Vector Analysis for Computer Graphics

1. Front Matter

   Pages I-XIII

   PDF

2. Scalars and Vectors

   • John Vince

   Pages 1-10

3. Vector Representation

   • John Vince

   Pages 11-59

4. Straight Lines

   • John Vince

   Pages 61-99

5. The Plane

   • John Vince

   Pages 101-121

6. Reflections

   • John Vince

   Pages 123-127

7. Intersections

   • John Vince

   Pages 129-177

8. Rotating Vectors

   • John Vince

   Pages 179-200

9. Vector Differentiation

   • John Vince

   Pages 201-211

10. Projections

    • John Vince

    Pages 213-224

11. Rendering

    • John Vince

    Pages 225-239

12. Motion

    • John Vince

    Pages 241-245

13. Back Matter

    Pages 253-253

    PDF

In my last book, Geometry for Computer Graphics, I employed a mixture of algebra and vector analysis to prove many of the equations used in computer graphics. At the time, I did not make any distinction between the two methodologies, but slowly it dawned upon me that I had had to discover, for the first time, how to use vector analysis and associated strategies for solving geometric problems. I suppose that mathematicians are taught this as part of their formal mathematical training, but then, I am not a mathematician! After some deliberation, I decided to write a book that would introduce the beginner to the world of vectors and their application to the geometric problems encountered in computer graphics. I accepted the fact that there would be some duplication of formulas between this and my last book; however, this time I would concentrate on explaining how problems are solved. The book contains eleven chapters: The first chapter distinguishes between scalar and vector quantities, which is reasonably straightforward. The second chapter introduces vector repres- tation, starting with Cartesian coordinates and concluding with the role of direction cosines in changes in axial systems. The third chapter explores how the line equation has a natural vector interpretation and how vector analysis is used to resolve a variety of line-related, geometric problems. Chapter 4 repeats Chapter 3 in the context of the plane.

• Computer Analysis
• Computer Games
• calculus
• computer animation
• computer graphics
• development
• reflection
• rendering

From the reviews:

"Vince’s book applies to more than computer graphics: it is a resource for many areas in applied mathematics. … Students in computer graphics courses would find it very useful if their class discussions moved into the mathematical fundamentals underlying the tools. … Undergraduate students especially lack the mathematics background that this book provides. … It is comprehensive and coherent, and a good addition to the library of any computational scientist." (Anthony J. Duben, ACM Computing Reviews, Vol. 49 (8), August, 2008)

• Bournemouth University, UK

  John Vince

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