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- Eckhard Hitzer
- ArXiv
- 2013

We treat the quaternionic Fourier transform (QFT) applied to quaternion fields and investigate QFT properties useful for applications. Different forms of the QFT lead us to different Plancherelâ€¦ (More)

- Eckhard Hitzer
- 2013

We use the recent comprehensive research [17, 19] on the manifolds of square roots of âˆ’1 in real Cliffordâ€™s geometric algebras Cl(p,q) in order to construct the Clifford Fourier transform. Basicallyâ€¦ (More)

- Robert Benjamin Easter, Eckhard Hitzer
- CGI
- 2016

We introduce Clifford geometric algebra based multivector modeling of quartic and general quadric surfaces, Darboux cyclides, Dupin cyclies, tori and pairs of standard CGA objects. A computerâ€¦ (More)

- Roxana Bujack, Ingrid Hotz, Gerik Scheuermann, Eckhard Hitzer
- 2014 IEEE Pacific Visualization Symposium
- 2014

The analysis of 2D flow data is often guided by the search for characteristic structures with semantic meaning. One way to approach this question is to identify structures of interest by a humanâ€¦ (More)

- Eckhard Hitzer
- ArXiv
- 2013

We explain the orthogonal planes split (OPS) of quaternions based on the arbitrary choice of one or two linearly independent pure unit quaternions f ,g. Next we systematically generalize theâ€¦ (More)

- Eckhard Hitzer
- ArXiv
- 2013

A split hypercomplex learning algorithm for the training of nonlinear finite impulse response adaptive filters for the processing of hypercomplex signals of any dimension is proposed. The derivationâ€¦ (More)

- Roxana Bujack, Jens Kasten, Ingrid Hotz, Gerik Scheuermann, Eckhard Hitzer
- 2015 IEEE Pacific Visualization Symposiumâ€¦
- 2015

We generalize the framework of moments and introduce a definition of invariants for three-dimensional vector fields. To do so, we use the method of moment normalization that has been shown to beâ€¦ (More)

We survey the historical development of quaternion and Clifford Fourier transforms and wavelets.

- Roxana Bujack, Ingrid Hotz, Gerik Scheuermann, Eckhard Hitzer
- IEEE Transactions on Visualization and Computerâ€¦
- 2015

The analysis of 2D flow data is often guided by the search for characteristic structures with semantic meaning. One way to approach this question is to identify structures of interest by a humanâ€¦ (More)

In this text we present a software tool that visualises the symmetry properties of the space groups of 3D Euclidean space, which play an important role in the investigation of crystalline materials.â€¦ (More)