Loyc.Geometry.PolygonMath Class Reference

Contains useful basic polygon algorithms: hit testing, area calculation, orientation detection. More...

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Source file:

• /Core/Loyc.Utilities/Geometry/PolygonMathTT.cs

Remarks

Contains useful basic polygon algorithms: hit testing, area calculation, orientation detection.

Static Public Member Functions
static long	PolygonArea (IEnumerable< Point > polygon)
	Computes the area of a polygon. More...
static long	PolygonArea (IEnumerator< Point > e)
static int	Orientation (IEnumerable< Point > poly)
	Returns Math.Sign(PolygonArea(poly)): positive when clockwise and increasing Y goes upward. More...
static int	Orientation (IEnumerator< Point > poly)
static bool	IsPointInPolygon (IEnumerable< Point > poly, Point p)
	Finds out if a point is inside the polygon using a winding test. More...
static bool	IsPointInPolygon (IEnumerator< Point > e, Point p)
static int	GetWindingNumber (this IEnumerable< Point > poly, Point p)
	Counts the number of times the polygon winds around a test point, using a rightward raycasting test. More...
static int	GetWindingNumber (this IEnumerator< Point > e, Point p)
static float	PolygonArea (IEnumerable< Point > polygon)
	Computes the area of a polygon. More...
static float	PolygonArea (IEnumerator< Point > e)
static int	Orientation (IEnumerable< Point > poly)
	Returns Math.Sign(PolygonArea(poly)): positive when clockwise and increasing Y goes upward. More...
static int	Orientation (IEnumerator< Point > poly)
static bool	IsPointInPolygon (IEnumerable< Point > poly, Point p)
	Finds out if a point is inside the polygon using a winding test. More...
static bool	IsPointInPolygon (IEnumerator< Point > e, Point p)
static int	GetWindingNumber (this IEnumerable< Point > poly, Point p)
	Counts the number of times the polygon winds around a test point, using a rightward raycasting test. More...
static int	GetWindingNumber (this IEnumerator< Point > e, Point p)
static double	PolygonArea (IEnumerable< Point > polygon)
	Computes the area of a polygon. More...
static double	PolygonArea (IEnumerator< Point > e)
static int	Orientation (IEnumerable< Point > poly)
	Returns Math.Sign(PolygonArea(poly)): positive when clockwise and increasing Y goes upward. More...
static int	Orientation (IEnumerator< Point > poly)
static bool	IsPointInPolygon (IEnumerable< Point > poly, Point p)
	Finds out if a point is inside the polygon using a winding test. More...
static bool	IsPointInPolygon (IEnumerator< Point > e, Point p)
static int	GetWindingNumber (this IEnumerable< Point > poly, Point p)
	Counts the number of times the polygon winds around a test point, using a rightward raycasting test. More...
static int	GetWindingNumber (this IEnumerator< Point > e, Point p)
static FPL16	PolygonArea (IEnumerable< Point > polygon)
	Computes the area of a polygon. More...
static FPL16	PolygonArea (IEnumerator< Point > e)
static int	Orientation (IEnumerable< Point > poly)
	Returns Math.Sign(PolygonArea(poly)): positive when clockwise and increasing Y goes upward. More...
static int	Orientation (IEnumerator< Point > poly)
static bool	IsPointInPolygon (IEnumerable< Point > poly, Point p)
	Finds out if a point is inside the polygon using a winding test. More...
static bool	IsPointInPolygon (IEnumerator< Point > e, Point p)
static int	GetWindingNumber (this IEnumerable< Point > poly, Point p)
	Counts the number of times the polygon winds around a test point, using a rightward raycasting test. More...
static int	GetWindingNumber (this IEnumerator< Point > e, Point p)
static FPL32	PolygonArea (IEnumerable< Point > polygon)
	Computes the area of a polygon. More...
static FPL32	PolygonArea (IEnumerator< Point > e)
static int	Orientation (IEnumerable< Point > poly)
	Returns Math.Sign(PolygonArea(poly)): positive when clockwise and increasing Y goes upward. More...
static int	Orientation (IEnumerator< Point > poly)
static bool	IsPointInPolygon (IEnumerable< Point > poly, Point p)
	Finds out if a point is inside the polygon using a winding test. More...
static bool	IsPointInPolygon (IEnumerator< Point > e, Point p)
static int	GetWindingNumber (this IEnumerable< Point > poly, Point p)
	Counts the number of times the polygon winds around a test point, using a rightward raycasting test. More...
static int	GetWindingNumber (this IEnumerator< Point > e, Point p)

Member Function Documentation

static int Loyc.Geometry.PolygonMath.GetWindingNumber ( this IEnumerable< Point >  poly, Point  p  )

inlinestatic

Counts the number of times the polygon winds around a test point, using a rightward raycasting test.

Returns

Returns the winding number: the number of times that the polygon winds around the point. Positive means clockwise (assuming a coordinate system in which increasing Y goes upward), negative means counterclockwise. Always returns -1, 0 or +1 when the polygon does not self-intersect. Returns 0 for a degenerate polygon.

