D. Arc-Based Intersections

1. Circle; Arc

Figure D-1 is a diagram of a circle and Equation D-1 is its equation in terms of North and East coordinates.

Figure D-1
Circle

 

Equation D-1
where:  

O
i
R

  radius point
  point on circumference
  radius

An arc is a portion of a circle, Figure D-2.

Figure D-2
Arc portion of a circle

Generally we only need an arc long enough to meet an intersection condition. We'll cover other specific arc geometry in the Curvilinear Traverse chapter.