.