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2d polygons made up of an outer, and zero or more inner `Path2.t`

s. Includes basic shape creation helpers, manipulations, (including offset and basic transformations), measurement, and validation.

`type invalid = [ `

`| `SelfIntersection of int`

(*Raised during polygon validation if a path is found to self-intersect. The index refers to the culprit path (outer =

*)`0`

, with holes increasing).`| `CrossIntersection of int * int`

(*Raised during polygon validation if two paths are found to intersect eachother. The indices refer to the paths in question (outer =

*)`0`

, with holes increasing).`| `DuplicatePoints`

(*Raised during polygon validation if there are any duplicate points across all of the paths contained within

*)`t`

.

` ]`

2-dimensional polygon

This type is kept private to force use of `make`

, which performs `validation`

by default, hopefully providing an early warning that the shape may have issues rendering in a CAD backend.

`make ?validate ?holes outer`

Create a 2d polygon from an `outer`

path (perimeter), and zero or more `holes`

(default = `[]`

). If validate is `true`

(as it is by default), `validation`

is performed, raising exceptions if the defined polygon is not simple (and thus, may cause problems in CGAL).

`of_paths ?validate ps`

Create a 2d polygon from a list of paths, with the outline first, followed by the inner hole paths (if any), e.g. `(outer :: holes) as ps`

. See `make`

for details.

`of_list ps`

Create a 2d polygon from a list of paths. Same as `of_paths`

with `~validate:false`

.

`to_list t`

Convert the polygon `t`

into a list with the `outer`

path as the head.

`of_seq s`

Construct a polygon from a sequence of sequences of points `s`

.

`to_seq t`

Convert the polygon `t`

to a sequence of sequences of points.

`of_array a`

Construct a polygon from an array of arrays of points `a`

.

`to_array t`

Convert the polygon `t`

to an array of arrays of points.

`add_holes ?validate ~holes t`

Add `holes`

to `t`

. If validate is `true`

(as it is by default), `validation`

is performed, raising exceptions if the defined polygon is not simple (and thus, may cause problems in CGAL).

`val validation : ?eps:float -> t -> unit`

`validation ?eps t`

Validate that `t`

is a legal polygon, without self-intersections within paths, cross-intersections between paths, or any duplicate points. All checks are performed with the tolerance `eps`

. If valid, unit will be returned, otherwise an exception will be raised.

`val is_simple : ?eps:float -> t -> bool`

`is_simple ?eps t`

Return `true`

if `t`

is a simple polygon, without self-intersections within paths, cross-intersections between paths, or any duplicate points. All checks are performed with the tolerance `eps`

.

`val circle : ?fn:int -> ?fa:float -> ?fs:float -> float -> t`

`circle ?fn ?fa ?fs r`

Create a circle of radius `r`

.

```
val wedge :
?fn:int ->
?fa:float ->
?fs:float ->
centre:V2.t ->
radius:float ->
start:float ->
float ->
t
```

`wedge ?fn ?fa ?fs ~centre ~radius ~start a`

Create an arcing path (as in `Path2.arc`

), with the `centre`

point included to close the path, forming a wedge.

`square ?center dims`

Create a rectangular polygon with xy `dims`

(e.g. width and height). If `center`

is `true`

then the path will be centred around the origin (default = `false`

).

`ellipse ?fn ?fa ?fs radii`

Draw an ellipse with xy `radii`

. The greater of the two radii is used for fragment/resolution calculation.

`val star : r1:float -> r2:float -> int -> t`

`star ~r1 ~r2 n`

Draw an `n`

pointed star with inner radius `r1`

and outer radius `r2`

.

`ring ?fn ?fa ?fs ~thickness radii`

Draw an empty elliptical ring of outer xy `radii`

, with the given radial `thickness`

(difference between outer and inner radii). For a circular ring, use equal x and y radii.

`box ?center ~thickness dims`

Create a rectangular empty box of outer xy dimensions `dims`

, with the given xy `thickness`

(difference between outer and inner xy dimensions). If `center`

is `true`

, then the path will be centred around the origin (default = `false`

).

`centroid ?eps t`

Compute the centroid of the outer path of the polygon `t`

. If `t.outer`

is collinear or self-intersecting (within `eps`

tolerance), an `Invalid_argument`

exception is raised.

`val area : ?signed:bool -> t -> float`

`area ?signed t`

Compute the total area of the polygon `t`

. If `signed`

is `true`

, then the signed areas of the `outer`

and `holes`

paths of `t`

will be summed (keep in mind that this is dependent on winding direction, which should generally be opposite between outer and inner paths), otherwise the unsigned (positive) area of the `holes`

will be subtracted (default = `false`

).

```
val offset :
?fn:int ->
?fs:float ->
?fa:float ->
?check_valid:[ `Quality of int | `No ] ->
?mode:[< `Chamfer | `Delta | `Radius Delta ] ->
float ->
t ->
t
```

`offset ?fn ?fs ?fa ?check_valid ?mode d t`

Offset outer and inner paths of `t`

by the specified distance `d`

. The `mode`

governs how `d`

is used to create the new corners.

``Delta`

will create a new outline whose sides are a fixed distance`d`

(+ve out, -ve in) from the original outline (this is the default behaviour).``Chamfer`

fixed distance offset by`d`

as with delta, but with corners chamfered.``Radius`

creates a new outline as if a circle of some radius`d`

is rotated around the exterior (`d > 0`

) or interior (`d < 0`

) original outline.`fn`

,`fs`

, and`fa`

parameters govern the number of points that will be used for these arcs (they are ignored for delta and chamfer modes).- The
`check_valid`

default of``Quality 1`

will check the validity of shifted line segments by checking whether their ends and`n`

additional points spaced throughout are far enough from the original path. If there are no points that have been offset by the target`d`

, a`Failure`

exception will be raised. Checking can be turned off by setting this to``No`

.

`map f t`

Map the outer and inner paths of `t`

with the function `f`

.

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