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Polygons and polyhedra from points in 2-D and 3-D

An `alphaShape`

creates a bounding area or
volume that envelops a set of 2-D or 3-D points. You can manipulate the `alphaShape`

object to tighten or loosen the fit around the
points to create a nonconvex region. You also can add or remove points or suppress holes
or regions.

After you create an `alphaShape`

object, you can
perform geometric queries. For example, you can determine if a point is inside the shape
or you can find the number of regions that make up the shape. You also can calculate
useful quantities like area, perimeter, surface area, or volume, and plot the shape for
visual inspection.

To create an `alphaShape`

object, use the
`alphaShape`

function with input arguments that define the
shape's vertices. You also can specify an alpha radius and hole or region thresholds
when you create the `alphaShape`

.

`shp = alphaShape(x,y)`

`shp = alphaShape(x,y,z)`

`shp = alphaShape(P)`

`shp = alphaShape(___,a)`

`shp = alphaShape(___,Name,Value)`

creates a 2-D alpha shape of the points `shp`

= alphaShape(`x`

,`y`

)`(x,y)`

using the
default alpha radius. The default alpha radius produces the tightest fitting
alpha shape, which encloses all of the points.

`shp`

represents a polygon. The polygon has no isolated
points or edges, nor does it have dangling edges.

creates an alpha shape with alpha radius `shp`

= alphaShape(___,`a`

)`a`

using any of the
arguments in the previous syntaxes.

uses additional options specified by one or more `shp`

= alphaShape(___,`Name,Value`

)`Name,Value`

pair arguments. For example, you can suppress interior holes or voids using
`'HoleThreshold'`

.

`alphaSpectrum` | Alpha values giving distinct alpha shapes |

`criticalAlpha` | Alpha radius defining critical transition in shape |

`numRegions` | Number of regions in alpha shape |

`inShape` | Determine if point is inside alpha shape |

`alphaTriangulation` | Triangulation that fills alpha shape |

`boundaryFacets` | Boundary facets of alpha shape |

`perimeter` | Perimeter of 2-D alpha shape |

`area` | Area of 2-D alpha shape |

`surfaceArea` | Surface area of 3-D alpha shape |

`volume` | Volume of 3-D alpha shape |

`plot` | Plot alpha shape |

`nearestNeighbor` | Determine nearest alpha shape boundary point |

`boundary`

| `convhull`

| `criticalAlpha`

| `delaunayTriangulation`

| `triangulation`

| `trisurf`

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