Package pygeodesy :: Module vector3d |
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# Module vector3d

Extended 3-D vector class Vector3d and functions.

Function intersection3d3, intersections2, parse3d, sumOf, trilaterate2d2 and trilaterate3d2.

Version: 23.10.04

Classes
| Vector3dBase (INTERNAL) Generic 3-D vector base class.
| Vector3d Extended 3-D vector.

Functions
intersection3d3(start1, end1, start2, end2, eps=2.220446049250313e-16, useZ=True, **Vector_and_kwds) Compute the intersection point of two lines, each defined by two points or by a point and a bearing. |
intersections2(center1, radius1, center2, radius2, sphere=True, **Vector_and_kwds) Compute the intersection of two spheres or circles, each defined by a (3-D) center point and a radius. |
iscolinearWith(point, point1, point2, eps=2.220446049250313e-16, useZ=True) Check whether a point is colinear with two other (2- or 3-D) points. |
nearestOn(point, point1, point2, within=True, useZ=True, Vector=None, **Vector_kwds) Locate the point between two points closest to a reference (2- or 3-D). |
nearestOn6(point, points, closed=False, useZ=True, **Vector_and_kwds) Locate the point on a path or polygon closest to a reference point. |
parse3d(str3d, sep=',', Vector=<class 'pygeodesy.vector3d.Vector3d'>, **Vector_kwds) Parse an `"x, y, z"` string. |
sumOf(vectors, Vector=<class 'pygeodesy.vector3d.Vector3d'>, **Vector_kwds) Compute the vectorial sum of two oe more vectors. |
trilaterate2d2(x1, y1, radius1, x2, y2, radius2, x3, y3, radius3, eps=None, **Vector_and_kwds) Trilaterate three circles, each given as a (2-D) center and a radius. |
trilaterate3d2(center1, radius1, center2, radius2, center3, radius3, eps=2.220446049250313e-16, **Vector_and_kwds) Trilaterate three spheres, each given as a (3-D) center and a radius. |

Variables
| __all__ = `_ALL_LAZY.vector3d`

Function Details

### intersection3d3 (start1, end1, start2, end2, eps=2.220446049250313e-16, useZ=True, **Vector_and_kwds) |
Compute the intersection point of two lines, each defined by two points or by a point and a bearing. Arguments: `start1` - Start point of the first line (`Cartesian`, Vector3d, `Vector3Tuple` or `Vector4Tuple`). `end1` - End point of the first line (`Cartesian`, Vector3d, `Vector3Tuple` or `Vector4Tuple`) or the bearing at `start1` (compass `degrees`). `start2` - Start point of the second line (`Cartesian`, Vector3d, `Vector3Tuple` or `Vector4Tuple`). `end2` - End point of the second line (`Cartesian`, Vector3d, `Vector3Tuple` or `Vector4Tuple`) or the bearing at `start2` (Ccompass `degrees`). `eps` - Tolerance for skew line distance and length (`EPS`). `useZ` - If `True`, use the Z components, otherwise force `z=INT0` (`bool`). `Vector_and_kwds` - Optional class `Vector=None` to return the intersection points and optional, additional `Vector` keyword arguments, otherwise `start1`'s (sub-)class. Returns: An Intersection3Tuple`(point, outside1, outside2)` with `point` an instance of `Vector` or `start1`'s (sub-)class. Raises: `IntersectionError` - Invalid, skew, non-co-planar or otherwise non-intersecting lines. Note: The `outside` values is `0` for lines specified by point and bearing. See Also: Line-line intersection and line-line distance, skew lines and point-line distance.

### intersections2 (center1, radius1, center2, radius2, sphere=True, **Vector_and_kwds) |
Compute the intersection of two spheres or circles, each defined by a (3-D) center point and a radius. Arguments: `center1` - Center of the first sphere or circle (`Cartesian`, Vector3d, `Vector3Tuple` or `Vector4Tuple`). `radius1` - Radius of the first sphere or circle (same units as the `center1` coordinates). `center2` - Center of the second sphere or circle (`Cartesian`, Vector3d, `Vector3Tuple` or `Vector4Tuple`). `radius2` - Radius of the second sphere or circle (same units as the `center1` and `center2` coordinates). `sphere` - If `True` compute the center and radius of the intersection of two spheres. If `False`, ignore the `z`-component and compute the intersection of two circles (`bool`). `Vector_and_kwds` - Optional class `Vector=None` to return the intersection points and optional, additional `Vector` keyword arguments, otherwise `center1`'s (sub-)class. Returns: If `sphere` is `True`, a 2-tuple of the `center` and `radius` of the intersection of the spheres. The `radius` is `0.0` for abutting spheres (and the `center` is aka the radical center). If `sphere` is `False`, a 2-tuple with the two intersection points of the circles. For abutting circles, both points are the same instance, aka the radical center. Raises: `IntersectionError` - Concentric, invalid or non-intersecting spheres or circles. `TypeError` - Invalid `center1` or `center2`. `UnitError` - Invalid `radius1` or `radius2`. See Also: Sphere-Sphere and Circle-Circle Intersection.

