This class is subject to change. Programs using this class may require changes with a new version of VirtualLab.
Public class which defines a simple polygon (defined by an array of vertices). 'Simple' means, that there are no intersections of the vertices. More...

Inheritance diagram for SimplePolygon:

Public Member Functions

override void CalculateAxisAlignedBoundingBox ()

Method for (re)calculating the axis aligned bounding box.

override double CalculateDistanceOfPointToRegionBorder (VectorD point)

Calculates the distance of a point to the border of this region.

List< double > CalculateInternalAngles ()

Method which calculates all internal angles of the polygon.

VectorD[] CalculateIntersectionsOfHalfLineAndPolygon (VectorD startPositionOfHalfLine, VectorD directionOfHalfLine, string linesName, bool ignoreVirtualVertices, out string[] namesOfPoints)

Method for calculating the intersection points of a given half line and this polygon.

List<(VectorD intersectionPoint, string nameOfPoint)> CalculateIntersectionsOfLineAndPolygon (VectorD firstPointOnLine, VectorD secondPointOnLineOrDirectionOfLine, bool directionGivenInsteadOfSecondPointOnLine, string linesName, bool ignoreVirtualVertices, out List<(int edgeStart, int edgeEnd)> congruentEdges)

Method for calculating the intersection points of a given line and this polygon.

VectorD[] CalculateIntersectionsOfLineSegmentAndPolygon (VectorD startPositionOfSegment, VectorD endPositionOfSegment, string linesName, string nameOfSegmentStart, string nameOfSegmentEnd, bool ignoreVirtualVertices, out(string, string)[] namesOfPoints)

Method for calculating the intersection points of a given line segment and this polygon.

override object Clone ()

Deep copy of the object.

new void DeserializationPostProcessing (ref List< System.Reflection.FieldInfo > unfindableFields, RemainingData remainingData)

Method for doing post-processing after XML deserialization. Especially, handling of fields which have been altered since the version the data were saved with. But also additional operations (like filling caching variables etc.) can be done here.

override bool Equals (object obj, EqualityIntent equalityIntent)

Equality operator.

void ExtrapolatedRegionBorders (RectanglePhysical boundingBox, out List< Tuple< bool, double > > leftBorders, out List< Tuple< bool, double > > topBorders, out List< Tuple< bool, double > > rightBorders, out List< Tuple< bool, double > > bottomBorders)

Determine region borders that can be created by 'border continuation' extrapolation. //See ITN.064 for more information.

PolygonVertexList Get_EffectiveVertices ()

Method which creates a new PolygonVertexList containing only effective vertices.

override int GetHashCode ()

override InsideOutside GetInOutRelation (VectorD point, ExtrapolationInfo extrapolation2use=null)

Method which checks whether or not a point lies inside or outside the 2D region or on its boundary.

InsideOutside InOutRelation_boundingBoxBorder_extrapolated (VectorD point, RectanglePhysical boundingBox, List< Tuple< bool, double > > leftBorders, List< Tuple< bool, double > > topBorders, List< Tuple< bool, double > > rightBorders, List< Tuple< bool, double > > bottomBorders, ExtrapolationInfo extrapolation2use)

If a simple polygon is used inside a composed region, we may need a special handling for points near a given bounding box. If there are edges of neighbored vertices exactly on a border of the bounding box, the border may effectively disappear in case of 'periodic' or 'border continuation' extrapolation. See ITN.064 for more information on the mode 'border continuation'.

override void MayBeNonzeroOutside (out bool maybeNonZeroLeft, out bool maybeNonZeroRight, out bool maybeNonZeroBottom, out bool maybeNonZeroTop)

Method which determines whether or not non zero values (i.e. 'inside' states) may appear outside the polygon in case of 'border continuation' extrapolation.

SimplePolygon ()

Default constructor, creating a triangle with an edge length of 5mm, centered at (0, 0), and with its base line parallel to the x-axis.

SimplePolygon (bool useOnlyEffectiveVertices=true, VectorD[] vertices)

Initializes a new instance of the SimplePolygon class out of a list of VectorD. Each vertex gets the name "Vertex" and a running number. The boundaries are regarded as being outside, which you can change with the BoundariesAreInside property.

SimplePolygon (PolygonVertexList vertices, bool boundaryIsInside=false, PhysicalProperty propertyOfCoordinatesX=PhysicalProperty.Length, PhysicalProperty propertyOfCoordinatesY=PhysicalProperty.Length, bool dontCheckConsistency=false, bool useOnlyEffectiveVertices=true)

A constructor of the simple polygon class. Non-simple polygons (where at least two edges intersect) are not allowed. The constructor determines the type of the polygon.

SimplePolygon (RectanglePhysical rectangle, bool boundaryIsInside=false)

Constructor which gets a rectangle that shall be represented by a polygon.

