Module vector3d

Compute the intersection point of two (2- or 3-D) 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.

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 optionally, 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. For abutting circles, radius is 0.0 and center is 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.

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.

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.

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 optionally, 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 or 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.

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.

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.

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 optionally, 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.