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

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?