SimplePolygon (RectangularRegion rectangle)

Constructor which gets a rectangular region which shall be represented by a polygon.

SimplePolygon (SimplePolygon polygon)

copy constructor of the simple polygon class

override void UpdatePropertyOfCoordinates ()

Method for handling update after change of the physical property of the coordinate.

Public Member Functions inherited from ElementaryRegion2D

double CalculateDistanceOfPointToRegionBorder (VectorD point)

Calculates the distance of a point to the border of this region.

ElementaryRegion2D (bool boundariesAreInside, PhysicalProperty propertyOfCoordinatesX=PhysicalProperty.Length, PhysicalProperty propertyOfCoordinatesY=PhysicalProperty.Length)

Constructor which gets the _boundariesAreInside flag. To be called from derived classes constructors.

ElementaryRegion2D (ElementaryRegion2D region2bCopied)

Copy constructor.

Public Member Functions inherited from Region2D

void CalculateAxisAlignedBoundingBox ()

Method for (re)calculating the axis aligned bounding box.

override object Clone ()

Clones the current object.

override bool Equals (object obj, EqualityIntent equalityIntent)

Equality operation.

override int GetHashCode ()

InsideOutside GetInOutRelation (VectorD point, ExtrapolationInfo extrapolation2use=null)

Method which checks whether or not a point lies inside or outside the 2D region or on its boundary.

override FormDocument GetNewDocumentWindow (Form formMain, string fileName)

Gets a new document window containing this document.

Parameters

formMain	Reference to the main form (= MDI parent). Can be `null` if this form will not be shown (e.g. if it is generated just to get the view settings.
fileName	File name from which the document was opened for inserting into window caption. If this string is empty, the default document name is used.

Returns: A FormDocument containing this document.

bool IsInside (double pointX, double pointY)

Method which checks whether or not a point is inside the 2D region.

bool IsInside (VectorD point)

Method which checks whether or not a point is inside the 2D region.

void MayBeNonzeroOutside (out bool maybeNonZeroLeft, out bool maybeNonZeroRight, out bool maybeNonZeroBottom, out bool maybeNonZeroTop)

Method which determines whether or not the region can provide "inside" state outside of its boundary interval. This is not the case for extrapolation mode 'ConstantZero', of course.

Region2D (bool boundariesAreInside, PhysicalProperty propertyOfCoordinatesX=PhysicalProperty.Length, PhysicalProperty propertyOfCoordinatesY=PhysicalProperty.Length)

Constructor which gets the _boundariesAreInside flag. To be called from derived classes constructors.

Region2D (Region2D region2bCopied)

Copy constructor.

Static Public Member Functions
static VectorD	CalculateCentroid (SimplePolygon polygon)
	Calculates the centroid of a given polygon. Formula taken from Wikipedia.

static List< SimplePolygon >	CalculateIntersectionOfTwoPolygons (SimplePolygon polygon1, SimplePolygon polygon2, bool ignoreVirtualVertices)
	Method for calculating the intersection of two polygons. See ITN.067 for more information.

static ? SimplePolygon	CalculateUnionOfTwoPolygons (SimplePolygon polygon1, SimplePolygon polygon2, bool ignoreVirtualVertices, out List< SimplePolygon >? holes)
	Method for calculating the union of two polygons. See ITN.067 for more information.

static bool	CheckPolygonalChainForConvexityAndMonotony (VectorD[] polygonalPoints, out bool monotone_inX, out bool monotone_inY, out RectangleD boundingBox, out List< int > minX_vertexIndices, out List< int > maxX_vertexIndices, out List< int > minY_vertexIndices, out List< int > maxY_vertexIndices)
	Check whether a polygonal chain is convex and monotone.

static ? List<(string nameOfVertex1, string nameOfVertex2, bool criticalX, bool criticalY)>	CheckPolygonForCoordinateDifferencesWhichAreNumericalCritical (SimplePolygon polygon)
	Method which checks the vertices of a given SimplePolygon whether or not it contains (neighbored) vertices whose x- or y-coordinates are not identical but so close that numerical problems are probable.

static SimplePolygon	EnsureClockwisePolygon (SimplePolygon polygon2check)
	Method which checks whether the vertices of a polygon are given in clockwise order. If so, it will be returned unchanged. If not, a polygon with reversed vertex order is returned.

static SimplePolygon	EnsureCounterClockwisePolygon (SimplePolygon polygon2check)
	Method which checks whether the vertices of a polygon are given in counterclockwise order. If so, it will be returned unchanged. If not, a polygon with reversed vertex order is returned.

