# Old Wine in New Bottles: A New Algebraic Framework for Computational Geometry

```@inproceedings{Hestenes2001OldWI,
title={Old Wine in New Bottles: A New Algebraic Framework for Computational Geometry},
author={David Hestenes},
year={2001}
}```
My purpose in this chapter is to introduce you to a powerful new algebraic model for Euclidean space with all sorts of applications to computer-aided geometry, robotics, computer vision and the like. A detailed description and analysis of the model is soon to be published elsewhere, so I can concentrate on highlights here, although with a slightly different formulation that I find more convenient for applications. Also, I can assume that this audience is familiar with Geometric Algebra, so we…
94 Citations

### Applications of Conformal Geometric Algebra in Computer Vision and Graphics

• Mathematics, Computer Science
IWMM/GIAE
• 2004
A new method for pose and position interpolation based on CGA is discussed which firstly allows for existing interpolation methods to be cleanly extended to pose andposition interpolation, but also allows for this to be extended to higher-dimension spaces and all conformal transforms (including dilations).

### Some Considerations about Geometric Algebras in relation with Visibility in Computer Graphics

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### A 1d Up Approach to Conformal Geometric Algebra: Applications in Line Fitting and Quantum Mechanics

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### Conformal Geometric Algebra for Robotic Vision

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The authors believe that the framework of conformal geometric algebra can be, in general, of great advantage for applications using stereo vision, range data, laser, omnidirectional and odometry based systems.

### Advanced Geometric Approach for Graphics and Visual Guided Robot Object Manipulation

• Computer Science
Proceedings of the 2005 IEEE International Conference on Robotics and Automation
• 2005
Conformal Geometric Algebra appears to be a promising mathematical tool for building intelligent man-machine interfaces and is shown to be very well suitable for applications of all kind of robot manipulator kinematics, representation and visualization and object robot manipulation.

### Surface Evolution and Representation using Geometric Algebra

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IMA Conference on the Mathematics of Surfaces
• 2000
By moving from a projective to a conformal representation (5d representation of 3d space), one is able to extend the range of geometrical operations that can be carried out in an efficient and elegant way.

### Geometry of complex data

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This tutorial provides a basic introduction to geometric algebra and presents formulations of known electrical engineering and signal processing concepts to illustrate some inherent advantages of geometric algebra for formulating and solving problems involving vectors.

### New Tools for Computational Geometry and Rejuvenation of Screw Theory

This paper is a comprehensive introduction to a CGA tool kit and designs for a complete system of powerful tools for the mechanics of linked rigid bodies are presented.

### Geometric computing in computer graphics and robotics using conformal geometric algebra

The main contribution of this thesis is the geometrically intuitive and - nevertheless - efficient algorithm for a computer animation application, namely an inverse kinematicsgorithm for a virtual character based on an embedding of quaternions in Conformal Geometric Algebra.

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