UNIVERSITY OF KERALA - Marian Engineering College

B.Tech Comp. Sc. & Engg., University of Kerala 62
08.704 (1) COMPUTATIONAL GEOMETRY (ELECTIVE I) 3 – 1 – 0
Module I (17 hours)
Geometric Preliminaries, DCEL ( Doubly Connected Edge List) data structure, Geometric Duality,
Geometric Searching - Planar Straight Line Graph (PSLG), Point Location Problem, Location of a point in a
planar subdivision, Plane Sweep Algorithm, Slab method, Chain method, Regularization of PSLG, Range
Searching Problems.
Module II (17 hours)
Convex Hulls- Convex Hull Algorithms in the Plane -Graham’s Scan Algorithm, Jarvi’s March, Divide
and Conquer Algorithm, Dynamic Convex Hull Algorithm.
Triangulation—Triangulation of a point set, Triangulation Algorithms, Polygon Triangulation, Convexity,
Helly’s theorem, Delauny Triangulation, Voronoi Diagrams- Applications in the plane , Post Office
Problem.
Module III (18 hours)
Arrangements of Lines - Zone Theorem, Many Faces in arrangements, Constructing the arrangements,
Forbidden graph theorem, Bipartite graph for many face problems.
Linear Programming - Linear Programming in Two Dimensions, Prune - Eliminate Redundant Half-Planes.
Introduction to Visibility Problems - Definition of direct visibility, Point visibility and Edge visibility,
Algorithm for computing point-visible region inside a polygon.
Text Books:
1. Computational Geometry an Introduction – Franco P. Preparata and Michael Ian Shamos,
Texts and Monographs in Computer Science, Springer Verlag
2. Algorithms in Combinatorial Geometry – Herbert Edelsbrunner, EATCS Monographs on theoretical
computer science, Springer Verlag.
3. Art Gallery Theorems – Joseph O’ Rourke, Oxford Press.
Reference Books:
1. Computational Geometry and Computer Graphics in C++ – Michael J. Laszlo, Prentice Hall of India.
Internal Continuous Assessment (Maximum Marks-50)
25 Marks - Tests (minimum 2)
15 Marks - Assignments (minimum 3) such as home work, problem solving, literature survey, seminar,
term-project, software exercises, etc.
10 Marks - Regularity in the class
University Examination Pattern
PART A: Short answer questions 10 x 4 marks=40 marks
All questions are compulsory. There should be at least three questions
from each module and not more than four questions from any module.
PART B: Descriptive/Analytical/Problem solving questions 3 x 20 marks=60 marks
Candidates have to answer one question out of two or two questions
out of four from each module.
Maximum Total Marks: 100