Drawing a Topographical Map

Question

I\'ve been working on a visualization project for 2-dimensional continuous data. It\'s the kind of thing you could use to study elevation data or temperature patterns on a 2

Answer 1

Write the data out as an HGT file (very simple digital elevation data format used by USGS) and use the free and open-source gdal_contour tool to create contours. That works very well for terrestrial maps, the constraint being that the data points are signed 16-bit numbers, which fits the earthly range of heights in metres very well, but may not be enough for your data, which I assume not to be a map of actual terrain - although you do mention terrain maps.

Answer 2

I've wanted something like this myself, but haven't found a vector-based solution.

A raster-based solution isn't that bad, though, especially if your data is raster-based. If your data is vector-based too (in other words, you have a 3D model of your surface), you should be able to do some real math to find the intersection curves with horizontal planes at varying elevations.

For a raster-based approach, I look at each pair of neighboring pixels. If one is above a contour level, and one is below, obviously a contour line runs between them. The trick I used to anti-alias the contour line is to mix the contour line color into both pixels, proportional to their closeness to the idealized contour line.

Maybe some examples will help. Suppose that the current pixel is at an "elevation" of 12 ft, a neighbor is at an elevation of 8 ft, and contour lines are every 10 ft. Then, there is a contour line half way between; paint the current pixel with the contour line color at 50% opacity. Another pixel is at 11 feet and has a neighbor at 6 feet. Color the current pixel at 80% opacity.

alpha = (contour - neighbor) / (current - neighbor)

Unfortunately, I don't have the code handy, and there might have been a bit more to it (I vaguely recall looking at diagonal neighbors too, and adjusting by sqrt(2) / 2). I hope this enough to give you the gist.

Answer 3

compare what you have rendered with a real-world topo map - they look identical to me! i wouldn't change a thing...

Answer 4

In response to your comment to @erickson and to answer the point about calculating the gradient of your function. Instead of calculating the derivatives of your 300 term function you could do a numeric differentiation as follows.

Given a point [x,y] in your image you could calculate the gradient (direction of steepest decent)

g={  ( f(x+dx,y)-f(x-dx,y) )/(2*dx), 
  {  ( f(x,y+dy)-f(x,y-dy) )/(2*dy) 

where dx and dy could be the spacing in your grid. The contour line will run perpendicular to the gradient. So, to get the contour direction, c, we can multiply g=[v,w] by matrix, A=[0 -1, 1 0] giving

c = [-w,v]

Answer 5

Alternately, there is the marching squares algorithm which seems appropriate to your problem, although you may want to smooth the results if you use a coarse grid.

The topo curves you want to draw are isosurfaces of a scalar field over 2 dimensions. For isosurfaces in 3 dimensions, there is the marching cubes algorithm.

Answer 6

I always check places like http://mathworld.wolfram.com before going to deep on my own :)

Maybe their curves section would help? Or maybe the entry on maps.