### iscolinearWith (point, point1, point2, eps=2.220446049250313e-16, useZ=True) |
Check whether a point is colinear with two other (2- or 3-D) points. Arguments: `point` - The point (Vector3d, `Vector3Tuple` or `Vector4Tuple`). `point1` - First point (Vector3d, `Vector3Tuple` or `Vector4Tuple`). `point2` - Second point (Vector3d, `Vector3Tuple` or `Vector4Tuple`). `eps` - Tolerance (`scalar`), same units as `x`, `y` and `z`. `useZ` - If `True`, use the Z components, otherwise force `z=INT0` (`bool`). Returns: `True` if `point` is colinear `point1` and `point2`, `False` otherwise. Raises: `TypeError` - Invalid `point`, `point1` or `point2`. See Also: Function nearestOn.

### nearestOn (point, point1, point2, within=True, useZ=True, Vector=None, **Vector_kwds) |
Locate the point between two points closest to a reference (2- or 3-D). Arguments: `point` - Reference point (`Cartesian`, Vector3d, `Vector3Tuple` or `Vector4Tuple`). `point1` - Start point (`Cartesian`, Vector3d, `Vector3Tuple` or `Vector4Tuple`). `point2` - End point (`Cartesian`, Vector3d, `Vector3Tuple` or `Vector4Tuple`). `within` - If `True` return the closest point between both given points, otherwise the closest point on the extended line through both points (`bool`). `useZ` - If `True`, use the Z components, otherwise force `z=INT0` (`bool`). `Vector` - Class to return closest point (`Cartesian`, Vector3d or `Vector3Tuple`) or `None`. `Vector_kwds` - Optional, additional `Vector` keyword arguments, ignored if `Vector is None`. Returns: Closest point, either `point1` or `point2` or an instance of the `point`'s (sub-)class or `Vector` if not `None`. Raises: `TypeError` - Invalid `point`, `point1` or `point2`. See Also: 3-D Point-Line Distance, `Cartesian` and `LatLon` methods `nearestOn`, method sphericalTrigonometry.LatLon.nearestOn3 and function sphericalTrigonometry.nearestOn3.

### nearestOn6 (point, points, closed=False, useZ=True, **Vector_and_kwds) |
Locate the point on a path or polygon closest to a reference point. The closest point on each polygon edge is either the nearest of that edge's end points or a point in between. Arguments: `point` - Reference point (`Cartesian`, Vector3d, `Vector3Tuple` or `Vector4Tuple`). `points` - The path or polygon points (`Cartesian`, Vector3d, `Vector3Tuple` or `Vector4Tuple`[]). `closed` - Optionally, close the path or polygon (`bool`). `useZ` - If `True`, use the Z components, otherwise force `z=INT0` (`bool`). `Vector_and_kwds` - Optional class `Vector=None` to return the closest point and optional, additional `Vector` keyword arguments, otherwise `point`'s (sub-)class. Returns: A NearestOn6Tuple`(closest, distance, fi, j, start, end)` with the `closest`, the `start` and the `end` point each an instance of the `Vector` keyword argument of if {Vector=None} or not specified, an instance of the reference `point`'s (sub-)class. Raises: `PointsError` - Insufficient number of `points` `TypeError` - Non-cartesian `point` and `points`. Note: Distances measured with method Vector3d.equirectangular. For geodetic distances use function nearestOn5 or one of the `LatLon.nearestOn6` methods.

