Reference Implementation

The "reference implementation" is a Java (and C#) implementation of the algorithms discussed in Chapters 18 through 21 of the book. It contains an implementation of:

• Geometric algebra for basis blades.
• Geometric algebra for multivectors.
• Factorization, inversion, meet and join, exp, sin, cos.

The reference implementation was intended for educational purposes: the code was kept as simple as possible, and not designed with efficiency in mind. Hence the reference implementation is not suitable for compute-intensive applications; instead you can use the GA Sandbox or Gaigen 2 as a starting point for compute-intensive applications. To download the source code of the reference implementation, click on the following link:

Download the reference implementation in Java.

C# version

I have ported the Java version of the reference implementation to C# as a way to get some experience with that language. It is better documented and also can handle some simple symbolic scalar manipulations besides the numerical work. Personally I intend to use this for the code generation in a future version of Gaigen.

Download the reference implementation in C#.

Online Viewing of (Java) Source Code

You can also browse the code online, through the links below:

Basis Blades

• Basics
  • BasisBlade Storage
  • bitCount() method
  • canonicalReorderingSign() method
• Outer product:
  • Outer product
• Geometric product:
  • Geometric product in Euclidean metric
  • Geometric product in restricted non-Euclidean metric
  • Geometric product in arbitrary non-Euclidean metric
  • Computing the eigenbasis of a non-Euclidean metric
• Metric products:
  • Metric product filter (method that derives mp from gp)
• Reverse, Clifford conjugate, grade inversion:
  • minusOnePow(x) computes (-1)^x
  • reverse() method
  • gradeInversion() method
  • cliffordConjugate() method

Multivectors

• Basics:
  • Multivector Storage
  • simplify() method (Simplifies a multivector by adding basis blades that are a multiple of eachother. Used internally by some methods.)
• Distributive operations:
  • add() method
  • substract() method
  • gp() methods (geometric product with various way to specify metric)
  • op() method
  • ip() methods (inner product with various way to specify metric)
  • reverse() method
  • gradeInversion() method
  • cliffordConjugate() method
• Algorithms:
  • versorInverse() method
  • generalInverse() method
  • exp() method
  • expSeries() method (evaluates Taylor series)
  • sin() method
  • sinSeries() method (evaluates Taylor series)
  • cos() method
  • cosSeries() method (evaluates Taylor series)
  • MultivectorType class. (tests whether multivector is a blade or versor)
  • factorizeBlade() method
  • computation of meet and join

Copyright 2007-2008 Leo Dorst, Daniel Fontijne and Stephen Mann. Disclaimer: This website is maintained by the book authors. Morgan Kaufmann (an imprint of Elsevier) is in no way responsible for its content.