# pygplates.GreatCircleArc¶

class pygplates.GreatCircleArc

Bases: Boost.Python.instance

A great-circle arc on the surface of the unit globe.

Great circle arcs are equality (==, !=) comparable (but not hashable - cannot be used as a key in a dict).

__init__(start_point, end_point)

Create a great circle arc from two points.

Parameters: start_point (PointOnSphere or LatLonPoint or tuple (latitude,longitude), in degrees, or tuple (x,y,z)) – the start point of the arc. end_point (PointOnSphere or LatLonPoint or tuple (latitude,longitude), in degrees, or tuple (x,y,z)) – the end point of the arc. IndeterminateResultError if points are antipodal (opposite each other)
An arc is specified by a start-point and an end-point:
If these two points are not antipodal, a unique great-circle arc (with angle-span less than PI radians) will be determined between them. If they are antipodal then IndeterminateResultException will be raised. Note that an error is not raised if the two points are coincident.
great_circle_arc = pygplates.GreatCircleArc(start_point, end_point)


Methods

 __init__(start_point, end_point) Create a great circle arc from two points. get_arc_direction(…) Return the direction along the arc at a point on the arc. get_arc_length() Returns the arc length of this great circle arc (in radians). get_arc_point(…) Return a point on this arc. get_end_point() Return the arc’s end point geometry. get_great_circle_normal() Return the unit vector normal direction of the great circle this arc lies on. get_rotation_axis() Return the rotation axis of the arc as a 3D vector. get_rotation_axis_lat_lon() Return the (latitude, longitude) equivalent of get_rotation_axis(). get_start_point() Return the arc’s start point geometry. is_zero_length() Return whether this great circle arc is of zero length. to_tessellated(tessellate_radians) Returns a list of points new polyline that is tessellated version of this polyline.
get_arc_direction(normalised_distance_from_start_point)

Return the direction along the arc at a point on the arc.

Parameters: normalised_distance_from_start_point (float) – distance from start point where zero is the start point, one is the end point and between zero and one are points along the arc Vector3D ValueError if arc normalised_distance_from_start_point is not in the range [0,1] IndeterminateGreatCircleArcDirectionError if arc is zero length

The returned direction is tangential to the Earth’s surface and is aligned with the direction of the great circle arc (in the direction going from the start point towards the end point). This direction is perpendicular to the great circle normal direction (see get_great_circle_normal()).

The direction at the midpoint of an arc:

if not arc.is_zero_length():
arc_midpoint_direction = arc.get_arc_direction(0.5)


If normalised_distance_from_start_point is zero then the direction at start point is returned. If normalised_distance_from_start_point is one then the direction at end point is returned. Values of normalised_distance_from_start_point between zero and one return directions at points on the arc. If normalised_distance_from_start_point is outside the range from zero to one then then ValueError is raised.

get_arc_length()

Returns the arc length of this great circle arc (in radians).

Return type: float

To convert to distance, multiply the result by the Earth radius (see Earth).

get_arc_point(normalised_distance_from_start_point)

Return a point on this arc.

Parameters: normalised_distance_from_start_point (float) – distance from start point where zero is the start point, one is the end point and between zero and one are points along the arc PointOnSphere ValueError if arc normalised_distance_from_start_point is not in the range [0,1]

The midpoint of an arc:

arc_midpoint = arc.get_arc_point(0.5)


If normalised_distance_from_start_point is zero then the start point is returned. If normalised_distance_from_start_point is one then the end point is returned. Values of normalised_distance_from_start_point between zero and one return points on the arc. If normalised_distance_from_start_point is outside the range from zero to one then then ValueError is raised.

get_end_point()

Return the arc’s end point geometry.

Return type: PointOnSphere
get_great_circle_normal()

Return the unit vector normal direction of the great circle this arc lies on.

Returns: the unit-length 3D vector Vector3D IndeterminateGreatCircleArcNormalError if arc is zero length
if not arc.is_zero_length():
normal = arc.get_great_circle_normal()


Note

This returns the same (x, y, z) result as get_rotation_axis(), but in the form of a Vector3D instead of an (x, y, z) tuple.

Note

The normal to the great circle can be considered to be the tangential direction (to the Earth’s surface) at any point along the great circle arc that is most pointing away from (perpendicular to) the direction of the arc (from start point to end point - see get_arc_direction()).

The normal vector is the same direction as the cross product of the start point and the end point. In fact it is equivalent to pygplates.Vector3D.cross(arc.start_point().to_xyz(), arc.end_point().to_xyz()).to_normalised().

If the arc start and end points are the same (if is_zero_length() is True) then IndeterminateGreatCircleArcNormalError is raised.

get_rotation_axis()

Return the rotation axis of the arc as a 3D vector.

Returns: the unit-length 3D vector (x,y,z) the tuple (float, float, float) IndeterminateArcRotationAxisError if arc is zero length
if not arc.is_zero_length():
axis_x, axis_y, axis_z = arc.get_rotation_axis()


Note

This returns the same (x, y, z) result as get_great_circle_normal(), but in the form of an (x, y, z) tuple instead of a Vector3D.

The rotation axis is the unit-length 3D vector (x,y,z) returned in the tuple.

The rotation axis direction is such that it rotates the start point towards the end point along the arc (assuming a right-handed coordinate system).

If the arc start and end points are the same (if is_zero_length() is True) then IndeterminateArcRotationAxisError is raised.

get_rotation_axis_lat_lon()

Return the (latitude, longitude) equivalent of get_rotation_axis().

Returns: the axis as (latitude, longitude) the tuple (float, float) IndeterminateArcRotationAxisError if arc is zero length
if not arc.is_zero_length():
axis_lat, axis_lon = arc.get_rotation_axis_lat_lon()


The rotation axis is the (latitude, longitude) returned in the tuple.

The rotation axis direction is such that it rotates the start point towards the end point along the arc (assuming a right-handed coordinate system).

If the arc start and end points are the same (if is_zero_length() is True) then IndeterminateArcRotationAxisError is raised.

get_start_point()

Return the arc’s start point geometry.

Return type: PointOnSphere
is_zero_length()

Return whether this great circle arc is of zero length.

Return type: bool

If this arc is of zero length, it will not have a determinate rotation axis and a call to get_rotation_axis() will raise an error.

to_tessellated(tessellate_radians)

Returns a list of points new polyline that is tessellated version of this polyline.

Parameters: tessellate_radians (float) – maximum tessellation angle (in radians) list points

Adjacent points (in the returned list of points) are separated by no more than tessellate_radians on the globe.

Tessellate a great circle arc to 2 degrees:

tessellation_points = great_circle_arc.to_tessellated(math.radians(2))


Note

Since a GreatCircleArc is immutable it cannot be modified. Which is why a tessellated list of PointOnSphere is returned.