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# 54. `polygon` — Polygonal facets.

`Classes defined in module polygon`

class `polygon.``Polygon`(border, normal=2, holes=[])

  A Polygon is a flat surface bounded by a closed PolyLine.

  The border is specified as a Coords object with shape (nvertex,3) specifying the vertex coordinates in order. While the Coords are 3d, only the first 2 components are used.

  `npoints`()

    Return the number of points and edges.

  `vectors`()

    Return the vectors from each point to the next one.

  `angles`()

    Return the angles of the line segments with the x-axis.

  `externalAngles`()

    Return the angles between subsequent line segments.

    The returned angles are the change in direction between the segment ending at the vertex and the segment leaving. The angles are given in degrees, in the range ]-180,180]. The sum of the external angles is always (a multiple of) 360. A convex polygon has all angles of the same sign.

  `isConvex`()

    Check if the polygon is convex and turning anticlockwise.

    Returns:

    - +1 if the Polygon is convex and turning anticlockwise,
    - -1 if the Polygon is convex, but turning clockwise,
    - 0 if the Polygon is not convex.
  `internalAngles`()

    Return the internal angles.

    The returned angles are those between the two line segments at each vertex. The angles are given in degrees, in the range ]-180,180]. These angles are the complement of the

  `reverse`()

    Return the Polygon with reversed order of vertices.

  `fill`()

    Fill the surface inside the polygon with triangles.

    Returns a TriSurface filling the surface inside the polygon.

  `area`()

    Compute area inside a polygon.

  `addNoise`(*args, **kargs)

    Apply ‘addNoise’ transformation to the Geometry object.

    See `coords.Coords.addNoise()` for details.

  `affine`(*args, **kargs)

    Apply ‘affine’ transformation to the Geometry object.

    See `coords.Coords.affine()` for details.

  `align`(*args, **kargs)

    Apply ‘align’ transformation to the Geometry object.

    See `coords.Coords.align()` for details.

  `bump`(*args, **kargs)

    Apply ‘bump’ transformation to the Geometry object.

    See `coords.Coords.bump()` for details.

  `bump1`(*args, **kargs)

    Apply ‘bump1’ transformation to the Geometry object.

    See `coords.Coords.bump1()` for details.

  `bump2`(*args, **kargs)

    Apply ‘bump2’ transformation to the Geometry object.

    See `coords.Coords.bump2()` for details.

  `centered`(*args, **kargs)

    Apply ‘centered’ transformation to the Geometry object.

    See `coords.Coords.centered()` for details.

  `cylindrical`(*args, **kargs)

    Apply ‘cylindrical’ transformation to the Geometry object.

    See `coords.Coords.cylindrical()` for details.

  `egg`(*args, **kargs)

    Apply ‘egg’ transformation to the Geometry object.

    See `coords.Coords.egg()` for details.

  `flare`(*args, **kargs)

    Apply ‘flare’ transformation to the Geometry object.

    See `coords.Coords.flare()` for details.

  `hyperCylindrical`(*args, **kargs)

    Apply ‘hyperCylindrical’ transformation to the Geometry object.

    See `coords.Coords.hyperCylindrical()` for details.

  `isopar`(*args, **kargs)

    Apply ‘isopar’ transformation to the Geometry object.

    See `coords.Coords.isopar()` for details.

  `map`(*args, **kargs)

    Apply ‘map’ transformation to the Geometry object.

    See `coords.Coords.map()` for details.

  `map1`(*args, **kargs)

    Apply ‘map1’ transformation to the Geometry object.

    See `coords.Coords.map1()` for details.

  `mapd`(*args, **kargs)

    Apply ‘mapd’ transformation to the Geometry object.

    See `coords.Coords.mapd()` for details.

  `position`(*args, **kargs)

    Apply ‘position’ transformation to the Geometry object.

    See `coords.Coords.position()` for details.

  `projectOnCylinder`(*args, **kargs)

    Apply ‘projectOnCylinder’ transformation to the Geometry object.

    See `coords.Coords.projectOnCylinder()` for details.

  `projectOnPlane`(*args, **kargs)

    Apply ‘projectOnPlane’ transformation to the Geometry object.

    See `coords.Coords.projectOnPlane()` for details.

  `projectOnSphere`(*args, **kargs)

    Apply ‘projectOnSphere’ transformation to the Geometry object.

    See `coords.Coords.projectOnSphere()` for details.

  `reflect`(*args, **kargs)

    Apply ‘reflect’ transformation to the Geometry object.

    See `coords.Coords.reflect()` for details.