The test point is considered to be within the polygon if it lies on a top or left edge, but not on a bottom or right edge (within the precision limits of 'double' arithmetic). The test point will never be considered inside a degenerate (zero-width) area.

References Loyc.Geometry.PolygonMath.GetWindingNumber().

Referenced by Loyc.Geometry.PolygonMath.GetWindingNumber().

static int Loyc.Geometry.PolygonMath.GetWindingNumber ( this IEnumerable< Point >  poly, Point  p  )

inlinestatic

Counts the number of times the polygon winds around a test point, using a rightward raycasting test.

Returns

Returns the winding number: the number of times that the polygon winds around the point. Positive means clockwise (assuming a coordinate system in which increasing Y goes upward), negative means counterclockwise. Always returns -1, 0 or +1 when the polygon does not self-intersect. Returns 0 for a degenerate polygon.

The test point is considered to be within the polygon if it lies on a top or left edge, but not on a bottom or right edge (within the precision limits of 'double' arithmetic). The test point will never be considered inside a degenerate (zero-width) area.

References Loyc.Geometry.PolygonMath.GetWindingNumber().

Referenced by Loyc.Geometry.PolygonMath.GetWindingNumber().

static int Loyc.Geometry.PolygonMath.GetWindingNumber ( this IEnumerable< Point >  poly, Point  p  )

inlinestatic

Counts the number of times the polygon winds around a test point, using a rightward raycasting test.

Returns

Returns the winding number: the number of times that the polygon winds around the point. Positive means clockwise (assuming a coordinate system in which increasing Y goes upward), negative means counterclockwise. Always returns -1, 0 or +1 when the polygon does not self-intersect. Returns 0 for a degenerate polygon.

The test point is considered to be within the polygon if it lies on a top or left edge, but not on a bottom or right edge (within the precision limits of 'double' arithmetic). The test point will never be considered inside a degenerate (zero-width) area.

References Loyc.Geometry.PolygonMath.GetWindingNumber().

Referenced by Loyc.Geometry.PolygonMath.GetWindingNumber().

static int Loyc.Geometry.PolygonMath.GetWindingNumber ( this IEnumerable< Point >  poly, Point  p  )

inlinestatic

Counts the number of times the polygon winds around a test point, using a rightward raycasting test.

Returns

Returns the winding number: the number of times that the polygon winds around the point. Positive means clockwise (assuming a coordinate system in which increasing Y goes upward), negative means counterclockwise. Always returns -1, 0 or +1 when the polygon does not self-intersect. Returns 0 for a degenerate polygon.

The test point is considered to be within the polygon if it lies on a top or left edge, but not on a bottom or right edge (within the precision limits of 'double' arithmetic). The test point will never be considered inside a degenerate (zero-width) area.

References Loyc.Geometry.PolygonMath.GetWindingNumber().

Referenced by Loyc.Geometry.PolygonMath.GetWindingNumber().

static int Loyc.Geometry.PolygonMath.GetWindingNumber ( this IEnumerable< Point >  poly, Point  p  )

inlinestatic

Counts the number of times the polygon winds around a test point, using a rightward raycasting test.

Returns

Returns the winding number: the number of times that the polygon winds around the point. Positive means clockwise (assuming a coordinate system in which increasing Y goes upward), negative means counterclockwise. Always returns -1, 0 or +1 when the polygon does not self-intersect. Returns 0 for a degenerate polygon.

The test point is considered to be within the polygon if it lies on a top or left edge, but not on a bottom or right edge (within the precision limits of 'double' arithmetic). The test point will never be considered inside a degenerate (zero-width) area.

References Loyc.Geometry.PolygonMath.GetWindingNumber().

Referenced by Loyc.Geometry.PolygonMath.GetWindingNumber().

static bool Loyc.Geometry.PolygonMath.IsPointInPolygon ( IEnumerable< Point >  poly, Point  p  )

inlinestatic

Finds out if a point is inside the polygon using a winding test.

static bool Loyc.Geometry.PolygonMath.IsPointInPolygon ( IEnumerable< Point >  poly, Point  p  )

inlinestatic

Finds out if a point is inside the polygon using a winding test.

static bool Loyc.Geometry.PolygonMath.IsPointInPolygon ( IEnumerable< Point >  poly, Point  p  )

inlinestatic

Finds out if a point is inside the polygon using a winding test.

static bool Loyc.Geometry.PolygonMath.IsPointInPolygon ( IEnumerable< Point >  poly, Point  p  )

inlinestatic

Finds out if a point is inside the polygon using a winding test.

static bool Loyc.Geometry.PolygonMath.IsPointInPolygon ( IEnumerable< Point >  poly, Point  p  )

inlinestatic

Finds out if a point is inside the polygon using a winding test.

static int Loyc.Geometry.PolygonMath.Orientation ( IEnumerable< Point >  poly )

inlinestatic

Returns Math.Sign(PolygonArea(poly)): positive when clockwise and increasing Y goes upward.

