• Publications
  • Influence
Perspex Machine VIII: axioms of transreal arithmetic
Transreal arithmetic is a total arithmetic that contains real arithmetic, but which has no arithmetical exceptions. It allows the specification of the Universal Perspex Machine which unifies geometryExpand
Transreal Limits Expose Category Errors in IEEE 754 Floating-Point Arithmetic and in Mathematics
The IEEE 754 standard for oating-point arithmetic is widely used in computing. It is based on real arithmetic and is made total by adding both a positive and a negative infinity, a negative zero,Expand
Perspex machine XI: topology of the transreal numbers
The transreal numbers are a total number system in which even, arithmetical operation is well defined even-where. This has many benefits over the real numbers as a basis for computation and,Expand
Trans-Floating-Point Arithmetic Removes Nine Quadrillion Redundancies From 64-bit IEEE 754 Floating-Point Arithmetic
IEEE 754 floating-point arithmetic is widely used in modern, general-purpose computers. It is based on real arithmetic and is made total by adding both a positive and a negative infinity, a negativeExpand
Construction of the Transreal Numbers and Algebraic Transfields
The transreal numbers, introduced by James Anderson, are an extension of the real numbers. The four arithmetical operations of addition, subtraction, multiplication and division are closed on the setExpand
Perspex Machine IX: transreal analysis
  • James Anderson
  • Mathematics, Engineering
  • Electronic Imaging
  • 29 January 2007
We introduce transreal analysis as a generalisation of real analysis. We find that the generalisation of the real exponential and logarithmic functions is well defined for all transreal numbers.Expand
Global trajectory optimisation: can we prune the solution space when considering deep space manoeuvres?
This document contains a report on the work done under the ESA/Ariadna study 06/4101 on the global optimization of space trajectories with multiple gravity assist (GA) and deep space manoeuvresExpand
Exact numerical computation of the rational general linear transformations
  • James Anderson
  • Mathematics, Engineering
  • SPIE Optics + Photonics
  • 1 November 2002
The rational, general-linear transformations can be computed exactly using rational, matrix arithmetic. A subset of these transformations can be expressed in QR form as the product of a rational,Expand
Canonical description of the perspective projections
  • James Anderson
  • Computer Science, Engineering
  • Other Conferences
  • 9 April 1993
A unique parameterization of the perspective projections in all whole-numbered dimensions is reported. Expand
CAD-based vision
We describe work in progress on a robot inspection system which learns the appearance of objects given a CAD model of them. We also describe work on automatic camera-robot calibration and visualExpand