A traverse is a way of defining lines and area boundaries as they are described in surveying in the United States. Although traverses are best known for use in surveying in the US, they can be very useful worldwide in any situation where a line, a boundary, or a record of a path or course can be most easily recorded by noting a series of directions and distances instead of a list of latitude, longitude coordinates.
Traverses are also known as metes and bounds descriptions or, in ESRI jargon, COGO (computational geometry) descriptions. Manifold uses ESRIstyle descriptions for traverses, using ESRI traverse format in the Info pane's coordinates list when we choose Show Traverse.
GIS packages define a line by listing the coordinates that compose the line. Traverses define a line by describing how to walk that line, in terms of directions and distances to go. To see the difference, we begin by considering a line drawn in the form of a square, as in the illustration below.
The standard way of defining such a line in GIS is to give a list of the X,Y coordinates in order. Beginning at 15, 80 the line continues to 20, 80, then to 20, 75, then to 15, 75 and finally back to 15, 80.
Traverses describe how to walk the line instead of listing the coordinates. A simple way is to state the direction to walk and how far to go. A traverse like that shown above might say, "Start at the beginning point and walk in the 90 degree direction for five meters. Next, walk in the 180 degree direction for five meters. Next, walk in the 270 degree direction for five meters. Finally, walk in the 0 degree direction for five meters." If a traverse accurately describes the directions and the distances to walk, if we follow the instructions we will end up exactly where we started, walking the area boundary of a closed square. This style of writing a traverse is called direction and distance, abbreviated DD or Direction + Distance.
An alternate way to write a traverse that uses directions and distances is to use relative directions, that give a relative angle to turn for the next segment. The traverse above illustrates that approach, and might be written as, "Start at the beginning point and walk in the 90 degree direction for five meters. Next, turn 90 degrees to your right and walk for five more meters. Next, again turn 90 degrees to your right and walk five more meters. Finally, turn 90 degrees to your right and walk five meters." This style of writing a traverse is called angle and distance, abbreviated AD or Angle + Distance.
When using angle and distance descriptions, the direction for each segment is given by a relative angle to change the preceding direction. That means we cannot use an angle and distance description for the very first segment, since there is no preceding direction from which to start. The first segment therefore is always a DD, that is, a direction and distance segment, after which we can give relative angles AD style.
The above introduction to traverses discusses only straight line segments. Traverses can also include circular arcs, which involve fairly unintuitive, but geometrically accurate descriptions.
The Info pane's Coordinates tab is the primary interface for viewing, loading, and saving traverses.
The coordinate list format picker button allows us to choose between showing the coordinates that define a line or an area in either XY/XYZ format or in traverse format. Traverses are a way of defining lines or areas, but not points, so there is no traverse format for a point. Illustrations below show coordinates for an area with many coordinates.
XY/XYZ format simply lists the X,Y or X,Y,Z (in the case of lines or areas with a Z value) numbers for each vertex or control point of a curved segment. Traverse format describes lines or areas by giving the angle or direction, and distance to each next vertex. ESRI traverse format, using tokens such as SP, DD, AD, TC, and NC, is used in the coordinates list when we choose Show Traverse.
The Traverse Parameters choice in the pull down menu launches the Traverse Parameters dialog, which allows us to choose various ESRI options for specifying directions and distances in traverses.
ESRI traverse format provides options for how straight line segments and circular arc segments are described. For example, we cans switch from Direction + Distance style using DD tokens to Angle + Distance style using AD tokens (when allowed). In the Coordinates list, we use Ctrl+A to select all rows, and then we rightclick one of the DD rows and choose Angle + Distance. That will switch all selected rows to using Angle + Distance notation, with Manifold automatically recomputing the angles from directions to relative angles.
We can see how the Coordinates tab reports coordinates or traverses for the examples with which we started this topic, using a line that forms a closed square. To launch the Info pane we would pick the line by Altclicking it, and then choosing the Coordinates tab. Illustrations below do not show the altclicked line, but do show what the Coordinates tab would report:
The default display is X,Y coordinates, in the usual GIS way.
Using the coordinate list format picker button we can switch to Show Traverse. The default traverse format is DD, Direction + Distance format. The SP token at the beginning gives the coordinates of the Starting Point.
