Define 3 points coordinates from dip/azimuth

In case you have the dip angle and the azimuth angle (i.e. strike angle) of a plane, here is how to calculate the XYZ coordinates of 3 points of this plane.

Note that below we assume that dip value is measured from horizontal plane. If dip is towards north, it must be set positive, and if it is towards south, set to negative.

Also, azimuth is measured positively in clockwise direction starting from North, i.e East is 90°, South is 180°…

In order to calculate coordinates of points belonging to this plane, let’s start from a point O (X₀, Y₀, Z₀) as the origin.

Considering a distance d, a dip angle dip, and an azimuth (i.e. strike) angle az, we can use the spherical coordinates calculations to obtain the coordinates of a point A :

dX_A = d*cos(az)*cos(dip)

dY_A=d*sin(az)*cos(dip)

dZ_A=d*sin(dip)

X_A=X₀+dX_A

Y_A=Y₀+dY_A

Z_A=Z₀+dZ_A

All angles must be set into radians.

And for a second point B on the horizontal direction (strike direction), we can do :

dX_B=d*sin(az)

dY_B=d*cos(az)

dZ_B=0

X_B=X₀+dX_B

Y_B=Y₀+dY_B

Z_B=Z₀

Download a Calc file to do this here :

Usefull links to read also:

https://beckassets.blob.core.windows.net/product/readingsample/176217/9783540310549_excerpt_001.pdf

https://en.wikipedia.org/wiki/Spherical_coordinate_system#Cartesian_coordinates

https://gis.stackexchange.com/questions/13484/how-to-convert-distance-azimuth-dip-to-xyz