TY - JOUR
T1 - Three dimensional mathematical modeling of violin plate surfaces
T2 - An approach based on an ensemble of contour lines
AU - Piantadosi, Steven
N1 - Publisher Copyright:
© 2017 Steven Piantadosi. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
PY - 2017/2
Y1 - 2017/2
N2 - 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.
AB - 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.
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U2 - 10.1371/journal.pone.0171167
DO - 10.1371/journal.pone.0171167
M3 - Article
C2 - 28166230
AN - SCOPUS:85011636039
SN - 1932-6203
VL - 12
JO - PloS one
JF - PloS one
IS - 2
M1 - e0171167
ER -