Selecting all rows, rightclicking onto a DD row and choosing Angle + Distance switches the display to using AD, Angle + Distance format for all rows where AD format can be used.
The Info pane can read from a file or save to a file a coordinates list in either Manifold Coordinates format or ESRI Traverse format. Whichever format is displayed when we press the Save button will be the format used for the text file that is created. Coordinates format saves coordinates as X Y numbers, adding a third Z number if the object has a Z value. Traverse format saves coordinate geometry in standard ESRI traverse file format.
Manifold coordinates format closely matches what is displayed in the list and preserves all data.
The first line contains a single character specifying the type of object: P for point, L for line, or A for area. Lines following the first line contain coordinates, with each line beginning with a C, CC, CE, CS, or E code indicating the nature of the coordinate:
C <x> <y> [<z>]  coordinate.
CC <x> <y> [<z>]  circle arc coordinate.
CE <x> <y> [<z>]  ellipse arc coordinate.
CS <x> <y> [<z>]  spline coordinate.
E <x> <y> [<z>]  coordinate that ends a branch.
Coordinate values are separated by one or more whitespace characters.
Example: A text file saving coordinates for an area with four vertices might contain:
A
C 826590.1661996043 5425098.995517982
C 826608.2333529602 5425149.516990494
C 826635.595683797 5425139.733152165
C 826630.820077642 5425126.359355299
C 826617.5285304413 5425089.211733231
E 826590.1661996043 5425098.995517982
The area above has no Z value, so just X Y coordinates are listed.
ESRI traverse format preserves X Y values, but not Z, and preserves circle arcs, but not ellipse arcs or spline arcs. For details, see the ESRI Traverse file format page.
The first two line specifies the format for direction type, which can be QB for Quadrant Bearing, NA for North Azimuth, SA for South Azimuth, or P for Polar. Useful ESRI illustrations of direction type are at the ESRI Direction Formats page for ArcGIS Pro. The second line specifies direction units, which can be decimal degrees, degreesminutesseconds, radians, or gradians. Lines following the first two lines contain coordinates, with each line beginning with an S, EP, DD, AD, TC, or NC code indicating the nature of the coordinate:
SP <x> <y>  starting coordinate.
EP <x> <y>  ending coordinate.
DD <direction> <distance>  coordinate in the specified direction and distance.
AD <angle> <distance>  coordinate in the specified direction relative to the direction of the immediately preceding straight line segment.
TC <circle arc parameters>  circle arc tangent to the current direction. The arc parameters are any pair of: central angle, arc length, chord length, or radius, plus whether the arc turns left or right.
NC <circle arc parameters>  circle arc not necessarily tangent to the current direction. The arc parameters are those for a tangent arc plus one extra direction that can be: tangent, radial, or chord.
Example: A text file saving a traverse for an area with four vertices might contain:
DT NA
DU DD
SP 826590.1661996043 5425098.995517982
EP 826590.1661996043 5425098.995517982
DD 19.67772861193131 53.654834033368054
DD 109.67532131261366 29.058916725681254
DD 199.65097484711967 14.200875211356259
DD 199.687384449253 39.453910481159284
DD 289.67522183971334 29.05889868676386
Circle arc parameters come in two forms: tangent circle arcs, TC, and nontangent circle arcs, NC.
Tangent Circle Arcs (TC)  A tangent circle arc specification begins with TC and then includes two token specifications that define the circle arc, where each token specification is a D, A, C, or R followed by a value. A tangent circle arc specification ends with an L or an R, to indicate a leftturning or rightturning arc. See the illustrated guide to tangent and nontangent circle arcs, along with the summary below:
D <angle>  Angle subtended by the arc.
A <distance>  Length of the arc.
C <distance>  Length of the chord across the arc.
R <distance>  The radius of the circle from which the arc is taken.
Example:
TC D 47.117 R 167.288 L
Defines a tangent circle arc where the angle subtended by the arc is 47.117 degrees and the radius of the circle is 167.288 units. The arc is a leftturning arc.
Nontangent Circle Arcs (NC)  A nontangent circle arc specification begins with NC and then includes two token specifications that define the circle arc, where each token specification is a D, A, C, or R followed by a value.
D <angle>  Angle subtended by the arc.
A <distance>  Length of the arc.
