I. Curve and Line-Curve Fits

This chapter explains several curve and tangent line-curve fitting situations.  They can be used with other COGO tools to construct complex curvilinear traverses having to fit specific mathematical conditions.

A. Fitting arc through three points

Three non-linear points define a circular arc, Figure I-1

Figure I-1 Three point arc

If the coordinates of the three points (1, 2, and 3) are known, the arc radius (R) and radius point (O) coordinates can be determined.

Equations I-1 and I-2 are used to compute the radius point coordinates.

	Equation I-1
	Equation I-2

The coefficients for Equation I-1 are:

	Equation I-3
	Equation I-4
	Equation I-5
	Equation I-6

Once the radius point coordinates are determined, the arc radius can be computed from Equation I-7 .

Equation I-7

Point i is any of the three points used to define the arc.