Measuring Distance in 3D

DanPatterson_Retired

3D  

• Math check
• Conventional application
• The Map and the Profile
• Calculations
• Unconventional application

Math check

A bump ride along the x-axis

x       [ 0.,  1.,  2.,  3.,  4.,  5.,  6.,  7.,  8.,  9., 10.],
y       [ 0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.],
z       [ 0.,  1.,  0.,  1.,  0.,  1.,  0.,  1.,  0.,  1.,  0.]

total length/distance travelled   14.142...
segment length/distance travelled [1.41, 1.41, 1.41, 1.41, 1.41, 1.41, 1.41, 1.41, 1.41, 1.41]

Conventional application

• Take a DEM
• Construct a 3D polyline (Z-enabled) representing a profile path along it
• Densify it at some increment if you want to sample more elevation points along the line, but are too lazy to do it as you go (or you forgot).  This is optional, but there are builtin tools and/or 3rd party tools to do this (including some of mine)
• Feature vertices to points, to get the path as points
  • Poly* features to points .... any license  from Polygon_polyline_tools, or
  •  feature-vertices-to-points .... Advanced license
• Extract values to these points.
  • Extract Values to Points in the Spatial Analyst
  •  If you don't have SA, there are ways to get these data, but that is for another blog
• Add Geometry Attributes to get the x, y and z values for the points.
  • Add Geometry Attributes
• Off to numpy

The Map and the Profile

Start low, go high, or vice versa.  Vertical exaggeration on the Z values 

Calculations

Now for some distance calculations.

Points

array([[ 300012.56, 5001013.9 ,       3.  ],
       [ 300025.53, 5001010.2 ,       6.  ],
       [ 300037.26, 5001003.4 ,       9.  ],
             ...,
       [ 300972.11, 5000037.68,     198.  ],
       [ 300993.72, 5000021.01,     201.  ],
       [ 301014.1 , 5000008.04,     204.  ]])

2D  Total length, sequential lengths
 -     1505.25,

 -     array([13.49, 13.56, 14.4 , 18.42, 17.69, 21.99, 17.66, 17.49, 21.29, 20.08,
                ... snip
                37.54, 42.86, 32.03, 33.18, 20.75, 25.46, 24.84, 18.03, 27.29, 24.15]))

3D  Total, sequential

 -      1519.95,

 -      array([13.82, 13.88, 14.71, 18.66, 17.94, 22.19, 17.91, 17.74, 21.5 , 20.31,
                ... snip

                 37.66, 42.96, 32.17, 33.32, 20.96, 25.64, 25.02, 18.28, 27.46, 24.34]))

Quick calculation

np.sqrt(204**2 + 1505.25**2)  => 1519.01  Not to be unexpected given the line's shape.

Calculations made using  ... e_leng ... from arraytools. The gist link allow people to experiment.

Unconventional application

How far did the turkey vulture travel before it landed on its food?

2D start-end point distance  - 56.39

2D  Total length, sequential lengths

 -  1590.97

 -  array([0.16, 0.16, 0.17, 0.18,  ...,  8.76, 8.79, 8.81, 8.84]))

3D  Total, sequential

 -  1658.26

 -  array([1.01, 1.01, 1.01, 1.02,  ..., 8.82, 8.85, 8.87, 8.89]))

Archimedes spiral in 3D