static List<(long index, VectorD point)>	ExtendConvexPolygonWithOutlyingPoint (SimplePolygon polygon, List< long > pointIndicesOfPolygonVertices, NamedPolygonVertex singlePoint, long pointIndexOfSinglePoint, out List< TriangulationTriangle2D > newTrianglesForExtension)
	// Calculates the area of a given polygon. Formula taken from Wikipedia. //

static InsideOutside	IsInsideTriangle (VectorD point, VectorD vertex1, VectorD vertex2, VectorD vertex3, bool useNumericalChecks=true)
	Fast method for checking whether a point lies inside a given triangle. Important: No check for collinearity is done (for performance reasons).

static bool	IsSelfIntersecting (VectorD[] vertices, out double areaWithSign)
	Method which checks whether or not a polygon (for the given order of the vertices!) is self intersecting.

static bool	operator!= (SimplePolygon o1, SimplePolygon o2)
	Unequals operator.

static bool	operator== (SimplePolygon o1, SimplePolygon o2)
	Equals operator.

static SimplePolygon	RemoveVirtualVertices (SimplePolygon polygon)
	Method for creating a polygon without virtual vertices from an arbitrary polygon.

static SimplePolygon	Rotate (SimplePolygon polygon, double angle, VectorD centerOfRotation)
	Static method for transforming a given polygon to another one which is rotated by an angle around a given rotation center.

static SimplePolygon	Scale (SimplePolygon polygon, double factor)
	Static method for scaling a given polynom while keeping the center of its bounding box. See also the more general method TransformToTargetBox.

static SimplePolygon	TransformToTargetBox (SimplePolygon polygon, RectanglePhysical targetBoundingBox)
	Static method for transforming a given polygon to another one with defined position and size.

static SimplePolygon	Translate (SimplePolygon polygon, VectorD translationVector)
	Static method for transforming a given polygon to another one which is translated by a given vector.

Static Public Member Functions inherited from ElementaryRegion2D
static bool	operator!= (ElementaryRegion2D o1, ElementaryRegion2D o2)
	Unequals operator.

static bool	operator== (ElementaryRegion2D o1, ElementaryRegion2D o2)
	Equals operator.

Static Public Member Functions inherited from Region2D
static Region2D	InvertRegion (Region2D region2Invert)
	Creates a new region with inverted in / out regions compared to this.

static Region2D	Load (string fileName)
	Loads the specified file name. Works independently from whether the document has been saved without view settings (as prior to VL 6.0) or with view settings.

static bool	operator!= (Region2D o1, Region2D o2)
	Unequals operator.

static bool	operator== (Region2D o1, Region2D o2)
	Equals operator.

Public Attributes
int	startIndexOfNearestEdge
	Calculates the distance of a point to the border of this polygon. Important: This method will ignore all extrapolation settings!

Static Public Attributes
const string	NameOfRectanglesCorner_BL
	Vertex name of the bottom left corner of a rectangle which is represented as SimplePolygon.

const string	NameOfRectanglesCorner_BR
	Vertex name of the botom right corner of a rectangle which is represented as SimplePolygon.

const string	NameOfRectanglesCorner_TL
	Vertex name of the top left corner of a rectangle which is represented as SimplePolygon.

const string	NameOfRectanglesCorner_TR
	Vertex name of the top right corner of a rectangle which is represented as SimplePolygon.

const double	ThresholdForNumericalCriticalDifference
	Threshold below which a coordinate difference is considered critical. To be used by the method CheckPolygonForCoordinateDifferencesWhichAreNumericalCritical.

static List< NamedPolygonVertex >	upperChain
	Method which decomposes a suitable polygon into two separate polygonal chains, an upper and a lower one.

Static Public Attributes inherited from Region2D
const string	DefaultDocumentName
	The default document name (= type description) for an Order Collection.

static readonly string	FileDialogFilterString
	The filter string used in "Open File" dialogs.

const string	FileExtensionString
	The file extension for an Order Collection.

Properties
double	Area `[get]`
	Gets the area of the polygon.

bool	CounterClockwise `[get]`
	Gets whether or not the polygon is defined counterclockwise. It is determined during preprocessing.

virtual List< Parameter >	ParameterRunParameters `[get]`
	Gets all available parameters. For variable parameters (i.e. those double and int parameters which can be used in the Parameter Run, Parametric Optimization and so on) add a VaryParameterInfo object (derived from Parameter class) to the returned list.

PolygonType	Type `[get]`
	Gets the type of the polygon. It is determined during preprocessing.

PolygonVertexList	Vertices `[get]`
	public property to get the vertices of the polygon

Properties inherited from Region2D
RectanglePhysical	AxisAlignedBoundingBox `[get]`
	Gets the bounding box for the 2D region. Its sides are parallel to the x- and y-axis resp.

bool	BoundariesAreInside `[get, set]`
	Gets or sets whether or not the boundaries of the region belong to the inner region.

string	CommentOfCoordinates_X `[get, set]`
	Gets and sets the comment for the x-coordinates.

string	CommentOfCoordinates_Y `[get, set]`
	Gets and sets the comment for the y-coordinates.

