There used to be methods and rules for drawing contour lines by hand, especially before computers. You could draw potential lines and stream function lines, for instance, that would be everywhere mutually perpendicular. You’d mark boundaries with where the lines had to meet, and try to make the lines space evenly and have the spacing change in a way that was twice differentiable. In a certain sense it would have to be topologically equivalent to a subset of a square gridwork.
I think this was the theoretical version of what would be physically modelled with rubber sheeting. For example they’d stretch rubber to fit edges at different heights according to the boundary conditions in an electron tube, and this is how they’d visualize electron trajectories and other details.
Where are some instructions for and illustrations of this method?
Contact and mapping company or better yet an aerial mapping company and talk to one of the old timers who made maps with old projection plotters or ‘scribers’ who made the printable 'scribe coated mylar sheets, usually an orange color, and they can give you a few pointers. when I was in the business, it took a bit of training to get a person to do an acceptable job.
They have to be within the specified mapping limits as to actual ground elevations.
Just not done all that much by hand anymore. Final check and clean up still is in a lot of cases.
Thanks for the lead. There are a number of web references out there for mapmaking. But all but one of the ones I have found are only concerned with altitude contours, and the one that discusses their mutually orthagonal contours for the equivalent stream function in mapmaking, which would follow the locally steepest grades uphill and down and would show which way surface water drains, only talked about using the result, not generating it.
I think maybe mapmakers only use one side of this method.
>Would not ‘more’ potential to ‘less’ potential be the same as .higher’ elevation to ‘lower’ elevation?
Yes, but mapmakers don’t seem to create lines from higher to lower. I only see lines connecting points at the same elevation, i. e. a contour for 400 meters. Or am I missing something?
There are rules you can apply to the lines that go from high to low, just as there are for the isolines for the altitude (though I’m not sure if the differences between the two rule sets are trivial). Certainly one difference is that if there are singularities in the potential function then there can be radiant streamlines - that is, for the Dirichlet problem, the boundary value problem for the laPlace equation, there are no singularities, but solutions of the Poisson equation can have them. I think there are rules for how to force the lines to tend to be smooth and equidistant, absent information to the contrary. For example in computing contours or smoothed surfaces I know there are optimization functions, like a function to set the ratio of the integrated divergence to the integrated squared error, that achieve a similar grade of smoothness in a certain sense, regardless of the density of data. I think there are rules for doing these things by hand that accomplish roughly the same effects. I think they tend to come more from mathematics than from mapmaking but am not sure. This ring any bells for anyone?