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 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.

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 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.

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 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.

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.