D. Examples
1. Three point curve
Three known coordinate points are
Point | North (ft) | East (ft) |
A | 902.72 | 1751.91 |
B | 870.76 | 1237.76 |
C | 538.57 | 1293.16 |
Determine the radius of the circle passing through the points and coordinates of the radius point.
Sketch
Compute the coefficients using Equations I-3 through I-6
Use the coefficients in Equations I-1 and I-2 to get radius point coordinates
Get radius from Equation I-7
Using point A
Check using point B
Checks within rounding.
Answers
Radius | 294.42' | |
Radius pt coords | 744.39' N | |
1503.68' E |
2. Tangent line
What is the direction of the line line tangent to the arc shown below? What are the coordinates of the intersection point?
Inverse from point W to the radius point O
Using Equation I-12 compute the angle g between the line to the radius point and tangent line.
Determine the azimuth and length of the tangent line
.
Since the tangent line is left of the line to the radius point, to get its azimuth subtract g from Az_{WO'} Equation, I-16.
Its length comes from Equation I-13
Forward Computation, Equations I-17 and I-18, to compute tangent point coordinates
Answers
Tangent azimuth | 72°45'42" | |
Tangent pt coords | 1501.00' N | |
1810.34' E |
3. Three-tangent arc
What is the radius of the arc that is tangent to the three line shown?
Label the geometry
Establsh points G and H using direction-direction intersections (results shown, comps left to user)
Point | North | East |
G | 1849.672 | 1305.139 |
H | 1735.850 | 1670.923 |
Δ_{G} and Δ_{H} from the azimuths (comps left to user)
Δ_{G} | 63°05'03" |
Δ_{H} | 49°03'40" |
Inverse Computation to obtain distance from point G to point H (comps left to user): 383.084
Apply Equation I-19 to get the arc radius
Tangent distance for first arc section (comps left to user): 219.721
Radius point coordinates (comps left to user): 1,442.592' N and 1,408.580' E
Answers
Radius | 357.96' | |
Radius pt coords | 1,442.59' N | |
1,408.58' E |