Length of a line in 3 dimensions

[entombedtrade]

All,

I am trying to determine the length of line across 3 dimensions (XYZ). My X&Y are WGS 84 coordinates and my Z value is HAE (Height Above Ellipsoid) in meters.

I can determine the XY length on a plane, but how do I account for the additional length added by a change in Height?

Example

50,50,50 -- 60,60,50 -- 60,60,40, -- 70,70,40 -- 70,70,50 In this case you can see I can 10 meters in length between coordinate triplets 2 & 3 as well as between 4 & 5 even though they share the same XY values

Does anyone have any thoughts on how to efficiently calculate this information?

Thanks,

 

[pat_connell]

JohnThe easiest way to calculate the length of a line across three dimensions is to use the Pythagorean theorem. This states that in a right triangle, the sum of the squares of two sides is equal to the square of the hypotenuse. The hypotenuse is the longest side of the triangle. We can apply this to the XYZ coordinates by calculating the differences between each coordinate and then using the Pythagorean theorem to calculate the total length. For example, if we have the coordinates (50,50,50), (60,60,50), (60,60,40), (70,70,40) and (70,70,50). To calculate the total length, first calculate the difference between each coordinate:X Difference: 10Y Difference: 10Z Difference: 10Then use the Pythagorean theorem to calculate the total length:Length = sqrt(10^2 + 10^2 + 10^2) = sqrt(1000) = 31.62 meters