  `replace`(*args, **kargs)

    Apply ‘replace’ transformation to the Geometry object.

    See `coords.Coords.replace()` for details.

  `rollAxes`(*args, **kargs)

    Apply ‘rollAxes’ transformation to the Geometry object.

    See `coords.Coords.rollAxes()` for details.

  `rot`(*args, **kargs)

    Apply ‘rotate’ transformation to the Geometry object.

    See `coords.Coords.rotate()` for details.

  `rotate`(*args, **kargs)

    Apply ‘rotate’ transformation to the Geometry object.

    See `coords.Coords.rotate()` for details.

  `scale`(*args, **kargs)

    Apply ‘scale’ transformation to the Geometry object.

    See `coords.Coords.scale()` for details.

  `shear`(*args, **kargs)

    Apply ‘shear’ transformation to the Geometry object.

    See `coords.Coords.shear()` for details.

  `spherical`(*args, **kargs)

    Apply ‘spherical’ transformation to the Geometry object.

    See `coords.Coords.spherical()` for details.

  `superSpherical`(*args, **kargs)

    Apply ‘superSpherical’ transformation to the Geometry object.

    See `coords.Coords.superSpherical()` for details.

  `swapAxes`(*args, **kargs)

    Apply ‘swapAxes’ transformation to the Geometry object.

    See `coords.Coords.swapAxes()` for details.

  `toCylindrical`(*args, **kargs)

    Apply ‘toCylindrical’ transformation to the Geometry object.

    See `coords.Coords.toCylindrical()` for details.

  `toSpherical`(*args, **kargs)

    Apply ‘toSpherical’ transformation to the Geometry object.

    See `coords.Coords.toSpherical()` for details.

  `transformCS`(*args, **kargs)

    Apply ‘transformCS’ transformation to the Geometry object.

    See `coords.Coords.transformCS()` for details.

  `translate`(*args, **kargs)

    Apply ‘translate’ transformation to the Geometry object.

    See `coords.Coords.translate()` for details.

  `trl`(*args, **kargs)

    Apply ‘translate’ transformation to the Geometry object.

    See `coords.Coords.translate()` for details.

  `nelems`()

    Return the number of elements in the Geometry.

    This method should be re-implemented by the derived classes. For the (empty) Geometry class it always returns 0.

  `setProp`(prop=None, blocks=None)

    Create or destroy the property array for the Geometry.

    A property array is a rank-1 integer array with dimension equal to the number of elements in the Geometry. Each element thus has its own property number. These numbers can be used for any purpose. They play an import role when creating new geometry: new elements inherit the property number of their parent element. Properties are also preserved on most geometrical transformations.

    Because elements with different property numbers can be drawn in different colors, the property numbers are also often used to impose color.

    Parameters:

    - prop: a single integer value or a list/array of integer values. If the number of passed values is less than the number of elements, they wil be repeated. If you give more, they will be ignored.

      The special value ‘range’ will set the property numbers equal to the element number.

      A value None (default) removes the properties from the Geometry.

    - blocks: a single integer value or a list/array of integer values. If the number of passed values is less than the length of prop, they wil be repeated. If you give more, they will be ignored. Every prop will be repeated the corresponding number of times specified in blocks.

  `getCoords`()

    Get the coords data.

    Returns the full array of coordinates stored in the Geometry object. Note that subclasses may store more points in this array than are used to define the geometry.

  `level`()

    Return the dimensionality of the Geometry, or -1 if unknown

  `copy`()

    Return a deep copy of the Geometry object.

    The returned object is an exact copy of the input, but has all of its data independent of the former.

  `resized`(size=1.0, tol=1e-05)

    Return a copy of the Geometry scaled to the given size.

    size can be a single value or a list of three values for the three coordinate directions. If it is a single value, all directions are scaled to the same size. Directions for which the geometry has a size smaller than tol times the maximum size are not rescaled.

  `write`(fil, sep=' ', mode='w')

    Write a Geometry to a .pgf file.

    If fil is a string, a file with that name is opened. Else fil should be an open file. The Geometry is then written to that file in a native format, using sep as separator between the coordinates. If fil is a string, the file is closed prior to returning.

`Functions defined in module polygon`

`polygon.``projected`(X, N)

  Returns 2-D coordinates of a set of 3D coordinates.

  The returned 2D coordinates are still stored in a 3D Coords object. The last coordinate will however (approximately) be zero.

`polygon.``delaunay`(X)

  Return a Delaunay triangulation of the specified Coords.

  While the Coords are 3d, only the first 2 components are used.

  Returns a TriSurface with the Delaunay trinagulation in the x-y plane.

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