Lets not get lost in conflicts over word usage. Words are often reappropriated for particular purpose, and often have distinct usage in different languages.
I'm using geometry, construction, ratio, and proportion in ways that I believe are clear enough to be understood. For me, that's enough. Even though both ratio and proportion historically have been given more specific meanings, I'm using both interchangeably to refer loosely to comparing things by simple integer counts of a shared unit. Please allow this casual usage.
The word geometry has been used in so many ways. It doesn't just mean 'earth measurement' anymore. My particular usage --to refer to line and compass constructions, with or without specific ratios or measures -- is close to the usage in Euclid. So, if you will, please be lenient and just roll with it?
Yes, for the artist especially, portions often reference surfaces. Or more completely, they reference 2-demensional projects of a surface in 3 dimensions onto a plane which is normal to the viewer. Artists, and builders and designers more generally, tend to favor using proportions on based on these flat projects, without referencing the complications involved. Indeed, most of the 'proportions' or ratios mentioned by the likes of Vetruvius and Da Vinci don't if you measure lengths along the 3 dimensional surfaces instead of along the flat projections of those surfaces.
For violin making, some features fully involve these complications, and others don't so much.
The curves of the soundholes lie on a surface which is curved in 3 dimensions. So discussion of proportions will tend to be about the project of these shapes. However, there are ambiguities because work might be done directly on the curved surface, or on a flat surface and then transferred. Neither of these will exactly correspond to the projection onto a flat plane.
The curves of the volute and head present less complication. Even though the widths of the head change in complex ways, the arc shapes of curves correspond to cylinders that are square to the projected version of the shape, so there is no distortion in the design shape in this case. And this is were the casual use of the word 'outline' is handy. Even though the volute is a complicated 3 dimensional shape, it is very substantially governed by the projected outer boundaries of its shape. And this is what a mean using the convenient word 'outline'.
The plates present yet another specific case. Of course, the most interesting thing is the arching. Again, we have a 3 dimensional surface. But the plates are also bound by an outer edge, or 'outline'. The outline lies essentially in one plane, which makes it exactly equivalent to its normal projection. 'Geometry' gives a simple word to refer to the pattern of connecting arcs that give the right kind of shape. Ratio or proportion gives easy reference to the numeric ratios behind the geometry construction that give the exact shapes seen in particular instruments. The arching is indeed more complicated. And it's one of the few spots were freehand and smoothing (read bent splines) plays a significant role. Nevertheless, you can see that a few bounds or controls to free work run through classical arching. First, the channeling has a boundary in relation to the out edge. The width of the channel boundaries are generally set from simple ratios at the widest part of the upper and lower bouts, and the narrowest of the center bout. At these locations, the channel width is generally a simple ratio of the width from edge to center, for example 1/4, 1/6, 1/8. This width is then carried at a constant width through the bout, but free hand joined through the corners. So instruments, of cellos for example, present a different width at the top or bottom block which smoothly transitions to the main channel width for the bout. The execution of the channels within these boundaries are relatively varied in classical work. In earlier generations, the channel bottom tends to occur midway through the channel, with something approaching symmetrical curvature on either side. But in later generations we see a tendency for the channel bottom to push toward the outer edge. Since the channel shape must smoothly connect to the central arching, this forces a flatter curvature coming from the channel bottom toward the central arching. So we have three important boundary curves that help govern the arching. First is the plate outline, whose design is well determined by geometry and proportion. Second we have the channel boundary that is partially determined by ratio, and strongly relates to the outline. And last we have the channel bottom which might have been set by rule for some makers, but seems to have been set in a free relation to outline and channel boundary in later work. The last boundary governing the plate surface shape is the long arch running along the plates center line. This long arch is significantly different for the back and top plates, with the top plate's long arch having a long nearly flat portion running above and below the bridge toward the corner lines. The back in contrast tends to have only a very short near flat portion directly above the bridge line. Perhaps there are rules behind the long arc shape that I just haven't found. But it seems that this very important shape may have been essentially a production of smooth freehand and tradition. I find using the boat builder's technique of setting a few of the elevations along a division of the length of the arch to be helpful. For me, a divide the length of the plate into ninths and decide where along this the flat portions will end, and where the height will fall half way in its path to the channel boundary. But working a plate's long arch remains substantially freehand. Once the long arch is set, we have now four boundaries to govern the plate arching: the outline, the channel boundary, the channel bottom, and the long center line arch of the plate. This in itself would not be enough to well govern the plate arching, except that we can see that we can observe the central portion of classical plate arching conform to a simple workshop friendly rule. This only applies to the cross arching of the central arching (convex viewed from outside) around the center line. We can note that in the cross arching, from the center line to the edge of the channel boundary the plate falls a certain distance. The plate falls from its maximum of any particular cross arch at the center line, down to the channel boundary (which is the height of the work edge as you make the plate). The simple rule is that 1/2 of this fall is reached 2/3 the way from the center line to the channel boundary. This rule is actually recursive, and completely determines the cross arching from the center line, out 2/3 the way to the channel boundary. The recursive version of the rule is that for any on the cross arch between channel boundary and the maximum of the cross arch at the center line, there is a distance from the point to the center line which we will call the 'run', and there is a height difference between the cross arch height at that point and its maximum, which we will call the fall, and: 1/2 the fall occurs in 2/3 the run. This easy to apply workshop rule completely determines the curve of the cross arching from the center line to 2/3 the way out to the channel boundary. But you are still free to place the channel bottom and carve the curve from channel bottom to edge however you will. And we see most of the differences in classical makers arching styles arising from this liberty. But after carving the channel curve from channel bottom to edge, and after carving the convex center 2/3 of the cross arch by rule, the channel boundary and the need for a smooth curve leave you almost no liberty in completing the cross arching. So we see that in classical arching there is some liberty in establishing the channel, and the long center line arch of a plate, but after that the process is well determined.