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Geometric algebra for computer science - an object-oriented approach to geometry
TLDR
An introduction to Geometric Algebra that will give a strong grasp of its relationship to linear algebra and its significance for 3D programming of geometry in graphics, vision, and robotics is found.
Discrete Representation of Straight Lines
  • L. Dorst, A. Smeulders
  • Computer Science
    IEEE Transactions on Pattern Analysis and Machine…
  • 1 April 1984
TLDR
It is proved that every ``straight'' chaincode string can be represented by a set of four unique integer parameters, and a mathematical expression is derived for the set of all continuous line segments which could have generated a given chain code string.
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Geometric Algebra
  • L. Dorst
  • Mathematics
    Computer Vision, A Reference Guide
  • 30 July 2019
TLDR
This half day tutorial will emphasize that Geometric Algebra is a unified language for a lot of mathematical systems used in Computer Graphics, and can be used in an easy and geometrically intuitive way in Computer graphics.
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First order error propagation of the Procrustes method for 3D attitude estimation
  • L. Dorst
  • Mathematics
    IEEE Transactions on Pattern Analysis and Machine…
  • 1 February 2005
TLDR
This paper performs the first order error analysis of the Procrustes method for the 3D case, fully specifying how directional noise in the point clouds affects the estimated parameters of the rigid body motion.
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Square Root and Logarithm of Rotors in 3D Conformal Geometric Algebra Using Polar Decomposition
TLDR
This chapter gives explicit formulas for the square root and the logarithm of rotors in 3D CGA and classifies the types of conformal transformations and their orbits.
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Length estimators for digitized contours
  • L. Dorst, A. Smeulders
  • Mathematics, Computer Science
    Comput. Vis. Graph. Image Process.
  • 1 December 1987
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Differential A*
TLDR
The algorithm is developed and an application to robot path planning in configuration space, where the graph topology, transition costs, or start/goals may change simultaneously, is discussed.
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Morphological signal processing and the slope transform
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Decomposition of discrete curves into piecewise straight segments in linear time
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Discrete straight line segments: parameters, primitives and properties
TLDR
For continuous straight lines and straight object boundaries, the best accuracy that can be reached in the estimation of length (and other properties) is shown, in the absence of noise.
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