A common approach to this problem is to look at the topmost point and the two points on either side. However, if one is not careful, this technique may be unable to detect the orientation in case the polygon has duplicate points, horizontal lines on top, or a degenerate top in which the top part of the polygon is zero-width (these problems can occur even if the polygon's lines do not cross one another.) That's why I chose to compute orientation based on area instead.

static int Loyc.Geometry.PolygonMath.Orientation ( IEnumerable< Point >  poly )

inlinestatic

Returns Math.Sign(PolygonArea(poly)): positive when clockwise and increasing Y goes upward.

A common approach to this problem is to look at the topmost point and the two points on either side. However, if one is not careful, this technique may be unable to detect the orientation in case the polygon has duplicate points, horizontal lines on top, or a degenerate top in which the top part of the polygon is zero-width (these problems can occur even if the polygon's lines do not cross one another.) That's why I chose to compute orientation based on area instead.

static int Loyc.Geometry.PolygonMath.Orientation ( IEnumerable< Point >  poly )

inlinestatic

Returns Math.Sign(PolygonArea(poly)): positive when clockwise and increasing Y goes upward.

A common approach to this problem is to look at the topmost point and the two points on either side. However, if one is not careful, this technique may be unable to detect the orientation in case the polygon has duplicate points, horizontal lines on top, or a degenerate top in which the top part of the polygon is zero-width (these problems can occur even if the polygon's lines do not cross one another.) That's why I chose to compute orientation based on area instead.

static int Loyc.Geometry.PolygonMath.Orientation ( IEnumerable< Point >  poly )

inlinestatic

Returns Math.Sign(PolygonArea(poly)): positive when clockwise and increasing Y goes upward.

A common approach to this problem is to look at the topmost point and the two points on either side. However, if one is not careful, this technique may be unable to detect the orientation in case the polygon has duplicate points, horizontal lines on top, or a degenerate top in which the top part of the polygon is zero-width (these problems can occur even if the polygon's lines do not cross one another.) That's why I chose to compute orientation based on area instead.

static int Loyc.Geometry.PolygonMath.Orientation ( IEnumerable< Point >  poly )

inlinestatic

Returns Math.Sign(PolygonArea(poly)): positive when clockwise and increasing Y goes upward.

A common approach to this problem is to look at the topmost point and the two points on either side. However, if one is not careful, this technique may be unable to detect the orientation in case the polygon has duplicate points, horizontal lines on top, or a degenerate top in which the top part of the polygon is zero-width (these problems can occur even if the polygon's lines do not cross one another.) That's why I chose to compute orientation based on area instead.

static long Loyc.Geometry.PolygonMath.PolygonArea ( IEnumerable< Point >  polygon )

inlinestatic

Computes the area of a polygon.

Returns

The area. The result is positive if the polygon is clockwise (assuming a coordinate system in which increasing Y goes upward), or negative if the polygon is counterclockwise.

http://www.codeproject.com/Tips/601272/Calculating-the-area-of-a-polygon

References Loyc.Geometry.PolygonMath.PolygonArea().

Referenced by Loyc.Geometry.PolygonMath.PolygonArea().

static float Loyc.Geometry.PolygonMath.PolygonArea ( IEnumerable< Point >  polygon )

inlinestatic

Computes the area of a polygon.

Returns

The area. The result is positive if the polygon is clockwise (assuming a coordinate system in which increasing Y goes upward), or negative if the polygon is counterclockwise.

http://www.codeproject.com/Tips/601272/Calculating-the-area-of-a-polygon

References Loyc.Geometry.PolygonMath.PolygonArea().

Referenced by Loyc.Geometry.PolygonMath.PolygonArea().

static double Loyc.Geometry.PolygonMath.PolygonArea ( IEnumerable< Point >  polygon )

inlinestatic

Computes the area of a polygon.

Returns

The area. The result is positive if the polygon is clockwise (assuming a coordinate system in which increasing Y goes upward), or negative if the polygon is counterclockwise.

http://www.codeproject.com/Tips/601272/Calculating-the-area-of-a-polygon

References Loyc.Geometry.PolygonMath.PolygonArea().

Referenced by Loyc.Geometry.PolygonMath.PolygonArea().

static FPL16 Loyc.Geometry.PolygonMath.PolygonArea ( IEnumerable< Point >  polygon )

inlinestatic

Computes the area of a polygon.

Returns

The area. The result is positive if the polygon is clockwise (assuming a coordinate system in which increasing Y goes upward), or negative if the polygon is counterclockwise.

http://www.codeproject.com/Tips/601272/Calculating-the-area-of-a-polygon

References Loyc.Geometry.PolygonMath.PolygonArea().

Referenced by Loyc.Geometry.PolygonMath.PolygonArea().

static FPL32 Loyc.Geometry.PolygonMath.PolygonArea ( IEnumerable< Point >  polygon )

inlinestatic

Computes the area of a polygon.

Returns

The area. The result is positive if the polygon is clockwise (assuming a coordinate system in which increasing Y goes upward), or negative if the polygon is counterclockwise.

http://www.codeproject.com/Tips/601272/Calculating-the-area-of-a-polygon

References Loyc.Geometry.PolygonMath.PolygonArea().

Referenced by Loyc.Geometry.PolygonMath.PolygonArea().