Struct Vector

Structure defining a vector in three-dimensional euclidean space.

Implements
IEquatable<Vector>
Namespace: BRIDGES.Geometry.Euclidean3D
Assembly: BRIDGES.dll
Syntax
public struct Vector : IDotProduct<Vector, double>, INorm<Vector>, IMetric<Vector>, IGroupAction<Vector, double>

Constructors

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Vector(Point, Point)

Initialises a new instance of Vector structure from two Point.

Declaration
public Vector(Point start, Point end)
Parameters
Type Name Description
Point start

Point at start.
Point end

Point at end.
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Vector(Vector)

Initialises a new instance of the Vector structure from another Vector.

Declaration
public Vector(Vector vector)
Parameters
Type Name Description
Vector vector

Vector to deep copy.
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Vector(Double, Double, Double)

Initialises a new instance of the Vector structure by defining its three coordinates.

Declaration
public Vector(double x, double y, double z)
Parameters
Type Name Description
Double x

Value of the first coordinate.
Double y

Value of the second coordinate.
Double z

Value of the third coordinate.
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Vector(Double[])

Initialises a new instance of Vector structure by defining its coordinates.

Declaration
public Vector(double[] coordinates)
Parameters
Type Name Description
Double[] coordinates

Value of the coordinates.

Properties

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Dimension

Gets the dimension of this Vector's euclidean space.

Declaration
public readonly int Dimension { get; }
Property Value
Type Description
Int32
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Item[Int32]

Gets or sets the value of the coordinate at the given index.

Declaration
public double this[int index] { get; set; }
Parameters
Type Name Description
Int32 index

Index of the coordinate to get or set.
Property Value
Type Description
Double

The value of the coordinate at the given index.
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WorldX

Gets a new Vector with coordinates (1.0, 0.0, 0.0).

Declaration
public static readonly Vector WorldX { get; }
Property Value
Type Description
Vector
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WorldY

Gets a new Vector with coordinates (0.0, 1.0, 0.0).

Declaration
public static readonly Vector WorldY { get; }
Property Value
Type Description
Vector
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WorldZ

Gets a new Vector with coordinates (0.0, 0.0, 1.0).

Declaration
public static readonly Vector WorldZ { get; }
Property Value
Type Description
Vector
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X

Gets or sets the first coordinate of this Vector.

Declaration
public double X { get; set; }
Property Value
Type Description
Double
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Y

Gets or sets the second coordinate of this Vector.

Declaration
public double Y { get; set; }
Property Value
Type Description
Double
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Z

Gets or sets the third coordinate of this Vector.

Declaration
public double Z { get; set; }
Property Value
Type Description
Double
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Zero

Gets a new Vector with coordinates (0.0, 0.0, 0.0).

Declaration
public static readonly Vector Zero { get; }
Property Value
Type Description
Vector

Methods

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Add(Point, Vector)

Computes left the addition of a Vector with a Point.

Declaration
public static Vector Add(Point left, Vector right)
Parameters
Type Name Description
Point left

Point for the addition.
Vector right

Vector for the addition.
Returns
Type Description
Vector

The new Vector resulting from the addition.
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Add(Vector, Point)

Computes right the addition of a Vector with a Point.

Declaration
public static Vector Add(Vector left, Point right)
Parameters
Type Name Description
Vector left

Vector for the addition.
Point right

Point for the addition.
Returns
Type Description
Vector

The new Vector resulting from the addition.
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Add(Vector, Vector)

Computes the addition of two Vector.

Declaration
public static Vector Add(Vector left, Vector right)
Parameters
Type Name Description
Vector left

Vector for the addition.
Vector right

Vector for the addition.
Returns
Type Description
Vector

The new Vector resulting from the addition.
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AngleBetween(Vector, Vector)

Computes the angle between two Vector.

Declaration
public static double AngleBetween(Vector vectorA, Vector vectorB)
Parameters
Type Name Description
Vector vectorA

Vector for the angle evaluation.
Vector vectorB

Vector for the angle evaluation.
Returns
Type Description
Double

The value of the angle between the two Vector (in radians).
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AngleWith(Vector)

Computes the angle made by this Vector with another Vector.

Declaration
public double AngleWith(Vector other)
Parameters
Type Name Description
Vector other

Vector to compare with.
Returns
Type Description
Double

The value of the angle (in radians).
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AreOrthogonal(Vector, Vector)

Evaluates whether two Vector are orthogonal.

Declaration
public static bool AreOrthogonal(Vector vectorA, Vector vectorB)
Parameters
Type Name Description
Vector vectorA

Vector for the comparison.
Vector vectorB

Vector for the comparison.
Returns
Type Description
Boolean

true if the two Vector are orthogonal, false otherwise.
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AreOrthogonal(Vector[])

Evaluates whether a collection of Vector are orthogonal to one another.

Declaration
public static bool AreOrthogonal(params Vector[] vectors)
Parameters
Type Name Description
Vector[] vectors

Collection of Vector to evaluate.
Returns
Type Description
Boolean

true if the Vector are orthogonal, false otherwise.
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AreParallel(Vector, Vector)

Evaluates whether two Vector are parallel.

Declaration
public static bool AreParallel(Vector vectorA, Vector vectorB)
Parameters
Type Name Description
Vector vectorA

Vector for the comparison.
Vector vectorB

Vector for the comparison.
Returns
Type Description
Boolean

true if the two Vector are parallel, false otherwise.
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CrossProduct(Vector, Vector)

Returns the cross product of two Vector.

