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Line
✖
Line

✖
Line[{p1,p2,…}]

represents the line segments joining a sequence for points pi.

✖
Line[{{p11,p12,…},{p21,…},…}]

represents a collection of lines.

Details and Options

Background & Context

  • Line is a graphics and geometry primitive that represents a geometric line segment or sequence of connected line segments (a "poly-line"). The location of a Line connecting points in -dimensional space is specified as a list argument consisting of sublists, with each sublist containing Cartesian coordinate values. The coordinate sublists of Line objects may consist of exact or approximate values, where RegionEmbeddingDimension can be used to determine the dimension for a given Line expression. A collection of lines (or poly-lines) may be represented as a nested lists of -tuples inside a single Line primitive (a "multiline"). The coordinates of Line objects may have exact or approximate values.
  • Line objects can be visually formatted in two and three dimensions using Graphics and Graphics3D, respectively. Line objects can also be used in geographical maps using GeoGraphics and GeoPosition (e.g. GeoGraphics[Line[GeoPosition[{{38.9,-77.0},{40.1,-88.3}}]]]). In addition, Line may serve as a region specification over which a computation should be performed.
  • While lines themselves have dimension 1 (as reported by the RegionDimension function) with zero thickness, Line objects in formatted graphics expressions are by default styled to appear "thicker" than a one-dimensional mathematical line. Furthermore, in graphical visualizations, lines are displayed at the same size regardless of varying distances from the view point. The appearance of Line objects in graphics can be modified by specifying thickness directives such as Thickness, AbsoluteThickness, Thick, and Thin; dashing directives such as Dashing, AbsoluteDashing, Dashed, Dotted, and DotDashed; edge and cap directives EdgeForm and CapForm; color directives such as Red; the transparency directive Opacity; and the style option Antialiasing. In addition, the colors of multilines may be specified using VertexColors, while the shading and simulated lighting of multilines within Graphics3D may be specified using VertexNormals.
  • GeometricTransformation and more specific transformation functions such as Translate and Rotate can be used to change the coordinates at which a Line object is displayed while leaving the underlying Line expression untouched.
  • Other graphics primitives such as Tube, Arrow, HalfLine, and InfiniteLine may resemble those of stylized Line objects. While poly-lines consist only of straight line segments, smooth curves may be constructed via splines using BSplineCurve or BezierCurve or via an interpolating function using Interpolation. A function related to Line as a geometric region is Interval, which interprets pairs of numbers as endpoints of a line segment lying on the number line and which can be directly operated on using arithmetic and relational operators.
  • While the Line primitive explicitly appears in graphics and geometric region specification expressions, it should be noted that coordinates are commonly represented as bare lists in other contexts in the Wolfram Language. However, a number of graphics functions including Plot, ParametricPlot, ParametricPlot3D, and ContourPlot return graphical expressions that explicitly include Line objects.

Examples

open allclose all

Basic Examples  (4)Summary of the most common use cases

A line primitive:

In[1]:=1
✖
https://wolfram.com/xid/0haxw-bgla6
Out[1]=1
In[2]:=2
✖
https://wolfram.com/xid/0haxw-flckz1
Out[2]=2

Differently styled 2D lines:

In[1]:=1
✖
https://wolfram.com/xid/0haxw-ho51ix
In[2]:=2
✖
https://wolfram.com/xid/0haxw-e65am0
Out[2]=2

Differently styled 3D lines:

In[1]:=1
✖
https://wolfram.com/xid/0haxw-faw0nx
In[2]:=2
✖
https://wolfram.com/xid/0haxw-h5set8
Out[2]=2

Compute the ArcLength of a line:

In[1]:=1
✖
https://wolfram.com/xid/0haxw-bocko4
Out[1]=1

Centroid:

In[2]:=2
✖
https://wolfram.com/xid/0haxw-ciwitf
Out[2]=2

Scope  (24)Survey of the scope of standard use cases

Graphics  (14)

Specification  (3)

Single line segment:

In[2]:=2
✖
https://wolfram.com/xid/0haxw-64lsb
Out[2]=2

Multiple connected line segments:

In[1]:=1
✖
https://wolfram.com/xid/0haxw-gbrkl
Out[1]=1

Multiple disconnected line segments:

In[1]:=1
✖
https://wolfram.com/xid/0haxw-mlyae
In[2]:=2
✖
https://wolfram.com/xid/0haxw-k7s9me
Out[2]=2

