Struct Point4

Inherited Members

System.Object.Equals(System.Object, System.Object)

System.Object.GetType()

System.Object.ReferenceEquals(System.Object, System.Object)

Syntax

public struct Point4 : IEquatable<Point4>

Constructors

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Point4(Point3)

Initializes a new instance of the Point4 class from the coordinates of a point.

Declaration

public Point4(Point3 point)

Parameters

Type	Name	Description
Point3	point	Coordinates of the control point.

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Point4(Point3, Double)

Initializes a new instance of the Point4 class from the coordinates of a point and a weight.

Declaration

public Point4(Point3 point, double weight)

Parameters

Type	Name	Description
Point3	point	Coordinates of the control point.
System.Double	weight	Weight factor of the control point. You should not use weights less than or equal to zero.

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Point4(Double, Double, Double, Double)

Initializes a new instance of the Point4 class based on coordinates.

Declaration

public Point4(double x, double y, double z, double w)

Parameters

Type	Name	Description
System.Double	x	The X (first) dimension.
System.Double	y	The Y (second) dimension.
System.Double	z	The Z (third) dimension.
System.Double	w	The W (fourth) dimension, or weight.

Properties

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IsValid

Each coordinate of the a control point must pass the IsValidDouble(Double) test.

Declaration

public readonly bool IsValid { get; }

Property Value

Type	Description
System.Boolean

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Item[Int32]

Declaration

public double this[int i] { get; set; }

Parameters

Type	Name	Description
System.Int32	i

Property Value

Type	Description
System.Double

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Size

Dimension of point.

Declaration

public readonly int Size { get; }

Property Value

Type	Description
System.Int32

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Unset

Gets the value of a control point with all coordinates set as RhinoMath.UnsetValue.

Declaration

public static readonly Point4 Unset { get; }

Property Value

Type	Description
Point4

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W

Gets or sets the W (fourth) coordinate -or weight- of this control point.

Declaration

public double W { readonly get; set; }

Property Value

Type	Description
System.Double

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X

Gets or sets the X (first) coordinate of this control point.

Declaration

public double X { readonly get; set; }

Property Value

Type	Description
System.Double

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Y

Gets or sets the Y (second) coordinate of this control point.

Declaration

public double Y { readonly get; set; }

Property Value

Type	Description
System.Double

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Z

Gets or sets the Z (third) coordinate of this control point.

Declaration

public double Z { readonly get; set; }

Property Value

Type	Description
System.Double

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Zero

Gets the value of a control point with all coordinates set as zero.

Declaration

public static readonly Point4 Zero { get; }

Property Value

Type	Description
Point4

Methods

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DistanceTo(Point4)

Computes the distance between two control points.

Declaration

public double DistanceTo(Point4 other)

Parameters

Type	Name	Description
Point4	other	Other control points for distance measurement.

Returns

Type	Description
System.Double	The length of the line between this and the other control points; or 0 if any of the control points is not valid.

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EpsilonEquals(Point4, Double)

Check that all values in other are within epsilon of the values in this

Declaration

public bool EpsilonEquals(Point4 other, double epsilon)

Parameters

Type	Name	Description
Point4	other
System.Double	epsilon

Returns

Type	Description
System.Boolean

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Equals(Point4)

Determines whether the specified point has same value as the present point.

Declaration

public bool Equals(Point4 point)

Parameters

Type	Name	Description
Point4	point	The specified point.

Returns

Type	Description
System.Boolean	true if point has the same value as this; otherwise false.

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Equals(Object)

Determines whether the specified System.Object is Point4d and has same coordinates as the present point.

Declaration

public override bool Equals(object obj)

Parameters

Type	Name	Description
System.Object	obj	The specified object.

Returns

Type	Description
System.Boolean	true if obj is Point4d and has the same coordinates as this; otherwise false.

Overrides

System.ValueType.Equals(System.Object)

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GetHashCode()

Computes the hash code for the present point.

Declaration

public override int GetHashCode()

Returns

Type	Description
System.Int32	A non-unique hash code, which uses all coordiantes of this object.

Overrides

System.ValueType.GetHashCode()

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GetWeights(IEnumerable<Point4>)

Obtains the weight from a collection of control points in homogeneous space, assuming all are the same dimension.

Declaration

public static List<double> GetWeights(IEnumerable<Point4> homogenizedPoints)

Parameters

Type	Name	Description
System.Collections.Generic.IEnumerable<Point4>	homogenizedPoints	Control points represented by an array (wi*pi, wi) with length (dim+1).

Returns

Type	Description
System.Collections.Generic.List<System.Double>	A set of values, represented by a set pi with length (dim).

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GetWeights2d(IEnumerable<IEnumerable<Point4>>)

Obtains the weight from a two-dimensional collection of control points in homogeneous space, assuming all are the same dimension.

