Appropriate for undergraduate courses in Computational Geometry and/or Computer Graphics.
This book describes some basic problems in computer graphics and computational geometry, and presents some practical methods for solving them, using these problems and solutions as an introduction to the fields of Computational Geometry and Computer Graphics. Introducting the reader to the design and analysis of algorithms provides the framework for studying the algorithms covered in the text.
Features:
provides fully functioning, object-oriented C++ implementations of all material covered.
features intuitive discussions, complemented by many examples and figures.
presents the fundamentals of the design and analysis of algorithms, data structures, and geometric data structures, and employs these fundamentals in the presentation of computational geometry and computer graphics methods.
consists of two parts:
Part One, Basics, presents background — the fundamentals of data structures and algorithms, and the necessary geometrical concepts and tools.
Part Two, Applications, organized by algorithmic paradigm — poses problems and presents solutions.
Content:
I. BASICS.
1. Introduction.
Framework. Our Use of the C++ Language. Robustness.
2. Analysis of Algorithms.
Models of Computation. Complexity Measures. Asymptotic Analysis. Analysis of Recursive Algorithms. Problem Complexity. Chapter Notes. Exercises.
3. Data Structures.
What are Data Structures? Linked Lists. Lists. Stacks. Binary Search Trees. Braided Binary Search Trees. Randomized Search Trees. Chapter Notes. Exercises.
4. Geometric Data Structures.
Vectors. Points. Polygons. Edges. Geometric Objects in Space. Finding the Intersection of a Line and a Triangle. Chapter Notes. Exercises.
II. APPLICATIONS.
5. Incremental Insertion.
Insertion Sort. Finding Star-Shaped Polygons. Finding Convex Hulls: Insertion Hull. Point Enclosure: The Ray-Shooting Method. Point Enclosure: The Signed Angle Method. Line Clipping: The Cyrus-Beck Algorithm. Polygon Clipping: The Sutherland-Hodgman Algorithm. Triangulating Monotone Polygons. Chapter Notes. Exercises.
6. Incremental Selection.
Selection Sort. Finding Convex Hulls: Gift-Wrapping. Finding Complex Hulls: Graham Scan. Removing Hidden Surfaces: The Depth-Sort Algorithm. Intersection of Convex Polygons. Finding Delaunay Triangulations. Chapter Notes. Exercises.
7. Plane-Sweep Algorithms.
Finding the Intersections of Line Segments. Finding Convex Hulls: Insertion Hull Revisited. Contour of the Union of Rectangles. Decomposing Polygons into Monotone Pieces. Chapter Notes. Exercises.
8. Divide-and-Conquer Algorithms.
Merge Sort. Computing the Intersection of Half-Planes. Finding the Kernel of a Polygon. Finding Voronoi Regions. Merge Hull. Closest Points. Polygon Triangulation. Chapter Notes. Exercises.
9. Spatial Subdivision Methods.
The Range Searching Problem. The Grid Method. Quadtrees. Two-Dimensional Search Trees. Removing Hidden Surfaces: Binary Space Partition Trees. Chapter Notes. Exercises.
Bibliography.
Index.
