UnitCartesian Structure

A set of rectilinear 3-dimensional coordinates with unit magnitude.

Namespace: AGI.Foundation.Coordinates
Assembly: AGI.Foundation.Core (in AGI.Foundation.Core.dll) Version: 24.2.419.0 (24.2.419.0)

Syntax

C++

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public struct UnitCartesian : IEquatable<UnitCartesian>, 
	IEquatableEpsilon<UnitCartesian>

Public Structure UnitCartesian
	Implements IEquatable(Of UnitCartesian), IEquatableEpsilon(Of UnitCartesian)

public value class UnitCartesian : IEquatable<UnitCartesian>, 
	IEquatableEpsilon<UnitCartesian>

[<SealedAttribute>]
type UnitCartesian =  
    struct
        interface IEquatable<UnitCartesian>
        interface IEquatableEpsilon<UnitCartesian>
    end

The UnitCartesian type exposes the following members.

Constructors

	Name	Description
	UnitCartesian(Cartesian)	Initializes a set of UnitCartesian coordinates from the provided set of Cartesian coordinates.
	UnitCartesian(Double)	Initializes a set of UnitCartesian coordinates from the first 3 consecutive elements in the provided array.
	UnitCartesian(UnitRectangular)	Initializes a set of UnitCartesian coordinates from the provided set of UnitRectangular coordinates.
	UnitCartesian(UnitSpherical)	Initializes a set of UnitCartesian coordinates from the provided set of UnitSpherical coordinates.
	UnitCartesian(Cartesian, Double)	Initializes a set of UnitCartesian coordinates from the provided set of Cartesian coordinates.
	UnitCartesian(Double, Double)	Initializes a set of UnitCartesian coordinates from the provided spherical coordinates.
	UnitCartesian(Double, Int32)	Initializes a set of UnitCartesian coordinates from 3 consecutive elements in the provided array.
	UnitCartesian(Double, Double, Double)	Initializes a set of UnitCartesian coordinates from the provided values.
	UnitCartesian(Double, Double, Double, Double)	Initializes a set of UnitCartesian coordinates from the provided values.

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Properties

	Name	Description
	IsUndefined	Gets a value indicating whether any of the coordinates for this instance have the value NaN.
	Item	Gets the value of the specified element with index of 0, 1, and 2 corresponding to the coordinates X, Y, and Z.
	Length	Gets the number of elements in this set of coordinates.
	MostOrthogonalAxis	Gets the axis which is most orthogonal to this instance.
	MostParallelAxis	Gets the axis which is most parallel to this instance.
	Undefined	Gets a set of UnitCartesian coordinates with values of NaN.
	UnitX	Gets a set of UnitCartesian coordinates representing the x-axis.
	UnitY	Gets a set of UnitCartesian coordinates representing the y-axis.
	UnitZ	Gets a set of UnitCartesian coordinates representing the z-axis.
	X	Gets the linear coordinate along the positive x-axis.
	Y	Gets the linear coordinate along the positive y-axis.
	Z	Gets the linear coordinate along the positive z-axis.

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Methods

	Name	Description
	Add(Cartesian)	Adds the specified set of Cartesian coordinates to this instance.
	Add(UnitCartesian)	Adds the specified set of UnitCartesian coordinates to this instance.
	AngleBetween	Determines the angle in radians between the specified set of UnitCartesian coordinates and this instance.
	ConvertMotion	Converts the motion given in terms of a set of Cartesian coordinates to motion of the corresponding set of UnitCartesian coordinates.
	Cross(Cartesian)	Forms the cross product of the specified set of Cartesian coordinates with this instance.
	Cross(UnitCartesian)	Forms the cross product of the specified set of UnitCartesian coordinates with this instance.
	DihedralAngle(UnitCartesian, UnitCartesian, UnitCartesian)	Calculates the scalar dihedral angle of the three given values.
	DihedralAngle(MotionUnitCartesian, Cartesian, MotionUnitCartesian, Cartesian, MotionUnitCartesian, Cartesian, Int32)	Calculates the scalar dihedral angle (and derivatives) of the three given values with Cartesian derivative information.
	Divide	Divides this instance by a scalar.
	Dot(Cartesian)	Forms the dot product of the specified set of Cartesian coordinates with this instance.
	Dot(UnitCartesian)	Forms the dot product of the specified set of UnitCartesian coordinates with this instance.
	Equals(Object)	Indicates whether another object is exactly equal to this instance. (Overrides ValueTypeEquals(Object).)
	Equals(UnitCartesian)	Indicates whether another instance of this type is exactly equal to this instance.
	EqualsEpsilon	Indicates whether each coordinate value of another instance of this type is within the required tolerance of the corresponding coordinate value of this instance.
	GetHashCode	Returns a hash code for this instance, which is suitable for use in hashing algorithms and data structures like a hash table. (Overrides ValueTypeGetHashCode.)
	GetType	Gets the Type of the current instance. (Inherited from Object.)
	Invert	Inverts this instance.
	Multiply	Multiplies this instance by a scalar.
	Rotate(ElementaryRotation)	Produces a set of UnitCartesian coordinates representing this instance, which results from rotating the original axes used to represent this instance by the provided ElementaryRotation rotation.
	Rotate(Matrix3By3)	Produces a set of UnitCartesian coordinates representing this instance which results from rotating the original axes used to represent this instance by the provided Matrix3By3 rotation.
	Rotate(UnitQuaternion)	Produces a set of UnitCartesian coordinates representing this instance which results from rotating the original axes used to represent this instance by the provided UnitQuaternion rotation.
	Subtract(Cartesian)	Subtracts the specified set of Cartesian coordinates from this instance.
	Subtract(UnitCartesian)	Subtracts the specified set of UnitCartesian coordinates from this instance.
	ToString	Returns the string representation of the value of this instance. (Overrides ValueTypeToString.)

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Operators

	Name	Description
	Addition(Cartesian, UnitCartesian)	Adds a specified set of UnitCartesian coordinates to a specified set of Cartesian coordinates.
	Addition(UnitCartesian, Cartesian)	Adds a specified set of Cartesian coordinates to a specified set of UnitCartesian coordinates.
	Addition(UnitCartesian, UnitCartesian)	Adds a specified set of UnitCartesian coordinates to another specified set of UnitCartesian coordinates.
	Division	Divides a specified set of UnitCartesian coordinates by a scalar.
	Equality	Returns if the two instances are exactly equal.
	Inequality	Returns if the two instances are not exactly equal.
	Multiply(Double, UnitCartesian)	Multiplies a scalar by a specified set of UnitCartesian coordinates.
	Multiply(UnitCartesian, Double)	Multiplies a specified set of UnitCartesian coordinates by a scalar.
	Subtraction(Cartesian, UnitCartesian)	Subtracts a specified set of UnitCartesian coordinates from a specified set of Cartesian coordinates.
	Subtraction(UnitCartesian, Cartesian)	Subtracts a specified set of Cartesian coordinates from a specified set of UnitCartesian coordinates.
	Subtraction(UnitCartesian, UnitCartesian)	Subtracts a specified set of UnitCartesian coordinates from another specified set of UnitCartesian coordinates.
	UnaryNegation	Negates the specified UnitCartesian, yielding a new UnitCartesian.

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Remarks

The normalization of the cartesian components is accomplished in the usual way. It should be noted that this does not guarantee a result whose magnitude will be 1.0 in cases where an individual component underflows upon squaring.

The corresponding 2-dimensional coordinates are UnitRectangular coordinates.

Reference

AGI.Foundation.Coordinates Namespace