Declaration

public static List<List<double>> GetWeights2d(IEnumerable<IEnumerable<Point4>> homogenizedPoints)

Parameters

Type	Name	Description
System.Collections.Generic.IEnumerable<System.Collections.Generic.IEnumerable<Point4>>	homogenizedPoints	Two-dimensional set of control points represented by an array (wi*pi, wi) with length (dim+1)

Returns

Type	Description
System.Collections.Generic.List<System.Collections.Generic.List<System.Double>>	Two-dimensional set of values, each represented by an array pi with length (dim)

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Interpolate(Point4, Point4, Double)

Interpolate between two control points returning a new control points at the given interpolation parameter.

Declaration

public static Point4 Interpolate(Point4 pA, Point4 pB, double t)

Parameters

Type	Name	Description
Point4	pA	First point.
Point4	pB	Second point.
System.Double	t	Interpolation parameter. If t=0 then this point is set to pA. If t=1 then this point is set to pB. Values of t in between 0.0 and 1.0 result in control point between pA and pB.

Returns

Type	Description
Point4

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PointDehomogenizer(Point4)

Gets a dehomogenized point from a homogenized curve point.

Declaration

public static Point3 PointDehomogenizer(Point4 homogenizedCurvePoint)

Parameters

Type	Name	Description
Point4	homogenizedCurvePoint	A control point represented by an array (wi*pi, wi) with length (dim+1).

Returns

Type	Description
Point3	A dehomogenized point.

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PointDehomogenizer1d(IEnumerable<Point4>)

Gets a set of dehomogenized points.

Declaration

public static List<Point3> PointDehomogenizer1d(IEnumerable<Point4> homogenizedPoints)

Parameters

Type	Name	Description
System.Collections.Generic.IEnumerable<Point4>	homogenizedPoints	A collection of points represented by an array (wi*pi, wi) with length (dim+1).

Returns

Type	Description
System.Collections.Generic.List<Point3>	Set of dehomogenized points.

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PointDehomogenizer2d(IEnumerable<IEnumerable<Point4>>)

Gets a two-dimensional set of dehomogenized points.

Declaration

public static List<List<Point3>> PointDehomogenizer2d(IEnumerable<IEnumerable<Point4>> homogenizedPoints)

Parameters

Type	Name	Description
System.Collections.Generic.IEnumerable<System.Collections.Generic.IEnumerable<Point4>>	homogenizedPoints	Two-dimensional set of points represented by an array (wi*pi, wi) with length (dim+1)

Returns

Type	Description
System.Collections.Generic.List<System.Collections.Generic.List<Point3>>	Two-dimensional set of dehomogenized points.

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PointsHomogeniser(List<Point3>, List<Double>)

Transforms a collection of control points into their homogeneous equivalents.
http://deltaorange.com/2012/03/08/the-truth-behind-homogenous-coordinates/

Declaration

public static List<Point4> PointsHomogeniser(List<Point3> controlPoints, List<double> weights)

Parameters

Type	Name	Description
System.Collections.Generic.List<Point3>	controlPoints	Control points, a set of size (points count x points dimension).
System.Collections.Generic.List<System.Double>	weights	Control point weights, the same size as the set of control points (points count x 1).

Returns

Type	Description
System.Collections.Generic.List<Point4>	A set of control points where each point is (wi*pi, wi) where wi the ith control point weight and pi is the ith control point, hence the dimension of the point is dim + 1.

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PointsHomogeniser(List<Point3>, Double)

Transforms a collection of control points into their homogeneous equivalents, by a given weight value.
http://deltaorange.com/2012/03/08/the-truth-behind-homogenous-coordinates/

Declaration

public static List<Point4> PointsHomogeniser(List<Point3> controlPoints, double weight)

Parameters

Type	Name	Description
System.Collections.Generic.List<Point3>	controlPoints	Control points, a set of size (points count x points dimension).
System.Double	weight	Weight value for each point.

Returns

Type	Description
System.Collections.Generic.List<Point4>	A set of control points where each point is (wi*pi, wi) where wi the ith control point weight and pi is the ith control point, hence the dimension of the point is dim + 1.

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PointsHomogeniser2d(List<List<Point3>>, List<List<Double>>)

Transforms a two-dimension collection of control points into their homogeneous equivalents.
http://deltaorange.com/2012/03/08/the-truth-behind-homogenous-coordinates/

Declaration

public static List<List<Point4>> PointsHomogeniser2d(List<List<Point3>> controlPoints, List<List<double>> weights = null)

Parameters

Type	Name	Description
System.Collections.Generic.List<System.Collections.Generic.List<Point3>>	controlPoints	Control points, a two-dimensional set of size (points count x points dimension).
System.Collections.Generic.List<System.Collections.Generic.List<System.Double>>	weights	Control point weights, the same size as the set of control points (points count x 1).

Returns

Type	Description
System.Collections.Generic.List<System.Collections.Generic.List<Point4>>	A two-dimensional set of control points where each point is (wi*pi, wi) where wi the ith control point weight and pi is the ith control point, hence the dimension of the point is dim + 1.

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Rational2d(IEnumerable<IEnumerable<Point4>>)

Obtains the point from a two-dimensional set of homogeneous points without dehomogenization, assuming all are the same length.

