Creating Points at Intersections

There are four basic types of intersections needed in surveying. They are bearing-bearing, distance-distance, bearing-distance and bearing-line.


Two lines, starting at different points and with different bearings, intersect at a single point. No intersection is computed if the lines are parallel.


Two circles, having different center or radius points, intersect at none, one (tangent circles) or two points. The circles may have different radii and may not intersect at all if one circle is inside the other or the distance between radius points is greater than the sum of their radii.

Each circle is defined by a center point and a distance for the radius.


A line and a circle intersect at none, one (tangent) or two points.

A center point (either Pt1 or Pt2) and a distance for the radius define the circle.


A line defined by a starting point and bearing/azimuth intersects the curve defined by two end points.

When computing a Bearing-Curve intersect, you can also tell TPC to allow intersections beyond the end points of the curve. By default, TPC only considers intersections between the end points of the curve.

Using the intersection dialog box

The Intersection dialog box will display only one valid intersection for a bearing-bearing intersection. It will display two valid intersections for a bearing-distance or distance-distance intersection. When TPC finds a valid intersection, one or both Computed Intersection fields will be available for entry (white rather than gray).

Note: Neither Computed Intersection field will be available if TPC can't find a valid intersection based on the data you entered.

To see how the intersection points are related:

Creating an Intersection Using Offsets

This example is a bearing-bearing intersection with offsets. The actual intersection point is offset to the left of the line from 1 to 2 and offset right of the line from 3 to 2

The offset distances specified do not have to be the same.

The intersection dialog box for this example would look like this, assuming an offset of 10 units to the left of the line from 1 to 2 and 12 units right of the line from 3 to 2.

The Bearing for Point 1 was derived from the equation 1..2 entered for this field. The Bearing for Point 2 was derived from the equation 3..2 entered for its field. Equations make it very easy to recall an azimuth, bearing or distance.

Bearing-Curve Intersection

In this example, we want to find out where a line 10 units left of the property line from 1 to 2 intersects the curve from 5 to 1:1.

The intersection routine does not care if the curve is a tangent curve or not.

Now let’s look at the dialog box for this example. The rule for intersecting a bearing and a curve is that we enter the bearing information for Point 1 and use boxes on the right to define the curve.

Enter the starting point and bearing of the line in Point 1.

Now enter the end points of the curve or press 'Or select a line >' and left click the curve in the current drawing.

Grid vs Ground / Geodetic

Intersections are computed based on the distance and direction types selected in the dialog.

As of this version, TPC does not compute geodesic intersects (the intersection of two geodesics) if geodetic distance and direction types are selected. Instead, if the [x] Latitude Arc is selected, TPC will compute a PLSS compatible geodetic intersection on the latitudinal arc defined by points 2 and 3 in the dialog.

Tangent Intersections

TPC uses the term Tangent intersections for a special kind of intersections that are constrained to be tangent to an arc. See Tangent Intersections.


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Related Topics

Using COGO

COGO Commands - reference