A discussion about violin reduction: geometric analysis of contour lines
  and channel of minima
Philémon Beghin Anne-Emmanuelle Ceulemans François Glineur
Some early violins have been reduced during their history to fit imposed
morphological standards, while more recent ones have been built directly to
these standards. We can observe differences between reduced and unreduced
instruments, particularly in their contour lines and channel of minima. In a
recent preliminary work, we computed and highlighted those two features for two
instruments using triangular 3D meshes acquired by photogrammetry, whose
fidelity has been assessed and validated with sub-millimetre accuracy. We
propose here an extension to a corpus of 38 violins, violas and cellos, and
introduce improved procedures, leading to a stronger discussion of the
geometric analysis. We first recall the material we are working with. We then
discuss how to derive the best reference plane for the violin alignment, which
is crucial for the computation of contour lines and channel of minima. Finally,
we show how to compute efficiently both characteristics and we illustrate our
results with a few examples.