C <distance>  Length of the chord across the arc.
R <distance>  The radius of the circle from which the arc is taken.
The first two values are followed by a single token specification that specifies the orientation, using a single token that is C, R, or T followed by a value.
C <direction>  Chord direction.
R <direction>  Radial direction, to the center of the circle.
T <direction>  Tangent direction, bearing of a line tangent to the start of the arc.
A nontangent circle arc specification ends with an L or an R, to indicate a leftturning or rightturning arc.
Example:
NC D 154.366 R 57.431 T 180.683 L
Defines a nontangent circle arc where the angle subtended by the arc is 154.366 degrees and the radius of the circle is 57.431 units. The arc is oriented by a tangent line with a directional bearing of 180.683. The arc is a leftturning arc.
After loading a coordinate list from an ESRI traverse format file, the system remembers the format used for direction type and direction units as well as the format used for each coordinate, and retains those settings during editing. Future builds may provide user interfaces to allow changing the format for direction type and direction units, and may also provide a command for closing a branch by distributing any closing error between branch coordinates.
See an example of loading an ESRI traverse file in the Example: Create Parcels from Traverse Files topic.
The Traverse Parameters choice in the dropdown menu launches the Traverse Parameters dialog,
The Traverse Parameters dialog specifies the format used to show traverse numbers, allowing us to choose from various ESRI formats for direction type and direction units.
Direction type 
Standard ESRI options as described on the ESRI Direction Formats page. Described in terms of clock positions:

Direction units 
Standard ESRI options for angular units of measure:

We can switch traverse parameters at any time, to display the coordinate list numbers as we like.
For example, if we switch from the default North azimuth and Degrees settings to Quadrant bearing and Degreesminutesseconds, the Coordinates list in traverse format will instantly switch to displaying numbers using the new formats:
In the above list, a DD value like 53.339445... in North Azimuth and Degrees format would become N532022.003492...E in Quadrant bearing and Degreesminutesseconds format.
Manifold can show segment/coordinates positions using standard ESRI variations in ESRI display parameter formats. ESRI traverse segments, also called courses, can be straight line segments, or they can be circle arc segments.
ESRI traverse segments can be straight line segments, using DD (direction distance) or AD (angle distance) parameters, as allowed by ESRI Traverse file format standard. we can set the display option for a straight line segment in a particular row in the Coordinates list to use a desired ESRI parameter style. That can make it much easier to compare values in the display list with those in a traverse file that use a particular ESRI parameter style. To change the parameter style for a given row, rightclick the row and choose the desired display parameter style. If a row is selected, changing the display parameter style for that row will also change it to the same style for all selected rows.
Rightclicking on the third row and choosing Angle + Distance will switch the display of that row from DD (Direction + Distance) to AD (Angle + Distance) style.
The third row in the Coordinates list gives the position of the third coordinate of the object, using traverse format. The first row gives the location of the first coordinate, called the starting point, SP, in ESRI nomenclature. The second row gives the location of the second coordinate of the object, which is the end of the first line segment. In ESRI traverse format, the location of the second coordinate is given using a direction and distance from the first coordinate, that is, the angular direction of the line segment and the length of that line segment. We can read from the Coordinates table that the angular direction is (rounding) 53.3 degrees, with a distance of 24.6 units. We will ignore the distance since the distance parameter is the same in both DD and AD format  only the way the angular direction is specified is different.
The third coordinate is the end of the second line segment. In DD format, the location of the third coordinate is at direction of 54.8 degrees and a distance of 25.9 units. When we switch to AD, Angle + Distance, style, the angle is reported in the Coordinates list as 1.5 degrees. That is an angular direction relative to the prior segment. That makes sense, because travelling in the 54.8 degree direction is continuing in the same direction as the prior segment, 53.3 degrees, plus 1.5 degrees, that is, a slight nudge in the clockwise direction.
When we rightclick a selected row to change format, the change applies to all selected records. In the illustrations above, we have pressed CtrlA to select all rows, and then we rightclicked on the fifth row to choose Angle + Distance. All selected rows that use Direction + Distance (DD) style are immediately changed to AD style.