ExtrapolationInfo	ExtrapolationHandling `[get, set]`
	The extrapolation mode for this region. See ITN.064 for more information on the mode 'border continuation'.

bool	IsOneD `[get]`
	Gets whether this IRegion1D2D is 1D or 2D.

string	Name `[get, set]`
	The name which can be given to the region by the user.

PhysicalProperty	PropertyOfCoordinatesX `[get, set]`
	Physical property of the x-coordinates of the region.

PhysicalProperty	PropertyOfCoordinatesY `[get, set]`
	Physical property of the y-coordinates of the region.

Region2DType	RegionType `[get]`
	Gets the type of the region.

SamplingParameters	SamplingForUsageWithComplexFields `[get, set]`
	Sampling parameters which will be used for a coordinate rescaling in case of using the region with a complex field.

Properties inherited from IDocument
VirtualLabSession	Session `[get, set]`
	every documents need to be handled in a session ==> default is the VirtualLab Mainsession

NodeVLExplorer	TreeStructure `[get]`
	every document should have a node (maybe with subnodes) in the VirtualLab Explorer

DocumentType	TypeOfDocument `[get]`
	Gets an enum entry specifying the type of the document.

Events
EventHandler?	PolygonChanged
	Event for changed vertices.

Detailed Description

This class is subject to change. Programs using this class may require changes with a new version of VirtualLab.
Public class which defines a simple polygon (defined by an array of vertices). 'Simple' means, that there are no intersections of the vertices.

Constructor & Destructor Documentation

◆ SimplePolygon() [1/5]

SimplePolygon	(	bool	useOnlyEffectiveVertices = true,
		VectorD[]	vertices )

Initializes a new instance of the SimplePolygon class out of a list of VectorD. Each vertex gets the name "Vertex" and a running number. The boundaries are regarded as being outside, which you can change with the BoundariesAreInside property.

Parameters

vertices	The vertices of the polygon.
useOnlyEffectiveVertices	If `true`, only effective vertices (instead of all defined vertices) will be used.

Exceptions

System.ArgumentException	At least three vertices must be given.
System.ArgumentException	Vertices have to be unique.

◆ SimplePolygon() [2/5]

SimplePolygon	(	PolygonVertexList	vertices,
		bool	boundaryIsInside = false,
		PhysicalProperty	propertyOfCoordinatesX = PhysicalProperty::Length,
		PhysicalProperty	propertyOfCoordinatesY = PhysicalProperty::Length,
		bool	dontCheckConsistency = false,
		bool	useOnlyEffectiveVertices = true )

A constructor of the simple polygon class. Non-simple polygons (where at least two edges intersect) are not allowed. The constructor determines the type of the polygon.

Parameters

vertices	The vertices that define the polygon. The order is important.
boundaryIsInside	Flag which says whether or not the boundary is part of the inner region or not.
propertyOfCoordinatesX	Physical property of the x-coordinate.
propertyOfCoordinatesY	Physical property of the y-coordinate.
dontCheckConsistency	If `true`, no consistency check will be done. (Make sure that you know what you're doing!)
useOnlyEffectiveVertices	If `true`, only effective vertices (instead of all defined vertices) will be used.

Exceptions

System.ArgumentNullException
System.ArgumentException	Not enough vertices specified. or Duplicate vertices found.

◆ SimplePolygon() [3/5]

SimplePolygon ( SimplePolygon polygon )

copy constructor of the simple polygon class

Parameters

polygon the polygon which shall be copied

◆ SimplePolygon() [4/5]

SimplePolygon	(	RectanglePhysical	rectangle,
		bool	boundaryIsInside = false )

Constructor which gets a rectangle that shall be represented by a polygon.

Parameters

rectangle	Rectangle to be converted to a polygon.
boundaryIsInside	Flag which says whether or not the boundary is part of the inner region or not.

◆ SimplePolygon() [5/5]

SimplePolygon ( RectangularRegion rectangle )

Constructor which gets a rectangular region which shall be represented by a polygon.

Parameters

rectangle Rectangle to be converted to a polygon.

Member Function Documentation

◆ CalculateCentroid()

static VectorD CalculateCentroid ( SimplePolygon polygon )

static

Calculates the centroid of a given polygon. Formula taken from Wikipedia.

Parameters

polygon Polygon to calculate the centroid for.

Returns: The centroid for the given polygon.

◆ CalculateDistanceOfPointToRegionBorder()

override double CalculateDistanceOfPointToRegionBorder ( VectorD point )

Calculates the distance of a point to the border of this region.

Parameters

point Point to calculate the distance for.

