# WindingPolygon

WindingPolygon[{p1,p2,,pn}]

gives a polygon representing all points for which the closed contour p1,p2,,pn,p1 winds around at least once.

WindingPolygon[{{p11,p12,},{p21,p22,},}]

gives a polygon from the closed contours p11,p12, and p21,p22,.

WindingPolygon[,"wrule"]

uses the specified winding rule "wrule" to define the polygon.

# Details and Options  • WindingPolygon is also known as winding filling rule.
• WindingPolygon is commonly used to define a polygon from self-intersecting closed curves.
• A point p is in the polygon if the number of revolutions of the closed contour around p is not zero. The number of revolutions is given by WindingCount.
• The number of winding counts are given below for each region:
• • Different winding rules "wrule" give different polygons. Possible winding rules include:
• • WindingPolygon[{p1,p2,}] is equivalent to WindingPolygon[{p1,p2,},"NonzeroRule"].
• The points pi can have any embedding dimension, but must all lie in a plane and have the same embedding dimension.
• WindingPolygon takes the same options as Polygon.

# Examples

open allclose all

## Basic Examples(2)

Define a polygon:

Construct a polygon from a self-intersecting contour:

Its area:

## Scope(14)

### Basic Uses(5)

Define a two-dimensional polygon:

Three-dimensional polygons:

n-dimensional polygons:

Construct polygons from self-intersecting contours:

Multiple contours:

### Nonzero Rule(3)

Polygons:

Three-dimensional polygons:

n-dimensional polygons:

### EvenOdd Rule(3)

Polygons:

Three-dimensional polygons:

n-dimensional polygons:

### Two Rule(3)

Polygons:

Three-dimensional polygons:

n-dimensional polygons:

## Options(6)

### VertexColors(2)

Polygon with vertex colors:

Specify vertex colors for 3D polygons:

### VertexNormals(1)

Compute normal vectors using the cross-product of edge vectors:

A triangle with normals pointing in the direction {1,-1,1}:

Using different normals will affect shading:

### VertexTextureCoordinates(3)

Texture mapping with 2D polygons:

Texture mapping with 3D polygons:

Repeat a texture by using non-unified texture coordinate values:

Texture mapping is preceded by VertexColors:

## Applications(3)

### Geometry(1)

Generation of regular star polygons:

### Computational Geometry(1)

Generate random polygons:

## Properties & Relations(2)

WindingPolygon is in general different than Polygon:

CrossingPolygon is an alternate polygon constructor:

## Possible Issues(2)

WindingPolygon always gives full-dimensional components:

The points in WindingPolygon must lie on a plane: 