geo2d.geometry.Line

class geo2d.geometry.Line(arg1, arg2)

An abstract mathematical Line.

It is defined by either two points or by a Point and a Vector.

Parameters :

arg1 : point-like

The passed in parameters can be either two points or a Point and a Vector. For more on Point-like see the Point class.

arg2 : {point-like, vector}

If a Vector is given as arg2 instead of a Point-like, then p2 will be calculated for t = 1 in the vectorial definition of the line (see notes).

See also

Point, Vector

Notes

A line can be defined in three ways, but we use here only the vectorial definition for which we need a Point and a Vector. If two points are given the Vector \(\boldsymbol{\mathtt{p_1p_2}}\) will be calculated and then we can define the Line as:

\[\boldsymbol{r} = \boldsymbol{r_0} + t \cdot \boldsymbol{\mathtt{p_1p_2}}\]

Here \(t\) is a parameter.

Attributes

p1	[point] Get the 1st Point that defines the Line.
p2	[point] Get the 2nd Point that defines the Line.
phi	[scalar] Get self.v.phi. Convenience method.
v	[vector] Get the Vector pointing from self.p1 to`self.p2`.

Methods

__contains__(x)	Searches for x in “itself”.
__getitem__(idx)	Get the points that define the Line by index.
__len__()	The Line is made of 2 points so it’s length is 2.’
has(point)	Inspect if point (Point-like) is part of this Line.
intersection(obj)	Find if self is intersecting the provided object.
is_line_like(obj)	Check if an object is in the form of Line-like for fast
parallel_to(obj)	Find out if provided Vector or Line-like is
perpendicular_to(obj)	Find out if provided Line is perpendicular to self.
rotate(theta[, point, angle])	Rotate self around pivot point.
translate(dx, dy)	Translate self by given amounts on x and y.

Detailed description

class geo2d.geometry.Line(arg1, arg2)

An abstract mathematical Line.

It is defined by either two points or by a Point and a Vector.

Parameters :

arg1 : point-like

The passed in parameters can be either two points or a Point and a Vector. For more on Point-like see the Point class.

arg2 : {point-like, vector}

If a Vector is given as arg2 instead of a Point-like, then p2 will be calculated for t = 1 in the vectorial definition of the line (see notes).

See also

Point, Vector

Notes

A line can be defined in three ways, but we use here only the vectorial definition for which we need a Point and a Vector. If two points are given the Vector \(\boldsymbol{\mathtt{p_1p_2}}\) will be calculated and then we can define the Line as:

\[\boldsymbol{r} = \boldsymbol{r_0} + t \cdot \boldsymbol{\mathtt{p_1p_2}}\]

Here \(t\) is a parameter.

__contains__(x)

Searches for x in “itself”. If we’re talking about a Point or a Vector then this searches within their components (x, y). For everything else it searches within the list of points (vertices).

Parameters :

x : {point, scalar}

The object to search for.

Returns :

out : {True, False}

True if we find x in self, else False.

__getitem__(idx)

Get the points that define the Line by index.

Parameters :

idx : scalar

The index for Point.

Returns :

ret : point

Selected Point by index.

__len__()

The Line is made of 2 points so it’s length is 2.’

has(point)

Inspect if point (Point-like) is part of this Line.

Parameters :

point : point-like

The Point to test if it’s part of this Line.

Returns :

ret : {True, False}

If it’s part of this Line then return True, else False.

See also

Line.intersection, Ray.has, Segment.has

intersection(obj)

Find if self is intersecting the provided object.

If an intersection is found, the Point of intersection is returned, except for a few special cases. For further explanation see the notes.

Parameters :

obj : geometric object

Returns :

out : {geometric object, tuple}

If they intersect then return the Point where this happened, else return None (except for Line and Polygon: see notes).

Raises :

TypeError :

If argument is not geometric object then a TypeError is raised.

Notes

• Line: in case obj is Line-like and self then self and the Line defined by obj are checked for colinearity also in which case utils.inf is returned.
• Polygon: in the case of intersection with a Polygon a tuple of tuples is returned. The nested tuple is made up by the index of the intersected side and intersection point (e.g. ((intersection_point1, 1), ( intersection_point2, 4)) where 1 is the first intersected side of the Polygon and 4 is the second one). If the Line doesn’t intersect any sides then None is returned as in the usual case.

static is_line_like(obj)

Check if an object is in the form of Line-like for fast computations (not necessary to build lines).

Parameters :

obj : anything

obj is checked if is of type Line (i.e. not Ray nor Segment) or if this is not true then of the form: ((0, 1), (3, 2)) or [[0, 2], [3, 2]] or even combinations of these.

Returns :

res : {True, False}

p1

[point] Get the 1st Point that defines the Line.

p2

[point] Get the 2nd Point that defines the Line.

parallel_to(obj)

Find out if provided Vector or Line-like is parllel to self.

Parameters :

obj : {vector, line-like}

The Vector or Line-like to compare parallelism with.

Returns :

ret : {True, False}

If self and Line are parallel then retrun True, else False.

perpendicular_to(obj)

Find out if provided Line is perpendicular to self.

Returns :ret : {True, False}

phi

[scalar] Get self.v.phi. Convenience method.

rotate(theta, point=None, angle='degrees')

Rotate self around pivot point.

Parameters :

theta : scalar

The angle to be rotated by.

point : {point-like}, optional

If given this will be used as the rotation pivot.

angle : {‘degrees’, ‘radians’}, optional

This tells the function how theta is passed: as degrees or as radians. Default is degrees.

translate(dx, dy)

Translate self by given amounts on x and y.

Parameters :

dx, dy : scalar

Amount to translate (relative movement).

v

[vector] Get the Vector pointing from self.p1 to`self.p2`.

[Arnon1983]

Arnon et al., A Linear Time Algorithm for the Minimum Area Rectangle Enclosing a Convex Polygon” (1983), Computer Science Technical Reports. Paper 382

[WPolygon]

http://en.wikipedia.org/wiki/Polygon