How to calculate Distance, Azimuth and Dip from two XYZ coordinates

Question

I have two XYZ coordinates and I would like to calculate the Distance, Azimuth and Dip between them.

I have come across a similar question on this site that calculates it the other way around (with a given starting coordinate and a given Distance, Azimuth and Dip and it calculates an end coordinate.)

I have been trying to figure it out and I am sure its very simple.

Here is that other question page. It says that this is a conversion between a spherical and Cartesian coordinates.

How to convert Distance, Azimuth, Dip to XYZ?

Answer 1

For a line, it is a plunge and not a dip (for 3D planes)

It is an elementary problem in analytic geometry:

The distance = SQRT((x2 –x1)2+(y2 –y1)2+(z2 –z1)2)

The plunge = arcsin ((z2 – z1) / distance)

The azimuth = arctan((x2 –x1)/(y2 –y1)) (always in two dimensions)

The value θ returned will be in the range of ±90° and must be corrected to give the true azimuth over the range of 0 to 360°

You can also use the direction cosines of the line (the slopes on the xy, xz and yz planes)

In Python:

 import math
 x1,y1,z1 = 5.0,6.7,1.5
 x2,y2,z2 = 4.0,1.2,1.6
 distance = math.sqrt((x2-x1)**2+(y2-y1)**2+(z2 -z1)**2)
 print distance
 5.5910642993977451
 plunge = math.degrees(math.asin((z2-z1)/distance)
 print plunge
 1.0248287567800018 # the resulting dip_plunge is positive downward if z2 > z1
 azimuth = math.degrees(math.atan2((x2-x1),(y2-y1)))
 print azimuth
 -169.69515353123398 # = 360 + azimuth = 190.30484646876602 or  180+ azimuth = 10.304846468766016 over the range of 0 to 360°

With the direction cosines:

cosalpha =(x2-x1)/distance
cosbeta=(y2-y1)/distance
cosgamma= (z2-z1)/distance
plunge = math.degrees(math.asin(cosgamma))
print plunge
1.0248287567800018 # the resulting dip_plunge is positive downward if z2 > z1
azimuth = math.degrees(math.atan2(cosa, cosb))
print azimuth
-169.69515353123398 #  = 360 + azimuth = 190.30484646876602 or  180+ azimuth = 10.304846468766016 over the range of 0 to 360°

Answer 2

azimuth in ruby

def cartographical_azimuth_radians(point1, point2)
  Math::atan2(point2.x-point1.x, point2.y-point1.y)
end

def cartographical_azimuth_decimal_degrees(point1, point2)
  180/Math::PI * cartographical_azimuth_radians(point1, point2)
end