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.

翻译：部分早期小提琴在历史上曾通过修形以符合既定的形态标准，而近代制作的乐器则直接遵循这些标准建造。我们观察到修形与未修形乐器之间存在差异，尤其体现在等高线与极小值通道的特征上。在近期初步工作中，我们利用摄影测量技术获取的三角三维网格，以亚毫米精度验证并计算了两件乐器的这两个特征。本文将该研究扩展至包含38把小提琴、中提琴及大提琴的数据库，并引入改进算法，从而构建更具说服力的几何分析讨论。首先回顾研究对象的基本特征，继而阐释如何推导小提琴对齐的最佳基准平面——该步骤对等高线与极小值通道的计算至关重要。最后展示两种特征的高效计算方法，并通过实例呈现分析结果。