### parse3d (str3d, sep=',', Vector=<class 'pygeodesy.vector3d.Vector3d'>, **Vector_kwds) |
Parse an `"x, y, z"` string. Arguments: `str3d` - X, y and z values (`str`). `sep` - Optional separator (`str`). `Vector` - Optional class (Vector3d). `Vector_kwds` - Optional `Vector` keyword arguments, ignored if `Vector is None`. Returns: A `Vector` instance or if `Vector` is `None`, a named Vector3Tuple`(x, y, z)`. Raises: `VectorError` - Invalid `str3d`.

### sumOf (vectors, Vector=<class 'pygeodesy.vector3d.Vector3d'>, **Vector_kwds) |
Compute the vectorial sum of two oe more vectors. Arguments: `vectors` - Vectors to be added (Vector3d[]). `Vector` - Optional class for the vectorial sum (Vector3d). `Vector_kwds` - Optional `Vector` keyword arguments, ignored if `Vector is None`. Returns: Vectorial sum as `Vector` or if `Vector` is `None`, a named Vector3Tuple`(x, y, z)`. Raises: `VectorError` - No `vectors`.

### trilaterate2d2 (x1, y1, radius1, x2, y2, radius2, x3, y3, radius3, eps=None, **Vector_and_kwds) |
Trilaterate three circles, each given as a (2-D) center and a radius. Arguments: `x1` - Center `x` coordinate of the 1st circle (`scalar`). `y1` - Center `y` coordinate of the 1st circle (`scalar`). `radius1` - Radius of the 1st circle (`scalar`). `x2` - Center `x` coordinate of the 2nd circle (`scalar`). `y2` - Center `y` coordinate of the 2nd circle (`scalar`). `radius2` - Radius of the 2nd circle (`scalar`). `x3` - Center `x` coordinate of the 3rd circle (`scalar`). `y3` - Center `y` coordinate of the 3rd circle (`scalar`). `radius3` - Radius of the 3rd circle (`scalar`). `eps` - Tolerance to check the trilaterated point delta on all 3 circles (`scalar`) or `None` for no checking. `Vector_and_kwds` - Optional class `Vector=None` to return the trilateration and optional, additional `Vector` keyword arguments, otherwise (Vector3d). Returns: Trilaterated point as `Vector(x, y, **Vector_kwds)` or Vector2Tuple`(x, y)` if `Vector is None`.. Raises: `IntersectionError` - No intersection, near-concentric or -colinear centers, trilateration failed some other way or the trilaterated point is off one circle by more than `eps`. `UnitError` - Invalid `radius1`, `radius2` or `radius3`. See Also: Issue #49, Find X location using 3 known (X,Y) location using trilateration and function pygeodesy.trilaterate3d2.

### trilaterate3d2 (center1, radius1, center2, radius2, center3, radius3, eps=2.220446049250313e-16, **Vector_and_kwds) |
Trilaterate three spheres, each given as a (3-D) center and a radius. Arguments: `center1` - Center of the 1st sphere (`Cartesian`, Vector3d, `Vector3Tuple` or `Vector4Tuple`). `radius1` - Radius of the 1st sphere (same `units` as `x`, `y` and `z`). `center2` - Center of the 2nd sphere (`Cartesian`, Vector3d, `Vector3Tuple` or `Vector4Tuple`). `radius2` - Radius of this sphere (same `units` as `x`, `y` and `z`). `center3` - Center of the 3rd sphere (`Cartesian`, Vector3d, `Vector3Tuple` or `Vector4Tuple`). `radius3` - Radius of the 3rd sphere (same `units` as `x`, `y` and `z`). `eps` - Pertubation tolerance (`scalar`), same units as `x`, `y` and `z` or `None` for no pertubations. `Vector_and_kwds` - Optional class `Vector=None` to return the trilateration and optional, additional `Vector` keyword arguments, otherwise `center1`'s (sub-)class. Returns: 2-Tuple with two trilaterated points, each a `Vector` instance. Both points are the same instance if all three spheres abut/intersect in a single point. Raises: `ImportError` - Package `numpy` not found, not installed or older than version 1.10. `IntersectionError` - Near-concentric, -colinear, too distant or non-intersecting spheres. `NumPyError` - Some `numpy` issue. `TypeError` - Invalid `center1`, `center2` or `center3`. `UnitError` - Invalid `radius1`, `radius2` or `radius3`. See Also: Norrdine, A. An Algebraic Solution to the Multilateration Problem, the implementation and function pygeodesy.trilaterate2d2.