The first row is a starting point, the coordinate of which is designed in absolute coordinate numbers, and cannot be changed. The second row cannot be changed from DD mode, since AD mode specifies direction based on the prior segment, but the very first segment has no prior segment based on which a relative change in direction can be specified. AD mode can only be used with the third or later row.
Note that the Manifold list uses only positive numbers for a relative direction change: instead of quoting a negative number, 2.8, for the directional change from the third row to the fourth row, the Coordinates list uses the equivalent positive number, a relative directional change of 357.2. That works because 360  2.8 = 357.2. Manifold uses positive numbers only to avoid confusing formatting when direction types like degreesminutesseconds are used. ESRI traverse files allow use of positive or negative numbers: if desired, future builds may introduce an option to use negative numbers in AD displays in the Coordinates list as well should the community prefer those.
ESRI traverse segments can be circle arc segments, also called courses, using TC (tangent circle arc) or NC (possibly nontangent circle arc) parameters, as allowed by ESRI Traverse file format standard. As with straight line segments, we can set the display option for a circle segment in a particular row in the Coordinates list to use a desired ESRI parameter style. That can make it much easier to compare values in the display list with those in a traverse file that use a particular ESRI parameter style. To change the parameter style for a given row, rightclick the row and choose the desired display parameter style. If a row is selected, changing the display parameter style for that row will also change it to the same style for all selected rows.
ESRI allows various different ways of specifying circular arc segments in a traverse. ESRI's allowed methods can seem complex, since they define a circular arc by giving distances, angles or bearings that mathematically imply what the arc must be. ESRI takes two approaches: in the case of circular arcs which can be said to continue from the bearing of a previous straight line segment, those are called tangent circle arcs, and the definition is slightly simpler since the bearing of the previous segment provides an important hint to what the arc must be. In cases of circle arc segments which do not start by continuing the same bearing as the prior straight line segment, the circle arc is said to be nontangent and the definition requires an extra step of defining a starting direction, which can be specified in any of three different ways, to provide the extra hint that tangent circle arcs can get automatically from the prior segment.
If this sounds complex and nonintuitive, we are well on the way to grasping the process, because it is indeed complex and nonintuitive. That is not ESRI's fault, as there are historical reasons why circle arcs have been defined in such ways in metes and bounds / COGO surveying definitions.
Consider a portion of a traverse, as seen below in a map. The traverse comes into view at left with a straight line segment, which is followed by a circle arc segment, which is followed by a straight line segment that continues out of view at the bottom of the window. The traverse has been altclicked to pick it, and then the coordinate at the end of the circular segment has been clicked to launch the traverse into Move Coordinates editing mode, which also opens the Coordinates tab of the Info pane, loaded with the coordinates of the traverse.
We have clicked the coordinate list format picker button, choosing Show traverse, to display the geometric definition of the traverse in ESRI format. The coordinates list cursor (dotted outline box) is on the row for the coordinate at the end of the circle arc, the coordinate that we clicked. We can see the circular arc is defined as a nontangent circular arc using an NC code.
The full entry for that circular arc is:
NC D 154.36583333394242 R 57.43099347890822 T 180.68291666680415 L
Rounding a bit, we can decode the above to understand the above defines a nontangent circle arc where the angle subtended by the arc is 154.366 degrees and the radius of the circle is 57.431 units. The arc is oriented by a tangent line with a directional bearing of 180.683, meaning the arc starts off heading almost due South. The arc is a leftturning arc, that is, leftturning relative to the starting direction. If we stand at the beginning of the arc, looking South, we see the arc turns to the left. See notes above, the illustrated guide to tangent and nontangent circle arcs, and the ESRI Traverse file format page for the parameters used.
We can rightclick that row for a dropdown menu of different choices of display parameter styles allowed by ESRI for nontangent circle arcs. We can choose one of the options above the dividing line and a second option below the dividing line. The two correspond to the two different classes of choices for specifying nontangent circle arcs in ESRI traverses. To understand the different choices, we should consider how tangent and nontangent circle arcs may be defined.
We will illustrate how tangent and nontangent circle arcs work with two examples, first looking at a traverse that ends in a tangent circle arc, and then looking at a traverse that ends in a nontangent circle arc. The actual circle arcs at the end of both traverses are the same: what makes one tangent and the other nontangent is the straight line segment that comes immediately before the circle arc segment.
