You can read a brief introduction of each topic.    The files are in pdf file format. To open pdf files, you may  download a free Adobe Acrobat Reader in the following pages:  Hong Kong Star  Adobe (official Page)  You need to have password to download the following files.

Section A
1. Chapter 1 Transformation
You will study Euclidean Geometry in the chapter. The chapter teaches how to use matrix for transfomation, like reflection and rotation. Also, you can learn the transformations that produce 2D images of 3D objects onto an image plane.
• Euclidean Geometry
• Rotation matrix
2. Chapter 2 Figures and Shapes
This chapter introduces some properties of regular and semi-regular solids. Barycentric co-ordinates are described for CAD applications. Euler Characteristics, Descartes's formula and Gauss-Bonnet theorem for polyhedron.

 
 

3. Chapter 3 Differential Geometry of Curves
   The chapter tells you how to determine Frenet Frame.
There are also some important computational formulae.

 
4. Chapter 4 Design of Curves
Approximation is useful in design.Blending funcions are the basic representation of both approximation and interpolation. You can learn some algorithms to approximate a curve in this chaper.
5. Chapter 5  Differential Geometry of Surfaces
The first and second fundamental forms & curvatures.

6. Chapter 6 Design of surfaces
 Bezier patches

Section B
1. Fractal Geometry

    Fractals have self-similar properties. If a portion of a fractal object is enlarged, the magnified portion always resembles the original figure, e.g., Cloud, ferm ...
    You have to know how to calculate the fractal dimension and familiarize it with the Iterative Function System (IFS).

2. Introduction of Computational Geometry

There is a brief introduction of convex hull and voronoi diagrams. Also, You will learn the algorithm of Triangulation which partitions a polygon into triangles by the addition of diagonals.

3. Convex Hulls in 2D

The chapter introduce some algorithms of making a convex hull, such as Gift Wrapping, Quick Hull and Grapham's Algorithm.
 

4. Voronoi Diagrams

Voronoi Diagram is a set of points that have more than one nearest neighbour. You need to familiarize with the properties of Delaunay Triangulation and Voronoi Diagrams.