Styling  (8)

Lines with different thicknesses:

In[3]:=3
✖
https://wolfram.com/xid/0haxw-ctsr8t
Out[3]=3
In[4]:=4
✖
https://wolfram.com/xid/0haxw-lyw0li
Out[4]=4

Thickness in scaled size:

In[1]:=1
✖
https://wolfram.com/xid/0haxw-gpgy0g
Out[1]=1

Thickness in printer's points:

In[2]:=2
✖
https://wolfram.com/xid/0haxw-c0zwps
Out[2]=2

Dashed lines:

In[1]:=1
✖
https://wolfram.com/xid/0haxw-phyxev
Out[1]=1
In[2]:=2
✖
https://wolfram.com/xid/0haxw-exlmkl
Out[2]=2

Colored lines:

In[1]:=1
✖
https://wolfram.com/xid/0haxw-dj8wfk
Out[1]=1

Line caps can be specified using CapForm:

In[1]:=1
✖
https://wolfram.com/xid/0haxw-icyy0n
Out[1]=1
In[2]:=2
✖
https://wolfram.com/xid/0haxw-2y2qo
Out[2]=2

Joining of line segments can be specified using JoinForm:

In[1]:=1
✖
https://wolfram.com/xid/0haxw-bnj940
Out[1]=1
In[2]:=2
✖
https://wolfram.com/xid/0haxw-fk5l81
Out[2]=2

Colors can be specified at vertices using VertexColors:

In[1]:=1
✖
https://wolfram.com/xid/0haxw-cn0av
Out[1]=1
In[2]:=2
✖
https://wolfram.com/xid/0haxw-gff7zx
Out[2]=2

Normals can be specified at vertices using VertexNormals for 3D lines:

In[1]:=1
✖
https://wolfram.com/xid/0haxw-hqxpxd
Out[1]=1

Coordinates  (3)

Use Scaled coordinates:

In[1]:=1
✖
https://wolfram.com/xid/0haxw-cuyath
Out[1]=1
In[2]:=2
✖
https://wolfram.com/xid/0haxw-bwu21r
Out[2]=2

Use ImageScaled coordinates in 2D:

In[1]:=1
✖
https://wolfram.com/xid/0haxw-h1zfoi
Out[1]=1

Use Offset coordinates in 2D:

In[1]:=1
✖
https://wolfram.com/xid/0haxw-2qad5
Out[1]=1

Regions  (10)

Embedding dimension is the dimension of the space in which the line lives:

In[1]:=1
✖
https://wolfram.com/xid/0haxw-y220
Out[1]=1
In[2]:=2
✖
https://wolfram.com/xid/0haxw-5k5s20
Out[2]=2

Geometric dimension:

In[3]:=3
✖
https://wolfram.com/xid/0haxw-bx9tom
Out[3]=3
In[4]:=4
✖
https://wolfram.com/xid/0haxw-lkww90
Out[4]=4

Point membership test:

In[1]:=1
✖
https://wolfram.com/xid/0haxw-6krfo4
In[2]:=2
✖
https://wolfram.com/xid/0haxw-p3b1hx
Out[2]=2

Get conditions for point membership:

In[3]:=3
✖
https://wolfram.com/xid/0haxw-2p4iz
Out[3]=3

Length:

In[1]:=1
✖
https://wolfram.com/xid/0haxw-bpai91
In[2]:=2
✖
https://wolfram.com/xid/0haxw-z6qch
Out[2]=2

Centroid:

In[3]:=3
✖
https://wolfram.com/xid/0haxw-69kuzf
Out[3]=3
In[4]:=4
✖
https://wolfram.com/xid/0haxw-3feta
Out[4]=4

Distance to a line:

In[1]:=1
✖
https://wolfram.com/xid/0haxw-oc6hy
In[2]:=2
✖
https://wolfram.com/xid/0haxw-bjikjq
Out[2]=2

Visualize it:

In[3]:=3
✖
https://wolfram.com/xid/0haxw-da2zys
Out[3]=3

Signed distance from a line segment:

In[1]:=1
✖
https://wolfram.com/xid/0haxw-cybvpc
In[2]:=2
✖
https://wolfram.com/xid/0haxw-bm4ed
Out[2]=2

Signed distance to a line segment:

In[3]:=3
✖
https://wolfram.com/xid/0haxw-g7ezsg
Out[3]=3

Nearest point in the region:

