Direct Linear Interpolation of Geometric Objects in Conformal Geometric Algebra
Published version
Peer-reviewed
Repository URI
Repository DOI
Change log
Authors
Hadfield, Hugo https://orcid.org/0000-0003-4318-050X
Lasenby, Joan https://orcid.org/0000-0002-0571-0218
Abstract
Typically we do not add objects in conformal geometric algebra (CGA), rather we apply operations that preserve grade, usually via rotors, such as rotation, translation, dilation, or via reflection and inversion. However, here we show that direct linear interpolation of conformal geometric objects can be both intuitive and of practical use. We present a method that generates useful interpolations of point pairs, lines, circles, planes and spheres and describe algorithms and proofs of interest for computer vision applications that use this direct averaging of geometric objects.
Description
Keywords
4904 Pure Mathematics, 49 Mathematical Sciences
Journal Title
Advances in Applied Clifford Algebras
Conference Name
Journal ISSN
0188-7009
1661-4909
1661-4909
Volume Title
29
Publisher
Springer