Guide to Geometric Algebra in Practice

Guide to Geometric Algebra in Practice edited by Leo Dorst, Joan Lasenby.

Geometric algebra (GA), also known as Clifford algebra, is a powerful unifying framework for geometric computations that extends the classical techniques of linear algebra and vector calculus in a structural manner. Its benefits include cleaner computer-program solutions for known geometric computat...

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Bibliographic Details
Corporate Author: SpringerLink (Online service)
Other Authors: Dorst, Leo (Editor), Lasenby, Joan (Editor)
Format: eBook
Language:English
Published: London : Springer London : Imprint: Springer, 2011.
Edition:1st ed. 2011.
Series:Springer eBook Collection.
Subjects:
Computer science—Mathematics.
Computer graphics.
Artificial intelligence.
Optical data processing.
Computer-aided engineering.
Electronic resources (E-books)
Online Access:Click to view e-book
Holy Cross Note:Loaded electronically.
Electronic access restricted to members of the Holy Cross Community.
Table of Contents:
  • How to Read this Guide to Geometric Algebra in Practice
  • Part I: Rigid Body Motion
  • Rigid Body Dynamics and Conformal Geometric Algebra
  • Estimating Motors from a Variety of Geometric Data in 3D Conformal Geometric Algebra
  • Inverse Kinematics Solutions Using Conformal Geometric Algebra
  • Reconstructing Rotations and Rigid Body Motions from Exact Point Correspondences through Reflections
  • Part II: Interpolation and Tracking
  • Square Root and Logarithm of Rotors in 3D Conformal Geometric Algebra using Polar Decomposition
  • Attitude and Position Tracking / Kinematics
  • Calibration of Target Positions using Conformal Geometric Algebra
  • Part III: Image Processing
  • Quaternion Atomic Function for Image Processing
  • Color Object Recognition Based on a Clifford Fourier Transform
  • Part IV: Theorem Proving and Combinatorics
  • On Geometric Theorem Proving with Null Geometric Algebra
  • On the Use of Conformal Geometric Algebra in Geometric Constraint Solving
  • On the Complexity of Cycle Enumeration for Simple Graphs
  • Part V: Applications of Line Geometry
  • Line Geometry in Terms of the Null Geometric Algebra over R3,3, and Application to the Inverse Singularity Analysis of Generalized Stewart Platforms
  • A Framework for n-dimensional Visibility Computations
  • Part VI: Alternatives to Conformal Geometric Algebra
  • On the Homogeneous Model of Euclidean Geometry
  • A Homogeneous Model for 3-Dimensional Computer Graphics Based on the Clifford Algebra for R3
  • Rigid-Body Transforms using Symbolic Infinitesimals
  • Rigid Body Dynamics in a Constant Curvature Space and the ‘1D-up’ Approach to Conformal Geometric Algebra
  • Part VII: Towards Coordinate-Free Differential Geometry
  • The Shape of Differential Geometry in Geometric Calculus
  • On the Modern Notion of a Moving Frame
  • Tutorial: Structure Preserving Representation of Euclidean Motions through Conformal Geometric Algebra.

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