Polygons
Polygons are used in many domains, including graphics to represent general shapes, geometry to represent regions and geography to represent areas. Polygons are simple yet powerful enough to approximate essentially any 2D shape. The Wolfram Language provides comprehensive support for polygon representation, visualization and computation. All the common definitions of polygons can easily be used, and polygons are deeply integrated in the system, including graphics, geometry and geography.
Polygon — polygon or collection of polygons with or without holes
Graphics »
Graphics, Graphics3D — visualize polygons in 2D and 3D with different styles
GraphicsComplex ▪ VertexColors ▪ VertexNormals ▪ EdgeForm ▪ FaceForm
Polygon Representation
CanonicalizePolygon — convert to a canonical polygon representation
PolygonCoordinates ▪ OuterPolygon ▪ InnerPolygon
Triangle ▪ Rectangle ▪ Parallelogram ▪ RegularPolygon ▪ Simplex
SSSTriangle ▪ SASTriangle ▪ ASATriangle ▪ AASTriangle
Alternate Polygon Constructors
CrossingPolygon — a polygon defined by ray crossing count
WindingPolygon — a polygon defined by winding count
General Polygon Classes
RandomPolygon — generate different classes of random polygons (convex, simple, etc.)
PolygonDecomposition — decompose a polygon into different classes of polygons
SimplePolygonQ ▪ ConvexPolygonQ
Measures »
Area — give the area of a polygon
Perimeter — give the perimeter of a polygon
RegionMeasure ▪ RegionCentroid ▪ RegionMoment ▪ MomentOfInertia ▪ ...
Operations »
RegionUnion, RegionIntersection — union, intersection operations on polygons
Rotate, Translate, Scale — geometric transformations of polygons
RegionDifference ▪ BooleanRegion ▪ TransformedRegion ▪ ...
Membership
RegionMember — test membership or give conditions for membership
RegionEqual ▪ RegionDisjoint ▪ RegionWithin ▪ RandomPoint
Distance »
RegionDistance — minimum distance from a point to a polygon
RegionNearest ▪ SignedRegionDistance ▪ ...
Mesh Parts & Components »
MeshCells — vertices, edges and faces of the polyhedron
ConnectedMeshComponents — split a polyhedron into connected components
MeshPrimitives ▪ MeshCellCount ▪ DimensionalMeshComponents ▪ ...
Region Representation »
Region — geometric representation and automatic visualization of polygons
ImplicitRegion ▪ RegionBounds ▪ ConstantRegionQ ▪ BoundingRegion ▪ ...
Solving with Polygons »
Solve — find curve crossings etc.
NSolve ▪ Reduce ▪ Minimize ▪ NMinimize ▪ Integrate ▪ NIntegrate ▪ ...
Import and Export »
"PLY" — import and export polygons