Returns: The distance of the given point to the border of this region

◆ CalculateInternalAngles()

List< double > CalculateInternalAngles ( )

Method which calculates all internal angles of the polygon.

Returns: A list of all internal angles. Negative values indicate concave vertices.

◆ CalculateIntersectionOfTwoPolygons()

static List< SimplePolygon > CalculateIntersectionOfTwoPolygons	(	SimplePolygon	polygon1,
		SimplePolygon	polygon2,
		bool	ignoreVirtualVertices )

static

Method for calculating the intersection of two polygons. See ITN.067 for more information.

Parameters

polygon1	First of the polygons to intersect.
polygon2	Second of the polygons to intersect.
ignoreVirtualVertices	If `true`, only effective vertices are used. That will be sufficient for most geometrical cases. If it is about triangulation, all vertices are needed instead.

Returns: A list of simple polygons representing the intersection(s) of the given polygons.

◆ CalculateIntersectionsOfHalfLineAndPolygon()

VectorD[] CalculateIntersectionsOfHalfLineAndPolygon	(	VectorD	startPositionOfHalfLine,
		VectorD	directionOfHalfLine,
		string	linesName,
		bool	ignoreVirtualVertices,
		out string[]	namesOfPoints )

Method for calculating the intersection points of a given half line and this polygon.

Parameters

startPositionOfHalfLine	The start position of the half line.
directionOfHalfLine	The direction of the half line.
linesName	Name of the line to intersect with the polygon.
ignoreVirtualVertices	If `true`, only effective vertices are used. That will be sufficient for most geometrical cases. If it is about triangulation, all vertices are needed instead.
namesOfPoints	Array which contains the names of the intersection points.

Returns: The intersection points of a given half line and this polygon.

◆ CalculateIntersectionsOfLineAndPolygon()

List<(VectorD intersectionPoint, string nameOfPoint)> CalculateIntersectionsOfLineAndPolygon	(	VectorD	firstPointOnLine,
		VectorD	secondPointOnLineOrDirectionOfLine,
		bool	directionGivenInsteadOfSecondPointOnLine,
		string	linesName,
		bool	ignoreVirtualVertices,
		out List<(int edgeStart, int edgeEnd)>	congruentEdges )

Method for calculating the intersection points of a given line and this polygon.

Parameters

firstPointOnLine	One point lying on the line to be intersecting.
secondPointOnLineOrDirectionOfLine	Either a second point on the line or the direction of the line, depending on the flag directionGivenInsteadOfSecondPointOnLine.
directionGivenInsteadOfSecondPointOnLine	If `true`, the second VectorD is interpreted as line direction instead of a second point on the line.
linesName	Name of the line to intersect with the polygon.
ignoreVirtualVertices	If `true`, only effective vertices are used. That will be sufficient for most geometrical cases. If it is about triangulation, all vertices are needed instead.
congruentEdges	A list of edge start and end indices of these edges which are congruent to the line to intersect.

Returns: A list of value tuples which give the found intersection points as well as the name of the point.

Exceptions

ArgumentException If directionGivenInsteadOfSecondPointOnLine is true and the absolute value of secondPointOnLineOrDirectionOfLine, an exception is thrown.

◆ CalculateIntersectionsOfLineSegmentAndPolygon()

VectorD[] CalculateIntersectionsOfLineSegmentAndPolygon	(	VectorD	startPositionOfSegment,
		VectorD	endPositionOfSegment,
		string	linesName,
		string	nameOfSegmentStart,
		string	nameOfSegmentEnd,
		bool	ignoreVirtualVertices,
		out(string, string)[]	namesOfPoints )

Method for calculating the intersection points of a given line segment and this polygon.

Parameters

startPositionOfSegment	The start position of the line segment.
endPositionOfSegment	The end position of the line segment.
linesName	Name of the line to intersect with the polygon.
nameOfSegmentStart	Name of the start point of the line segment to be intersected with the polygon.
nameOfSegmentEnd	Name of the end point of the line segment to be intersected with the polygon.
ignoreVirtualVertices	If `true`, only effective vertices are used. That will be sufficient for most geometrical cases. If it is about triangulation, all vertices are needed instead.
namesOfPoints	Array which contains the names of the intersection points.

Returns: A list of tuples which give the found intersection points as well as a bool flag indicating whether or not the edge from the current intersection to the next one is congruent to the line segment.

◆ CalculateUnionOfTwoPolygons()

static ? SimplePolygon CalculateUnionOfTwoPolygons	(	SimplePolygon	polygon1,
		SimplePolygon	polygon2,
		bool	ignoreVirtualVertices,
		out List< SimplePolygon >?	holes )

static

Method for calculating the union of two polygons. See ITN.067 for more information.

