CONTENTS

1. Two Dimensional Transformations

1.  Introduction    

2.  Representation of Points   

3.  Transformation and Matrices

4.  Transformation of Points (Scaling, Reflection & Shearing)  

5.  Rotation (about the Origin)

6.  Transformation of Straight Line 

7   Midpoint Transformation    

8.  Transformation of Parallel Lines

9.  Transformation of Intersecting Lines

10. Transformation and Area of Plane Figure    

11. Solid Body Transformations 

12. Homogeneous Co-ordinates and Translation   

13. Rotation about an Arbitrary Point

14. Reflection through an Arbitrary Line  

15. Projection – a Geometric Interpretation of Homogeneous Co-ordinates   

16. Overall Scaling 

17. Points at Infinity

2. Three Dimensional Transformations

1. Introduction

2. Three Dimensional Rotation  

3. Multiple Transformations    

4. Reflections through Co-ordinate Planes 

5. Reflection through an Arbitrary Plane

3. Projections 

1. Introduction

2. Affine and Perspective Geometry  

3. Orthographic Projection

4. Axonometric Projections

5. Oblique Projections    

6. Perspective Projection 

7. Vanishing Points

4. Plane Curves

1. Introduction

2. Curve Representation   

3. Non-Parametric Curves  

4. Parametric Curves

5. Parametric Representation of Circle

6. Parametric Representation of Ellipse   

7. Parametric Representation of a Parabola and Generation of Parabola

8. Parametric Representation of a Hyperbola

5. Space Curves

1. Introduction

2. Be’zier Curves