Consider a line that shows a path we have walked in the Tuileries Garden in Paris, between the Place de la Concorde and the Louvre.
The path starts at the upper left, at one side of a large, circular pond with a fountain in the center. We walk on four straight line segments and then we walk on a circular arc segment to the end, on the other side of the pond. The illustration above adds blue square icons at the locations of coordinates between segments. We use a Google satellite layer as a background.
For more legible display, we set the Google layer to 30% opacity in the Layers pane, so it is less visually intrusive. In the illustration we have colored the circular arc segment blue.
Zooming into the region of the circular arc segment, we can see four parameters that can be used to define the circular arc segment: the length of the chord, the length of the radius, the length of the arc, and the angle between the radius line and the perpendicular to the end of circular arc. Specifying any two of these parameters, plus saying whether the arc bends to the right or to the left, is enough to exactly and unambiguously define the circular arc.
D <angle>  Angle subtended by the arc.
A <distance>  Length of the arc.
C <distance>  Length of the chord across the arc.
R <distance>  The radius of the circle from which the arc is taken.
Comparing the different parameters, any two of which are required, to the choices in the dropdown menu, and to the token codes in the list above, we can see that the choices in the upper part of the menu provide a choice of the different combinations allowed by ESRI token codes (choices in the lower part of the menu are used for nontangent circle arcs).
For example, we can choose a specification that gives the length of the Chord and the length of the Radius, or we can choose a specification that gives the Angle and the length of the Chord. Manifold automatically recomputes the values to display in the Coordinates list for whatever style we want to use.
The illustration above shows why the circular arc segment in this case is called a tangent circular arc segment: the beginning of the circular arc is a smooth continuation from the bearing of the preceding straight line segment. If the preceding line segment was extended (shown in green with no dashes) through the Radius line, and if the circular arc was extended (shown in blue with no dashes) to form a complete circle, the circle and line would be tangent to each other.
The tangency of the circle and preceding line segment is lost if the left arc is used in the construction. However, using the left arc shows why the Radius length is called that, since it is the length of the radius of the circle from which the circular arc is taken. Likewise, the illustration above shows why given the Angle and any one of the three lengths (Arc, Chord, or Radius) defines the circular arc.
We can take any two of the parameters (Arc Length, Chord Length, Radius Length, Angle) and specify using the Leftturning arc and the circular arc is unambiguously, exactly, defined. Any combination of two parameters can be used either in the traverse file, or used by Manifold in the Coordinates list to display the parameters which define the tangent circular arc.
Nontangent circle arcs do not have the benefit of starting with an initial hint, the tangent direction, to provide needed orientation. Nontangent arcs therefore require one extra parameter, the specification of orientation, that tangent circle arcs do not require.
Specifying a nontangent circle arc begins the same way as specifying a tangent circle arc, by specifying any two of four parameters: the length of the chord, the length of the radius, the length of the arc, and the angle between the radius line and the perpendicular to the end of circular arc. Specifying any two of these parameters, plus specifying one of the three possible orientation parameters, plus saying whether the arc bends to the right or to the left, is enough to exactly and unambiguously define the circular arc.
D <angle>  Angle subtended by the arc.
A <distance>  Length of the arc.
C <distance>  Length of the chord across the arc.
R <distance>  The radius of the circle from which the arc is taken.
As with a tangent circle arc, we can see that the choices in the upper part of the menu provide a choice of the different combinations allowed by ESRI token codes. For example, we can choose a specification that gives the length of the Chord and the length of the Radius, or we can choose a specification that gives the Angle and the length of the Chord.
The illustration above shows why the circular arc segment in this case is called a nontangent circular arc segment: the beginning of the circular arc is not a smooth continuation from the bearing of the preceding straight line segment. If the preceding line segment was extended (shown in green with no dashes), and if the circular arc was extended (shown in blue with no dashes) to form a complete circle, the circle and line would not be tangent to each other.
Because the system cannot use the tangent direction of the previous segment as the implied orientation, we must add an orientation token, one of C, R, or T followed by a direction value, that gives the orientation.
Choices in the lower part of the dropdown menu correspond to the three orientation options allowed by ESRI token codes:
C <direction>  Chord direction.
R <direction>  Radial direction, to the center of the circle.