Parameters

polygon1	First of the polygons to unite.
polygon2	Second of the polygons to unite.
ignoreVirtualVertices	If `true`, only effective vertices are used. That will be sufficient for most geometrical cases. If it is about triangulation, all vertices are needed instead.
holes	A list of holes that do not belong to the mathematical union set but which can be not represented by the returned simple polygon.

Returns: A simple polygon representing the union of the given polygons. Null will be returned in case of the two given polygons being separate or touching in one single contact point at most.

◆ CheckPolygonalChainForConvexityAndMonotony()

static bool CheckPolygonalChainForConvexityAndMonotony	(	VectorD[]	polygonalPoints,
		out bool	monotone_inX,
		out bool	monotone_inY,
		out RectangleD	boundingBox,
		out List< int >	minX_vertexIndices,
		out List< int >	maxX_vertexIndices,
		out List< int >	minY_vertexIndices,
		out List< int >	maxY_vertexIndices )

static

Check whether a polygonal chain is convex and monotone.

Parameters

polygonalPoints	Points of the polygonal chain to check.
monotone_inX	Out parameter which is `true`, if the polygon is monotone in x.
monotone_inY	Out parameter which is `true`, if the polygon is monotone in y.
boundingBox	The bounding box of the polygon.
minX_vertexIndices	Out parameter which is a list of the indices of those vertices which have the minimum x-coordinate.
maxX_vertexIndices	Out parameter which is a list of the indices of those vertices which have the maximum x-coordinate.
minY_vertexIndices	Out parameter which is a list of the indices of those vertices which have the minimum y-coordinate.
maxY_vertexIndices	Out parameter which is a list of the indices of those vertices which have the maximum y-coordinate.

Returns: True if the polygon which is described by the chain is convex.

◆ CheckPolygonForCoordinateDifferencesWhichAreNumericalCritical()

static ? List<(string nameOfVertex1, string nameOfVertex2, bool criticalX, bool criticalY)> CheckPolygonForCoordinateDifferencesWhichAreNumericalCritical ( SimplePolygon polygon )

static

Method which checks the vertices of a given SimplePolygon whether or not it contains (neighbored) vertices whose x- or y-coordinates are not identical but so close that numerical problems are probable.

Parameters

polygon SimplePolygon to check.

Returns: List of tuples of names of vertices whose coordinates are nearly equal in one dimension at least.

◆ Clone()

override object Clone ( )

Deep copy of the object.

Returns: A deep copy of this.

◆ DeserializationPostProcessing()

new void DeserializationPostProcessing	(	ref List< System.Reflection.FieldInfo >	unfindableFields,
		RemainingData	remainingData )

Method for doing post-processing after XML deserialization. Especially, handling of fields which have been altered since the version the data were saved with. But also additional operations (like filling caching variables etc.) can be done here.

Parameters

unfindableFields	List of all those fields which are expected but could not be read from XML.
remainingData	Data contained in XML but which haven't been read yet.

◆ EnsureClockwisePolygon()

static SimplePolygon EnsureClockwisePolygon ( SimplePolygon polygon2check )

static

Method which checks whether the vertices of a polygon are given in clockwise order. If so, it will be returned unchanged. If not, a polygon with reversed vertex order is returned.

Parameters

polygon2check Polygon to check for clockwise vertex order.

Returns: Polygon with clockwise vertex order.

◆ EnsureCounterClockwisePolygon()

static SimplePolygon EnsureCounterClockwisePolygon ( SimplePolygon polygon2check )

static

Method which checks whether the vertices of a polygon are given in counterclockwise order. If so, it will be returned unchanged. If not, a polygon with reversed vertex order is returned.

Parameters

polygon2check Polygon to check for counterclockwise vertex order.

Returns: Polygon with counterclockwise vertex order.

◆ Equals()

override bool Equals	(	object	obj,
		EqualityIntent	equalityIntent )

Equality operator.

Parameters

obj
equalityIntent	Defines what kind of equality you want to check when comparing two objects, for example all values or physical equality.

Returns

◆ ExtendConvexPolygonWithOutlyingPoint()

static List<(long index, VectorD point)> ExtendConvexPolygonWithOutlyingPoint	(	SimplePolygon	polygon,
		List< long >	pointIndicesOfPolygonVertices,
		NamedPolygonVertex	singlePoint,
		long	pointIndexOfSinglePoint,
		out List< TriangulationTriangle2D >	newTrianglesForExtension )

static

// Calculates the area of a given polygon. Formula taken from Wikipedia. //

//

Parameters

polygon Polygon to calculate the area for.

//

Returns: The area for the given polygon.

Method which extends a convex polygon by a given point. The polygon is meant to be the convex hull of a triangulated point cloud as described in ITN.065.

