Three dimensional mathematical modeling of violin plate surfaces: An approach based on an ensemble of contour lines

摘要

This paper presents an approach to describing the three dimensional shape of a violin plate in mathematical form. The shape description begins with standard contour lines and ends with an equation for a surface in three dimensional space. The traditional specification of cross sectional arching is unnecessary. Advantages of this approach are that it employs simple and universal description of plate geometry and yields a complete, smoothed, precise mathematical equation of the plate that is suitable for modern three dimensional production. It is quite general and suitable for both exterior and interior plate surfaces, yielding the ability to control thicknesses along with shape. This method can produce mathematical descriptions with tolerances easily less than 0.001 millimeters suitable for modern computerized numerical control carving and hand finishing.