Declaration

public static List<List<Point3>> Rational2d(IEnumerable<IEnumerable<Point4>> homogenizedPoints)

Parameters

Type	Name	Description
System.Collections.Generic.IEnumerable<System.Collections.Generic.IEnumerable<Point4>>	homogenizedPoints	Two-dimensional set of points represented by an array (wi*pi, wi) with length (dim+1)

Returns

Type	Description
System.Collections.Generic.List<System.Collections.Generic.List<Point3>>	Two-dimensional set of rational points.

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RationalPoints(IEnumerable<Point4>)

Obtains the point from homogeneous point without dehomogenization, assuming all are the same length.

Declaration

public static List<Point3> RationalPoints(IEnumerable<Point4> homogenizedPoints)

Parameters

Type	Name	Description
System.Collections.Generic.IEnumerable<Point4>	homogenizedPoints	Sets of points represented by an array (wi*pi, wi) with length (dim+1).

Returns

Type	Description
System.Collections.Generic.List<Point3>	Set of rational points.

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ToString()

Constructs the string representation for the current point.

Declaration

public override string ToString()

Returns

Type	Description
System.String	The point representation in the form X,Y,Z,W.

Overrides

System.ValueType.ToString()

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Transform(TransformMatrix)

Transforms the control point using a transformation matrix.

Declaration

public Point4 Transform(TransformMatrix t)

Parameters

Type	Name	Description
TransformMatrix	t	The transformation matrix.

Returns

Type	Description
Point4	The transformed control point as a new instance.

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WeightedAddiction(Point4, Point4)

Calculates the weighted addition of two Point4 together.

Declaration

public static Point4 WeightedAddiction(Point4 ctrlPoint1, Point4 ctrlPoint2)

Parameters

Type	Name	Description
Point4	ctrlPoint1	First control point.
Point4	ctrlPoint2	Second control point.

Returns

Type	Description
Point4	A new control point that results from the weighted addition of ctrlPoint1 and ctrlPoint2.

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WeightedSubtraction(Point4, Point4)

Subtracts the second point from the first point.

Declaration

public static Point4 WeightedSubtraction(Point4 ctrlPoint1, Point4 ctrlPoint2)

Parameters

Type	Name	Description
Point4	ctrlPoint1	First point.
Point4	ctrlPoint2	Second point.

Returns

Type	Description
Point4	A new point that results from the weighted subtraction of ctrlPoint2 from ctrlPoint1.

Operators

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Addition(Point4, Point4)

Sums two Point4 together.

Declaration

public static Point4 operator +(Point4 ctrlPoint1, Point4 ctrlPoint2)

Parameters

Type	Name	Description
Point4	ctrlPoint1	First control point.
Point4	ctrlPoint2	Second control point.

Returns

Type	Description
Point4	A new control point that result of the addition of ctrlPoint1 and ctrlPoint2.

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Division(Point4, Double)

Divides a control point by a number.

Declaration

public static Point4 operator /(Point4 point, double d)

Parameters

Type	Name	Description
Point4	point	A control point.
System.Double	d	A number.

Returns

Type	Description
Point4	A new control point that results from the coordinatewise division of control point with d.

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Equality(Point4, Point4)

Determines whether two control point have equal values.

Declaration

public static bool operator ==(Point4 a, Point4 b)

Parameters

Type	Name	Description
Point4	a	The first control point.
Point4	b	The second control point.

Returns

Type	Description
System.Boolean	true if the coordinates of the two control points are equal; otherwise false.

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Implicit(Point4 to Vector)

Converts a control point in a vector, without needing casting.

Declaration

public static implicit operator Vector(Point4 point4)

Parameters

Type	Name	Description
Point4	point4	A control point.

Returns

Type	Description
Vector	The resulting Vector.

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Inequality(Point4, Point4)

Determines whether two control point have different values.

Declaration

public static bool operator !=(Point4 a, Point4 b)

Parameters

Type	Name	Description
Point4	a	The first control point.
Point4	b	The second control point.

Returns

Type	Description
System.Boolean	true if the two control points differ in any coordinate; false otherwise.

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Multiply(Point4, Point4)

Multiplies two Point4 together, returning the dot (internal) product of the two. This is not the cross product.

Declaration

public static double operator *(Point4 ctrlPoint1, Point4 ctrlPoint2)

Parameters

Type	Name	Description
Point4	ctrlPoint1	The first control point.
Point4	ctrlPoint2	The second control point.

Returns

Type	Description
System.Double	A value that results from the coordinatewise multiplication of ctrlPoint1 and ctrlPoint2.

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Multiply(Point4, Double)

Multiplies a control point by a number.

Declaration

public static Point4 operator *(Point4 point, double d)

Parameters

Type	Name	Description
Point4	point	A control point.
System.Double	d	A number.

Returns

Type	Description
Point4	A new control point that results from the coordinatewise multiplication of control point with d.

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Subtraction(Point4, Point4)

Sums two Point4 together.

Declaration

public static Point4 operator -(Point4 ctrlPoint1, Point4 ctrlPoint2)

Parameters

Type	Name	Description
Point4	ctrlPoint1	First point.
Point4	ctrlPoint2	Second point.

Returns

Type	Description
Point4	A new point that result of the subtraction of ctrlPoint1 and ctrlPoint2.

Implements

System.IEquatable<T>