Parameters

polygon	Polygon to be extended.
pointIndicesOfPolygonVertices	List of indices which correspond to the list of points the polygon is the convex hull for.
singlePoint	Outlying point to be a new vertex of the polygon.
pointIndexOfSinglePoint	Index of the single point in the point cloud.
newTrianglesForExtension	Adding the new vertex will usually remove old edges which lie inside the new polygon now. This out parameters gives all triangle which are defined by the removed edge and the new point.

Returns: A polygonal chain which represents a new convex polygon, extended by the given point.

◆ ExtrapolatedRegionBorders()

void ExtrapolatedRegionBorders	(	RectanglePhysical	boundingBox,
		out List< Tuple< bool, double > >	leftBorders,
		out List< Tuple< bool, double > >	topBorders,
		out List< Tuple< bool, double > >	rightBorders,
		out List< Tuple< bool, double > >	bottomBorders )

Determine region borders that can be created by 'border continuation' extrapolation. //See ITN.064 for more information.

Parameters

boundingBox	bounding box to limit the region
leftBorders	left horizontal extrapolated borders
topBorders	top vertical extrapolated borders
rightBorders	right horizontal extrapolated borders
bottomBorders	bottom vertical extrapolated borders

◆ Get_EffectiveVertices()

PolygonVertexList Get_EffectiveVertices ( )

Method which creates a new PolygonVertexList containing only effective vertices.

Returns

◆ GetInOutRelation()

override InsideOutside GetInOutRelation	(	VectorD	point,
		ExtrapolationInfo	extrapolation2use = null )

Method which checks whether or not a point lies inside or outside the 2D region or on its boundary.

Parameters

point	The point to be checked whether it lies inside.
extrapolation2use	Extrapolation info actually to be used.

Returns: Information where the point lies in relation to the region.

◆ InOutRelation_boundingBoxBorder_extrapolated()

InsideOutside InOutRelation_boundingBoxBorder_extrapolated	(	VectorD	point,
		RectanglePhysical	boundingBox,
		List< Tuple< bool, double > >	leftBorders,
		List< Tuple< bool, double > >	topBorders,
		List< Tuple< bool, double > >	rightBorders,
		List< Tuple< bool, double > >	bottomBorders,
		ExtrapolationInfo	extrapolation2use )

If a simple polygon is used inside a composed region, we may need a special handling for points near a given bounding box. If there are edges of neighbored vertices exactly on a border of the bounding box, the border may effectively disappear in case of 'periodic' or 'border continuation' extrapolation. See ITN.064 for more information on the mode 'border continuation'.

Parameters

point	Point to get the InOut-relation for.
boundingBox	Bounding box of the parenting composed region.
leftBorders	Help list of extrapolated horizontal borders left of the bounding box. The list has to be created in a previous preprocessing.
topBorders	Help list of extrapolated vertical borders above the top of the bounding box. The list has to be created in a previous preprocessing.
rightBorders	Help list of extrapolated horizontal borders right of the bounding box. The list has to be created in a previous preprocessing.
bottomBorders	Help list of extrapolated vertical borders right of the bounding box. The list has to be created in a previous preprocessing.
extrapolation2use	Extrapolation info actually to be used.

Returns: The InOut-relation for the given point.

◆ IsInsideTriangle()

static InsideOutside IsInsideTriangle	(	VectorD	point,
		VectorD	vertex1,
		VectorD	vertex2,
		VectorD	vertex3,
		bool	useNumericalChecks = true )

static

Fast method for checking whether a point lies inside a given triangle. Important: No check for collinearity is done (for performance reasons).

Parameters

point	Point to check.
vertex1	First triangle vertex.
vertex2	Second triangle vertex.
vertex3	Third triangle vertex.
useNumericalChecks	If `true`, NumericalChecks comparison is used in order to tolerate numerical errors.

Returns: InsideOutside state for the point.

◆ IsSelfIntersecting()

static bool IsSelfIntersecting	(	VectorD[]	vertices,
		out double	areaWithSign )

static

Method which checks whether or not a polygon (for the given order of the vertices!) is self intersecting.

Parameters

vertices	Vertices of the polygon to be checked. The order is important.
areaWithSign	The area of the polygon. It is signed because the sign informs about the orientation of the polygon.

Returns: true if the polygon is self intersecting.

◆ MayBeNonzeroOutside()

override void MayBeNonzeroOutside	(	out bool	maybeNonZeroLeft,
		out bool	maybeNonZeroRight,
		out bool	maybeNonZeroBottom,
		out bool	maybeNonZeroTop )

Method which determines whether or not non zero values (i.e. 'inside' states) may appear outside the polygon in case of 'border continuation' extrapolation.

Parameters

maybeNonZeroLeft	Are inside states possible at the left?
maybeNonZeroRight	Are inside states possible at the right?
maybeNonZeroBottom	Are inside states possible at the bottom?
maybeNonZeroTop	Are inside states possible at the top?

