# Surface Evolution and Representation using Geometric Algebra

@inproceedings{Lasenby2000SurfaceEA, title={Surface Evolution and Representation using Geometric Algebra}, author={Anthony N. Lasenby and Joan Lasenby}, booktitle={IMA Conference on the Mathematics of Surfaces}, year={2000} }

Recent developments in geometric algebra have shown that 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. For example, while in projective space one is able to intersect lines and planes in a simple fashion, in conformal space one is able to intersect and represent spheres, lines, circles and planes. In addition, all the operations of…

## 11 Citations

Conformal Geometry, Euclidean Space and Geometric Algebra

- MathematicsArXiv
- 2002

A solution to the problem of handling the Euclidean distance between points based on conformai geometry is discussed, including a compact formula for reflecting a line off a general spherical surface.

Circle and sphere blending with conformal geometric algebra

- MathematicsArXiv
- 2003

A simple, robust set of algorithms for performingcircle blends for performing circle blends for a range of cases is demonstrated and the basic idea is extended to the case of sphere blending to interpolate over a surface.

A covariant approach to geometry using geometric algebra

- Mathematics, Computer Science
- 2004

Using the mathematical framework of conformal geometric algebra – a 5-dimensional representation of 3-dimensional space – is shown to provide an elegant covariant approach to geometry, thus enabling us to deal simply with the projective and non-Euclidean cases.

The Twist Representation of Shape

- Mathematics
- 2004

We give a contribution to the representation problem of free-form curves and surfaces. Our proposal is an operational or kinematic approach based on the Lie group SE(3). While in Euclidean space the…

Twists - An Operational Representation of Shape

- MathematicsIWMM/GIAE
- 2004

An operational or kinematic approach based on the Lie group SE(3) that makes possible the robust and fast estimation of the pose of 3D objects from incomplete and noisy image data and the equivalence of the proposed shape model to that of the Fourier representations.

Monocular Pose Estimation of Kinematic Chains

- Mathematics
- 2002

In this paper conformal geometric algebra is used to formalize an algebraic embedding for the problem of monocular pose estimation of kinematic chains. The problem is modeled on a base of several…

Applications of Geometric Algebra in Electromagnetism, Quantum Theory and Gravity

- Physics, Mathematics
- 2004

We review the applications of geometric algebra in electromagnetism, gravitation and multiparticle quantum systems. We discuss a gauge theory formulation of gravity and its implementation in…

Estimating rigid motions via the conformal model of Euclidean space

- Computer Science, MathematicsProceedings of the 17th International Conference on Pattern Recognition, 2004. ICPR 2004.
- 2004

An origin independent semi-closed form is derived for the optimal transformation of rigid motions from 3-D point correspondences and image projections, solving it using an SVD-based technique.

6-DOF haptic rendering using geometric algebra

- Computer ScienceIEEE International Workshop HAVE Haptic Virtual Environments and Their
- 2002

This paper presents an approach that uses an evenly distributed collection of points to represent the tool and shows that there is a limit to this concentration where it yields a continuous model of the volume of the actual tool.

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