==== Path ====

A path is a series of points, connected by very thin (invisible) line segments. Paths can be created as a ''line'' from an array of points, or by calling various functions to create or extend another path.

<code javascript>
const { line } = require('@jscad/modeling').primitives
const { path2 } = require('@jscad/modeling').geometries

const mypathA = line([[10, 10], [-10, 10]])
const mypathB = line([[-10, -10], [10, -10]])
let mypath = path2.concat(mypathA, mypathB)
mypath = path2.close(mypath)
</code>

In addition, a path can be open or closed. An open path is typically used to create another by appending additional points. A closed path is final, and has a line segment between first and last points.

The 'path2' geometry is accessed through the modeling API using the following:

<code javascript>
const { path2 } = require('@jscad/modeling').geometries
</code>

=== Curved Paths ===

Curved paths can also be simulated. Paths can be created as an 'arc'. (See Appending Points below for more options.)

{{ :wiki:jscad-arc.png?nolink | Arc}}

The 'arc' primitive creates a curved path about a ''center''. The arc is created from line segments placed the same distance from the ''center'', at the given ''radius''. Start and end angles for the arc can also be supplied. The ''segments'' specify the number of segments to create per full rotation. 

Defaults:
  * center : [0, 0]
  * radius : 1
  * startAngle : 0
  * endAngle : PI * 2
  * segments : 32

<code javascript>
const { arc } = require('@jscad/modeling').primitives

const mypath = arc({radius: 5, startAngle: Math.PI / 2})
const mypath = arc({center: [5, 5], radius: 5, startAngle: Math.PI, endAngle: Math.PI / 2, segments: 4})
</code>

=== Appending Points ===

Any number of points can be appended to a path, which produces a new path.

<code javascript>
const { path2 } = require('@jscad/modeling').geometries
const { line } = require('@jscad/modeling').primitives

const mypath = line([[27, -22], [27, 22]])
const newpath = path2.appendPoints([[-27, 22], [-27, -27], [27, -22]], mypath)
</code>

An 'arc' can be appended to a path as well, which creates a series of line segments that simulate an 'arc'.

Defaults:
  * radius : [0, 0]
  * clockwise : false
  * large : false
  * segments : 32

//Note: This implementation follows the SVG specifications.//

<code javascript>
const { path2 } = require('@jscad/modeling').geometries

let p1 = path2.create([[10,-20]])
p1 = path2.appendPoints([[27.5,-3.28125]], p1)
p1 = path2.appendArc({endpoint: [12.5, -22.96875], radius: [15, -19.6875]}, p1)
</code>

In addition, 'bézier' curves can be appended to a path, which creates a series of line segments that simulate a 'bézier' curve.

The 'bézier' curve starts at the last point in the given path, and ends at the last control point. The other control points are intermediate control points to transition the curve from start to end points. The first control point may be 'null' to ensure a smooth transition occurs between curves.

//Note: This implementation follows the SVG specifications.//

<code javascript>
const { path2 } = require('@jscad/modeling').geometries

let p5 = path2.create([[10,-20]])
p5 = path2.appendBezier({controlPoints: [[10,-10],[25,-10],[25,-20]]}, p5)
p5 = path2.appendBezier({controlPoints: [null, [25,-30],[40,-30],[40,-20]]}, p5)
</code>

=== Conversion to 2D Shape ===

There are many ways to convert paths into to two dimensional shapes. The following provide some examples.

First, a two dimensional shape can be created from the points inside a path, but the path must be **closed**.

<code javascript>
const { geom2, path2 } = require('@jscad/modeling').geometries
const { line } = require('@jscad/modeling').primitives

// create a closed path in shape of triangle
const mypath = line([[10, 10], [-10, 10], [-10, -10], [10, 10]])
const myshape = geom2.fromPoints(path2.toPoints(mypath))
</code>

Second, a path can be expanded into a two dimensional shape. The result is a two dimensional shape that fits around the path.

<code javascript>
// create an open path in shape of L
const { expand } = require('@jscad/modeling').expansions
const { line } = require('@jscad/modeling').primitives

const mypath = line([[10, 10], [-10, 10], [-10, -10]])
const myshape = expand({delta: 2, corners: 'chamfer'}, mypath)
</code>

=== Conversion to 3D Shape ===

Two dimensional shapes can be extruded into three dimensional shapes.

<code javascript>
const { path2 } = require('@jscad/modeling').geometries
const { extrudeLinear } = require('@jscad/modeling').extrusions

// create a closed path in shape of triangle
const mypath = path2.fromPoints({ closed: true }, [[0, 0], [12, 0], [6, 10]])
// extrude into triangular prism
const myshape = extrudeLinear({ height: 15 }, mypath)
</code>