In[1]:=1
✖
https://wolfram.com/xid/0haxw-btejnv
In[2]:=2
✖
https://wolfram.com/xid/0haxw-et4yza
Out[2]=2

Nearest points:

In[3]:=3
✖
https://wolfram.com/xid/0haxw-eoyt0e
In[4]:=4
✖
https://wolfram.com/xid/0haxw-bidbt6
Out[4]=4

A line segment is bounded:

In[1]:=1
✖
https://wolfram.com/xid/0haxw-ngi1ht
In[2]:=2
✖
https://wolfram.com/xid/0haxw-b5d6xy
Out[2]=2

Get its range:

In[3]:=3
✖
https://wolfram.com/xid/0haxw-drm66k
Out[3]=3
In[4]:=4
✖
https://wolfram.com/xid/0haxw-mdwqe8
Out[4]=4

Integrate over a polygonal curve:

In[1]:=1
✖
https://wolfram.com/xid/0haxw-fivgav
In[2]:=2
✖
https://wolfram.com/xid/0haxw-banwkr
Out[2]=2

Optimize over a polygonal curve:

In[1]:=1
✖
https://wolfram.com/xid/0haxw-nf9ton
In[2]:=2
✖
https://wolfram.com/xid/0haxw-eamzcm
Out[2]=2

Solve equations in a polygonal curve:

In[1]:=1
✖
https://wolfram.com/xid/0haxw-bnrw6
In[2]:=2
✖
https://wolfram.com/xid/0haxw-c7lkth
Out[2]=2
In[3]:=3
✖
https://wolfram.com/xid/0haxw-h06b54
Out[3]=3

Options  (3)Common values & functionality for each option

VertexColors  (2)

Line with vertex colors:

In[1]:=1
✖
https://wolfram.com/xid/0haxw-203eo
Out[1]=1

Specify vertex colors for 3D lines:

In[1]:=1
✖
https://wolfram.com/xid/0haxw-bkt99m
Out[1]=1

VertexNormals  (1)

Specify vertex normals for 3D lines:

In[1]:=1
✖
https://wolfram.com/xid/0haxw-i5rfbj
Out[1]=1

Applications  (6)Sample problems that can be solved with this function

Complete graph with 11 nodes:

In[1]:=1
✖
https://wolfram.com/xid/0haxw-ol22x
In[2]:=2
✖
https://wolfram.com/xid/0haxw-dsedf3
Out[2]=2

The tangent bundle for a quadratic curve:

In[1]:=1
✖
https://wolfram.com/xid/0haxw-fsovn0
In[2]:=2
✖
https://wolfram.com/xid/0haxw-bamczv
In[3]:=3
✖
https://wolfram.com/xid/0haxw-sr0br
Out[3]=3

A vector field:

In[1]:=1
✖
https://wolfram.com/xid/0haxw-daj2ji
Out[1]=1

2D random walk on a regular lattice:

In[1]:=1
✖
https://wolfram.com/xid/0haxw-ljh4
Out[1]=1

3D random walk on a regular lattice:

In[2]:=2
✖
https://wolfram.com/xid/0haxw-bmmzlr
Out[2]=2

Replace Polygon with Line to have special rendering effects:

In[1]:=1
✖
https://wolfram.com/xid/0haxw-d9e2di
In[2]:=2
✖
https://wolfram.com/xid/0haxw-mxiar9
Out[2]=2
In[3]:=3
✖
https://wolfram.com/xid/0haxw-fr390h
Out[3]=3

Use a random collection of light sources:

In[4]:=4
✖
https://wolfram.com/xid/0haxw-bpe0hl
In[5]:=5
✖
https://wolfram.com/xid/0haxw-ggwj9n
Out[5]=5
In[6]:=6
✖
https://wolfram.com/xid/0haxw-hde79v
Out[6]=6

Use lines to estimate the length of a curve:

In[1]:=1
✖
https://wolfram.com/xid/0haxw-gbk19z
In[2]:=2
✖
https://wolfram.com/xid/0haxw-gjtk16
In[3]:=3
✖
https://wolfram.com/xid/0haxw-chqri1
In[4]:=4
✖
https://wolfram.com/xid/0haxw-n56jd6
Out[4]=4
In[5]:=5
✖
https://wolfram.com/xid/0haxw-cp6fn
Out[5]=5
In[6]:=6
✖
https://wolfram.com/xid/0haxw-dw5k9
Out[6]=6

