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Draft: Pencils and intersection of two Quadrics

Merged Clara Oeverink requested to merge quadric_intersection into develop

Closes #247 (closed)

  • Adds skript signatures.py at ddg/geometry with three new classes (Here, normalform means the corresponding sequence is brought into a canonical form for checking equivalence):
    • SignatureSequence (Normalform for dimension 4 (RP³))
    • IndexSequence (Normalform for dimension 4 (RP³))
    • SegreSymbol (Normalform for arbitrary dimension)
  • Moves classes Signature and AffineSignature from ddg.math.symmetric_matrices to ddg.geometry.signatures
  • Adds methods to ddg.geometry._quadrics.Pencil class
    • for calculation of sequences from pencils of quadrics (only in RP³)
    • for classification of the intersection curve of pencils of quadrics (only in RP³)
  • Adds class QuadricIntersection to ddg.geometry._quadrics as base for visualisation of the intersection curve

Still left to be implemented:

  • Normalform/Equivalence relation for arbitrary dimension for SignatureSequence and IndexSequence
  • normal_form() returns another Pencil in normal form (without transformation), only 3D
    • This is different from Quadric.normalize, which contains the transformation
    • Normal form is derived from the index sequence.