◆ operator!=()

static bool operator!=	(	SimplePolygon	o1,
		SimplePolygon	o2 )

static

Unequals operator.

Parameters

o1
o2

Returns

◆ operator==()

static bool operator==	(	SimplePolygon	o1,
		SimplePolygon	o2 )

static

Equals operator.

Parameters

o1
o2

Returns

◆ RemoveVirtualVertices()

static SimplePolygon RemoveVirtualVertices ( SimplePolygon polygon )

static

Method for creating a polygon without virtual vertices from an arbitrary polygon.

Parameters

polygon Polygon which may contain virtual vertices.

Returns: A polygon without virtual vertices.

◆ Rotate()

static SimplePolygon Rotate	(	SimplePolygon	polygon,
		double	angle,
		VectorD	centerOfRotation )

static

Static method for transforming a given polygon to another one which is rotated by an angle around a given rotation center.

Parameters

polygon	The polygon to be rotated.
angle	The angle to rotate the polygon with (given in radian).
centerOfRotation	The center to rotate the polygon around.

Returns: The rotated polygon.

◆ Scale()

static SimplePolygon Scale	(	SimplePolygon	polygon,
		double	factor )

static

Static method for scaling a given polynom while keeping the center of its bounding box. See also the more general method TransformToTargetBox.

Parameters

polygon	Polygon to be transformed.
factor	Scale factor.

Returns: The scaled polygon. The center of its bounding box is kept constant.

◆ TransformToTargetBox()

static SimplePolygon TransformToTargetBox	(	SimplePolygon	polygon,
		RectanglePhysical	targetBoundingBox )

static

Static method for transforming a given polygon to another one with defined position and size.

Parameters

polygon	Polygon to be transformed.
targetBoundingBox	Target position and size.

Returns: The transformed polygon.

◆ Translate()

static SimplePolygon Translate	(	SimplePolygon	polygon,
		VectorD	translationVector )

static

Static method for transforming a given polygon to another one which is translated by a given vector.

Parameters

polygon	The polygon to be shifted.
translationVector	The shifting vector.

Returns: The translated polygon.

Member Data Documentation

◆ startIndexOfNearestEdge

int startIndexOfNearestEdge

Calculates the distance of a point to the border of this polygon. Important: This method will ignore all extrapolation settings!

Parameters

point	Point to calculate the distance for.
ignoreVirtualVertices	If set to `true`, virtua vertices will be ignored.

Returns: A named tuple containing the vertex indices of the edge with the smallest distance as well as the distance itself.

◆ upperChain

List<NamedPolygonVertex> upperChain

static

Method which decomposes a suitable polygon into two separate polygonal chains, an upper and a lower one.

Parameters

polygon Polygon to be decomposed which is at least monotone in x-direction.

Returns: Two polygonal chains.

Exceptions

Exception	Thrown if more than two vertices are found as left most or right most ones.
ArgumentException	Thrown if a non-suitable polygon is given (not monotone in x).

Public Member Functions

Static Public Member Functions

Public Attributes

Static Public Attributes

Properties

Events

Detailed Description

Constructor & Destructor Documentation

◆ SimplePolygon() [1/5]

◆ SimplePolygon() [2/5]

◆ SimplePolygon() [3/5]

◆ SimplePolygon() [4/5]

◆ SimplePolygon() [5/5]

Member Function Documentation

◆ CalculateCentroid()

◆ CalculateDistanceOfPointToRegionBorder()

◆ CalculateInternalAngles()

◆ CalculateIntersectionOfTwoPolygons()

◆ CalculateIntersectionsOfHalfLineAndPolygon()

◆ CalculateIntersectionsOfLineAndPolygon()

◆ CalculateIntersectionsOfLineSegmentAndPolygon()

◆ CalculateUnionOfTwoPolygons()

◆ CheckPolygonalChainForConvexityAndMonotony()

◆ CheckPolygonForCoordinateDifferencesWhichAreNumericalCritical()

◆ Clone()

◆ DeserializationPostProcessing()

◆ EnsureClockwisePolygon()

◆ EnsureCounterClockwisePolygon()

◆ Equals()

◆ ExtendConvexPolygonWithOutlyingPoint()

◆ ExtrapolatedRegionBorders()

◆ Get_EffectiveVertices()

◆ GetInOutRelation()

◆ InOutRelation_boundingBoxBorder_extrapolated()

◆ IsInsideTriangle()

◆ IsSelfIntersecting()

◆ MayBeNonzeroOutside()

◆ operator!=()

◆ operator==()

◆ RemoveVirtualVertices()

◆ Rotate()

◆ Scale()

◆ TransformToTargetBox()

◆ Translate()

Member Data Documentation

◆ startIndexOfNearestEdge

◆ upperChain