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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.

 

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