# HalfLine

HalfLine[{p1,p2}]

represents the half-line from the point p1 through p2.

HalfLine[p,v]

represents the half-line from the point p in the direction v.

# Examples

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## Basic Examples(3)

A HalfLine in 2D:

And in 3D:

Different styles applied to a half-line:

The arc length of a half-line is infinite:

## Scope(18)

### Graphics(9)

#### Specification(3)

Define a HalfLine starting at in the direction :

Define the same half-line starting at and passing through :

Define a 3D half-line starting at and going in the direction :

Define the same half-line using the points and :

A half-line with symbolic direction:

#### Styling(5)

A HalfLine with varying thickness:

Thickness in scaled size:

Thickness in printer's points:

Half-lines can be rendered in dashed or dotted styles:

Color directives can be used to specify the color of a half-line:

Combine various directives to style a half-line:

#### Coordinates(1)

Points and vectors can be Dynamic:

### Regions(9)

Embedding dimension is the dimensionality of the vertices:

Geometric dimension is the dimension of the region itself:

Point membership testing:

Get conditions for membership:

A half-line has infinite measure and undefined centroid:

Computing distance to a half-line:

Plot it:

Nearest points:

Visualize it:

A half-line is unbounded:

But its range is not necessarily unbounded in all dimensions:

Integrate over a half-line:

Optimize over a half-line:

Solve equations on a half-line:

## Applications(4)

Create parallel rays aligned to :

Create rays perpendicular to the unit circle:

Illustrate asymptotes:

## Properties & Relations(4)

Any InfiniteLine is a union of two half-lines:

ParametricRegion can represent any HalfLine:

ImplicitRegion can represent any HalfLine:

HalfLine is a special case of ConicHullRegion:

## Neat Examples(3)

A random collection of half-lines:

An organized collection of half-lines:

Create moiré patterns:

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

#### Text

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

#### CMS

Wolfram Language. 2014. "HalfLine." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/HalfLine.html.

#### APA

Wolfram Language. (2014). HalfLine. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/HalfLine.html

#### BibTeX

@misc{reference.wolfram_2024_halfline, author="Wolfram Research", title="{HalfLine}", year="2014", howpublished="\url{https://reference.wolfram.com/language/ref/HalfLine.html}", note=[Accessed: 18-May-2024 ]}

#### BibLaTeX

@online{reference.wolfram_2024_halfline, organization={Wolfram Research}, title={HalfLine}, year={2014}, url={https://reference.wolfram.com/language/ref/HalfLine.html}, note=[Accessed: 18-May-2024 ]}