Increase the number of line segments for a better estimate:

In[7]:=7
✖
https://wolfram.com/xid/0haxw-dgts5m
Out[7]=7

Properties & Relations  (4)Properties of the function, and connections to other functions

Several visualization functions produce Line objects:

In[1]:=1
✖
https://wolfram.com/xid/0haxw-elzn28
In[2]:=2
✖
https://wolfram.com/xid/0haxw-wk9d0
Out[2]=2

Use directive styles appropriate for lines:

In[3]:=3
✖
https://wolfram.com/xid/0haxw-ctestx
Out[3]=3

You can also transform the output:

In[4]:=4
✖
https://wolfram.com/xid/0haxw-enz5r6
Out[4]=4

The same idea applies in 3D:

In[1]:=1
✖
https://wolfram.com/xid/0haxw-b4a7ja
Out[1]=1

This shows the points at which it was sampled:

In[2]:=2
✖
https://wolfram.com/xid/0haxw-cdrgcw
Out[2]=2

ImplicitRegion can be used to represent any Line region:

In[1]:=1
✖
https://wolfram.com/xid/0haxw-tzgsvz
In[2]:=2
✖
https://wolfram.com/xid/0haxw-xldpp9
Out[2]=2

ParametricRegion can be used to represent any Line region:

In[1]:=1
✖
https://wolfram.com/xid/0haxw-hw5ae3
In[2]:=2
✖
https://wolfram.com/xid/0haxw-kdkcer
Out[2]=2

Possible Issues  (1)Common pitfalls and unexpected behavior

Line objects need to be specified using numbers that can be represented by machine numbers:

In[1]:=1
✖
https://wolfram.com/xid/0haxw-iunjob
Out[1]=1
In[2]:=2
✖
https://wolfram.com/xid/0haxw-b4yass
Out[2]=2

Neat Examples  (4)Surprising or curious use cases

A random collection of lines:

In[1]:=1
✖
https://wolfram.com/xid/0haxw-b4jqea
Out[1]=1
In[2]:=2
✖
https://wolfram.com/xid/0haxw-shu78
Out[2]=2

Lines with lighting:

In[1]:=1
✖
https://wolfram.com/xid/0haxw-b5cv10
Out[1]=1

Moiré pattern:

In[1]:=1
✖
https://wolfram.com/xid/0haxw-gjji4w
Out[1]=1

Tangent vectors along an elliptic curve:

In[1]:=1
✖
https://wolfram.com/xid/0haxw-fikg7b
Out[1]=1
Wolfram Research (1988), Line, Wolfram Language function, https://reference.wolfram.com/language/ref/Line.html (updated 2014).
✖
Wolfram Research (1988), Line, Wolfram Language function, https://reference.wolfram.com/language/ref/Line.html (updated 2014).

Text

Wolfram Research (1988), Line, Wolfram Language function, https://reference.wolfram.com/language/ref/Line.html (updated 2014).

✖
Wolfram Research (1988), Line, Wolfram Language function, https://reference.wolfram.com/language/ref/Line.html (updated 2014).

CMS

Wolfram Language. 1988. "Line." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2014. https://reference.wolfram.com/language/ref/Line.html.

✖
Wolfram Language. 1988. "Line." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2014. https://reference.wolfram.com/language/ref/Line.html.

APA

Wolfram Language. (1988). Line. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/Line.html

✖
Wolfram Language. (1988). Line. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/Line.html

BibTeX

@misc{reference.wolfram_2025_line, author="Wolfram Research", title="{Line}", year="2014", howpublished="\url{https://reference.wolfram.com/language/ref/Line.html}", note=[Accessed: 23-April-2025 ]}

✖
@misc{reference.wolfram_2025_line, author="Wolfram Research", title="{Line}", year="2014", howpublished="\url{https://reference.wolfram.com/language/ref/Line.html}", note=[Accessed: 23-April-2025 ]}

BibLaTeX

@online{reference.wolfram_2025_line, organization={Wolfram Research}, title={Line}, year={2014}, url={https://reference.wolfram.com/language/ref/Line.html}, note=[Accessed: 23-April-2025 ]}

✖
@online{reference.wolfram_2025_line, organization={Wolfram Research}, title={Line}, year={2014}, url={https://reference.wolfram.com/language/ref/Line.html}, note=[Accessed: 23-April-2025 ]}