T <direction>  Tangent direction, bearing of a line tangent to the start of the arc.
Note from the illustrations above and below that because the circle arc is not tangent to the last line segment, the tangent direction for the circle arc is not the same direction as a continuation of the last straight line segment of the traverse. We have to specify it manually, or we can specify one of the other two directions, chord direction or radial direction, to specify the orientation of the nontangent circle arc.
The final step in specifying a nontangent circle arc is to specify whether the arc is leftturning or rightturning:
In this case, we specify a Leftturning circle arc.
AD tokens cannot come first  When defining straight line segments in a traverse, an AD (angle + distance) token specification cannot be used for the first segment, and it cannot come immediately a circle arc definition. An AD token specifies a straight line segment in a direction relative to the direction of the immediately preceding straight line segment. If there is no immediately preceding straight line segment, there is no basis for knowing the relative direction given in an AD token. A DD (direction + distance) token, in contrast, uses an absolute direction that does not depend on the direction of a preceding straight line segment. DD tokens can therefore be the first line segment token in a traverse and can also be the first line segment token following a circular arc segment.
Why do the dropdown menus always have two parts? Why do nontangent circle specification options always appear in the dropdown menu, even if the circle arc is a tangent circle arc? The choices appear because we can define a tangent circle arc using nontangent definition if we want.
A tangent circle arc can take the tangent direction from the previous segment. If we use that same direction for the Tangent Direction (the last choice in the dropdown menu) in an NC (nontangent circle arc) definition, we get an equivalent definition to the TC (tangent circle arc) definition where that tangent direction is implied.
If we rightclick a TC (tangent) row in the Coordinates list and choose Chord Direction or Radial Direction from the dropdown menu, the row automatically will be converted to an NC (nontangent) token. Conversely, if we rightclick an NC (nontangent) row in the Coordinates list and choose Tangent Direction from the dropdown menu, the row automatically will be converted to a TC (tangent) token if there is a preceding straight line segment and the difference between the tangent of that preceding segment and the starting tangent of the arc is sufficiently small.
Tangent circle arcs cannot come first  A tangent circle arc using a TC code can be used as a definition only if it is preceded by a straight line segment. It cannot be the first segment in a traverse and it cannot come immediately after another circle arc segment. If a straight line segment does not immediately precede the circle arc segment, there is no direction that can be taken from a preceding straight line segment to provide a tangent direction. We can always use the equivalent NC definition, adding a tangent direction parameter, to define a circle arc segment which is not preceded by a straight line segment.
Why are traverses used? GIS users outside of the US are often puzzled by what seems to be an inefficient way of describing geometry that is used in traverses in the US. Given that very slight errors in angles and distances over a complicated sequence of segments described in a traverse can cause the traverse not to close, that is, the line does not end up where it started and thus the line does not describe an accurate area boundary, it seems like asking for trouble to use traverses to define real estate parcels, their primary use in the US.
As with many legacy formats, there are good, sensible, historical reasons why traverses are used to define parcels in the US. The primary reason is that while it was not so easy in historical times for a surveyor in a field to measure the exact latitude and longitude location of each vertex that defines a parcel (let alone to decompose a curved portion of a parcel into many such vertices), it has been relatively straightforward for hundreds of years to measure simple angles and distances. Starting with a marker at a known, recorded position, a surveyor with good accuracy could jot down the bearing direction of a boundary line, and measure with good accuracy how far that boundary line ran to the next turn. What seems to be a nonintuitive way of describing a circular arc segment, in terms of chord lengths, angles, and so on, in the field can be measured accurately and reliably using simple instruments.
In modern times it may be impractical to record a path walked or a linear feature by noting the latitude and longitude of each coordinate that marks the path, but it may be possible to record the compass direction and distance travelled. Entering such notes into a traverse file using whichever ESRI notation is most convenient makes it possible to import such linear features into Manifold as a line.
Example: Create Parcels from Traverse Files  Traverse files using ESRI traverse file format are widely used by surveyors and government organizations in the US to define parcels and lines by describing a sequence of directions, distances and curves from a starting point. Manifold automatically handles both tangent and nontangent curves in ESRI traverse file format as well as the full variety of options used to specify angles, distances and curves. This video shows how it's easy to create a parcel from a traverse file.