Meeting

\( 17^{th} \) of July \(2019\)

Since our last meeting

 

  • Papers
    • Transverse approach (Mapping)
    • Aligned Quadrics and Eckhard Notation
    • Garamon implementation
  • Teachings:
    • Too much

 

  • Projects

Projects

Geometric Algebra (Theory)

  • Construction of QCGA with Projective transformations

    • Construction of QCGA with Projective Transformations
Already done To be done
Rotation   non-isotropic scale
Translation skewing
Isotropic scale hyperbolic rotations

Projects

Geometric Algebra (Theory)

Quadric Intersection interpretation

\(\mathbf{c}^{*} = \mathbf{q}_{1}^{*} \wedge \mathbf{q}_2^{*}\)

\( \hookrightarrow \) Intersection?

\( \hookrightarrow \) Imaginary intersection?

Projects

Discretization

Quadric Intersection interpretation

\(\mathbf{c}^{*} = \mathbf{q}_{1}^{*} \wedge \mathbf{q}_2^{*}\)

\( \hookrightarrow \) Discretization with structuring element (circle)

tests were done with Conformal method 

Projects

Low dimensions for cubic and quadrics definition

Up to now:

more and more surface \( \Rightarrow\) increase dimension

\( \hookrightarrow \) Include  basis changes in the metric

Projects

Implementation

Garamon

At the moment:

      \( \hookrightarrow \) best for high dimension

      \( \hookrightarrow \) but not the best for low dimensions

 

\( \Rightarrow \) Make our Prefix tree compatible with Template metaprogramming in C++

To summarize

  • GA \( \& \) Projective transformations 
  • GA Discretization with QCGA
  • make GA able to define more objects in low dimensions
  • Prefix tree suitable with compile time approach

Intern ?

  • Sakura project (4th september) ??
  • Other things ?

 

Workshop in GA?