MCA-211
Computer Graphics
Drawing with mathematics — scan conversion and transformations, clipping and projection, curves and animation, then hidden surfaces and shading.
- Semester
- Semester 3
- Credits
- 3
- Scheme
- 3 lectures a week
- Contact hours
- 45 across four units
- Category
- Core Elective - II
What the paper is
Computer Graphics is the most algorithmic and most geometric paper in the elective list. Every unit is a set of named algorithms applied to coordinates, and almost every exam question asks you to run one of them on given numbers rather than to describe it.
The order follows the graphics pipeline, which is worth noticing: primitives are scan-converted, transformed, clipped to a window, projected to two dimensions, and finally shaded with hidden surfaces removed. Learning the pipeline gives each algorithm a place rather than leaving you with a list.
Unit III adds curves and surfaces — Bezier and B-spline, including NURBS — plus animation and OpenGL. It is twelve hours and the most modern-feeling material; the OpenGL portion is where the paper meets its lab.
What to concentrate on
- Bresenham's line and midpoint circle algorithms are asked as “generate the points from this start to this end”, every year, in some form. They are the cheapest marks in the paper once practised.
- For transformations, work in homogeneous coordinates from the start and learn rotation about an arbitrary point and reflection about an arbitrary line as compositions. The composition is the question; the individual matrices are just the pieces.
- Cohen-Sutherland line clipping with its region codes is the most examined algorithm in Unit II. Sutherland-Hodgeman polygon clipping is the second. Both are traceable on a diagram and worth rehearsing that way.
Syllabus, unit by unit
Summarised from the approved scheme. Hours are the contact hours the scheme allots, which is a fair guide to where the marks sit.
Unit I · Scan conversion and transformations
12 hours- Computer graphics and its applications; video display devices, raster-scan and random-scan systems, graphics software
- Line drawing algorithms: DDA and Bresenham; circle by midpoint and Bresenham; ellipse by midpoint
- Two- and three-dimensional geometric transformations: translation, scaling, rotation, reflection, shearing
- Homogeneous coordinates, composite transformations, rotation about an arbitrary point, reflection about an arbitrary line, affine transformations
Unit II · Clipping, projection and solid modelling
11 hours- Windowing and clipping, the 2D viewing pipeline, computing the viewport, window-to-viewport transformation
- Point and line clipping: Cohen-Sutherland and Cyrus-Beck; polygon clipping with Sutherland-Hodgeman
- Projections: parallel — oblique, orthographic, axonometric — and perspective: one-, two- and three-point, vanishing points, perspective anomalies
- Solid modelling: regularised Boolean set operations, sweep and spatial partitioning representations, boundary representation, octrees, constructive solid geometry, fractals
Unit III · Curves, surfaces, animation and OpenGL
12 hours- Parametric and non-parametric curves; Bezier curves: cubic and higher order, blending functions, Bernstein polynomials, continuity conditions, limitations
- B-splines: construction, cubic B-splines, knot vectors, uniform, open-uniform and non-uniform; beta and rational splines, NURBS
- Bezier and B-spline surfaces
- Animation: principles, methods and tools
- OpenGL: features and operations, immediate mode, extensions, OpenGL as a state machine, animation and event handling with GLUT
Unit IV · Hidden surfaces, illumination and shading
10 hours- Hidden surface removal: the need for it and the categories of method
- Z-buffer and A-buffer, depth sorting, BSP trees, back-face removal, scan-line and area-subdivision methods
- Illumination: ambient, diffuse and specular reflection, ray tracing
- Shading models: flat, Gouraud and Phong shading
- Colour models: RGB, CMY, HSV and HSL
How it is examined
- Question 1 is compulsory, covers the whole syllabus, and is made of objective or short-answer questions. It carries 12 marks.
- The rest of the paper is four units matching the four above. Each unit sets two questions and you attempt one, so there are four more answers at 12 marks each.
- Examiners are asked to map every question to a course outcome using Bloom's taxonomy, which is why questions are phrased as “apply”, “analyse” or “evaluate” rather than only “explain”.
The pass mark is 40 out of 100 in every paper.
Learning objectives
- Basic building blocks and core concepts of computer graphics
- The typical graphics pipeline
- Theoretical, mathematical and practical aspects of graphics algorithms
- Fundamental concepts of animation and related technologies for interactive applications
Assumed beforehand
- Basic mathematical concepts
Paired in the scheme with MCA-265 Lab based on Core Elective II.
Books it is taught from
- TB1Donald Hearn and M. Pauline Baker, “Computer Graphics with OpenGL”, Pearson, 4th edition, 2014
- TB2James D. Foley et al., “Computer Graphics: Principles and Practice”, Addison-Wesley Professional, 3rd edition, 2013
- TB3Rogers and Adams, “Mathematical Elements for Computer Graphics”, McGraw-Hill, 2nd edition, 2002
Notes for MCA-211
Lecture notes, question papers and assignments filed against MCA-211 are in the library. Everything there has been checked by a moderator before it appears, and an account is free — new ones are approved by hand, which is what keeps the shelf clean.