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Currently software and maps represent earth in many different ways, the latest is Point Clouds as this is the most common surveying tools currently available. For the needs of visualisation, construction etc. this seems to suffice for now. Not sure this is an engineering question but I tried in the philosophy forum and been advised this is applied science.

What is the most accurate representation of earth in a digital format (or mathematical equation):

  • 3D splines
  • solids and primitives
  • breaklines/contours
  • polygonal mesh, TIN
  • square 3D pixels

?

Rott
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You are confusing methods of organizing data with the accuracy of that data or the accuracy of the interpolation method. The two are orthogonal.

For example, you could describe a surface in Z as a function of X and Y as a rectangular grid of points. At each point, the Z for that X,Y is known explicitly. For X,Y between points, you do a 2D linear interpolation between the 4 nearest points.

Alternatively, you could describe the surface as a set of contour lines, like a topo map. For any point not on a contour, you interpolate between the two nearest countours.

Which one is more accurate? Either can be made arbitrarily accurate. If you put a grid point every mile and compare that to a map with 10 foot countours, the contour map will usually give you far better accuracy. On the other hand, consider a grid point every meter versus 100 foot contours. Most of the time the grid will be much more accurate.

Olin Lathrop
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