These two illustations are from the field of surveying but they should still apply.
As Martin has said, in triangulation, you work with angles as illustrated in the following figure.
The positions of the points of interest are computed based on measured angles and two know points. From those angles, the distances are computed which are in ...
It's already explained in the terms:
Triangulation = working with angles
Trilateration = working with distances.
In real world applications you often work with both, or combine them. For example, total station surveys measure both distances and angles. On the other hand, GPS receivers use trilateration concepts, where speed and time equals a distance, to ...
Using scipy and numpy:
import numpy as np
from scipy.spatial import Delaunay
points = np.random.rand(4, 3)
tri = Delaunay(points)
See the documentation here.
Form (whole circle) bearing, zenith angle and horizontal distance to X, Y, Z
X = X0 + h_distance * sin(deg / 360 * pi())
Y = Y0 + h_distance * cos(deg / 360 * pi())
Z = Z0 + h_distance / tan(zenith / 360 * pi())
X0, Y0, Z0 are the coordinates of the station
deg / 360 * pi() changes angle from deg to radians
Horizontal distance from slope distance and ...
Here's one (probably very naive) way of doing it using the sigloc package.
Once the sigloc package is installed the following should work
df <- data.frame(
Date = '1/11/2016',
Observers = 'MickyT',
GID = 1,
Time = c(1,2,3,4,5,6,7,8),
Easting = c(473789,473755,473728,473730,473848,473926,473925,473850),
Assuming that we're dealing with the planar coordinate case (that is not actually what the OP suggested, but I offer this as a better answer to the one given so far – and so far, accepted, by the OP – for the planar case), it helps to first determine the direction cosines from the two clockwise bearings, βAC and βBC, from known points A ...
If you are working from land survey plats, the basis of bearing, even though it is referenced to California Grid Zone 5, should have a starting, or reference line for the basis of bearing.
This should be at the beginning of the description for the easement.
It may start at a section corner, or some other aliquot corner, and describe the traverse to the ...
I am not from California but in my state the declination should be listed on the plat or record of instrument, at least it usually is. If not I believe this may help, put in the area the survey was done and the date it was done and it should give you declination. NGS has alot of cool tools btw
The difference between ...
The gIntersection function from the rgeos library might help you. See the commented code below.
pointB <- SpatialPoints(cbind(1,1))
pointC <- SpatialPoints(cbind(4,2))
distanceA2B <- 2
distanceA2C <- 3
# create the circle polygons around the points with the distances
polyB <- gBuffer(pointB, width = distanceA2B)
KevinMayall's suggestion of intersecting circles is the easiest. A good theoretical treatment can be found at Wolfram Mathworld, which may get into more detail than you want to get this working (but is nice background for writing a paper about your methodology).
This StackOverflow answer has a broken link but outlines a basic approach.
Or if you are happy with just plane trig solution in just 19 lines of code. Here it is in U-Basic.
This differs from the algorithms for geodesics solution by about 6mm at a distance of 175 meters.
5 'interx.ub adapted from code at
7 'In U Basic by yuji ...