Declaration
public static Vector CrossProduct(Vector left, Vector right)
Parameters
Type Name Description
Vector left

Left Vector for the cross product.
Vector right

Right Vector for the cross product.
Returns
Type Description
Vector

A new Vector resulting from the cross product of two Vector.
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Divide(Vector, Double)

Computes the scalar division of a Vector with a -precision real number.

Declaration
public static Vector Divide(Vector operand, double divisor)
Parameters
Type Name Description
Vector operand

Vector to divide.
Double divisor

-precision real number to divide with.
Returns
Type Description
Vector

The new Vector resulting from the scalar division.
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DotProduct(Vector, Vector)

Computes the dot product of two Vector.

Declaration
public static double DotProduct(Vector left, Vector right)
Parameters
Type Name Description
Vector left

Vector for the dot product.
Vector right

Vector for the dot product.
Returns
Type Description
Double

The new Vector resulting from the dot product of two Vector.
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Equals(Vector)

Evaluates whether this Vector is memberwise equal to another Vector.

Declaration
public bool Equals(Vector other)
Parameters
Type Name Description
Vector other

Vector to compare with.
Returns
Type Description
Boolean

true if the two Vector are equal, false otherwise.
Remarks

Two Vector are equal if their coordinates are equal.

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Equals(Object)

Structure defining a vector in three-dimensional euclidean space.

Declaration
public override bool Equals(object obj)
Parameters
Type Name Description
Object obj
Returns
Type Description
Boolean
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GetCoordinates()

Gets the coordinates of this Vector.

Declaration
public double[] GetCoordinates()
Returns
Type Description
Double[]

The array representation of the Vector's coordinates.
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GetHashCode()

Structure defining a vector in three-dimensional euclidean space.

Declaration
public override int GetHashCode()
Returns
Type Description
Int32
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IsUnit()

Evaluates whether this Vector's length is one.

Declaration
public bool IsUnit()
Returns
Type Description
Boolean

true if this Vector is of unit length, false otherwise.
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Length()

Computes the length of this Vector (using the L2-norm).

Declaration
public double Length()
Returns
Type Description
Double

The value of this Vector's length.
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Multiply(Vector, Double)

Computes the right scalar multiplication of a Vector with a number.

Declaration
public static Vector Multiply(Vector operand, double factor)
Parameters
Type Name Description
Vector operand

Vector to multiply.
Double factor

number.
Returns
Type Description
Vector

The new Vector resulting from the scalar multiplication.
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Multiply(Double, Vector)

Computes the left scalar multiplication of a Vector with a number.

Declaration
public static Vector Multiply(double factor, Vector operand)
Parameters
Type Name Description
Double factor

number.
Vector operand

Vector to multiply.
Returns
Type Description
Vector

The new Vector resulting from the scalar multiplication.
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SquaredLength()

Computes the squared length of this Vector (using the L2-norm).

Declaration
public double SquaredLength()
Returns
Type Description
Double

The value of this Vector's squared length.
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Subtract(Point, Vector)

Computes left the subtraction of a Vector with a Point.

Declaration
public static Vector Subtract(Point left, Vector right)
Parameters
Type Name Description
Point left

Point to subtract.
Vector right

Vector to subtract with.
Returns
Type Description
Vector

The new Vector resulting from the subtraction.
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Subtract(Vector, Point)

Computes right the subtraction of a Vector with a Point.

Declaration
public static Vector Subtract(Vector left, Point right)
Parameters
Type Name Description
Vector left

Vector to subtract.
Point right

Point to subtract with.
Returns
Type Description
Vector

The new Vector resulting from the subtraction.
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Subtract(Vector, Vector)

Computes the subtraction of two Vector.

Declaration
public static Vector Subtract(Vector left, Vector right)
Parameters
Type Name Description
Vector left

Vector to subtract.
Vector right

Vector to subtract with.
Returns
Type Description
Vector

The new Vector resulting from the subtraction.
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ToString()

Structure defining a vector in three-dimensional euclidean space.

Declaration
public override string ToString()
Returns
Type Description
String
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Unitise()

Unitises this Vector (using the L2-norm).

Declaration
public void Unitise()

Operators

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Addition(Vector, Point)

Computes right the addition of a Vector with a Point.

Declaration
public static Vector operator +(Vector left, Point right)
Parameters
Type Name Description
Vector left

Vector for the addition.
Point right

Point for the addition.
Returns
Type Description
Vector

The new Vector resulting from the addition.
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Addition(Vector, Vector)

Computes the addition of two Vector.

Declaration
public static Vector operator +(Vector left, Vector right)
Parameters
Type Name Description
Vector left

Vector for the addition.
Vector right

Vector for the addition.
Returns
Type Description
Vector

The new Vector resulting from the addition.
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Division(Vector, Double)

Computes the scalar division of a Vector with a -precision real number.

Declaration
public static Vector operator /(Vector operand, double divisor)
Parameters
Type Name Description
Vector operand

Vector to divide.
Double divisor

-precision real number to divide with.
Returns
Type Description
Vector

The new Vector resulting from the scalar division.
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Implicit(Point to Vector)

Converts a Point into a Vector.

Declaration
public static implicit operator Vector(Point point)
Parameters
Type Name Description
Point point

Point to convert.
Returns
Type Description
Vector

The new Vector resulting from the conversion.
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Multiply(Vector, Vector)

Computes the dot product of two Vector.

Declaration
public static double operator *(Vector left, Vector right)
Parameters
Type Name Description
Vector left

Vector for the dot product.
Vector right

Vector for the dot product.
Returns
Type Description
Double

The new Vector resulting from the dot product of two Vector.
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Multiply(Vector, Double)

Computes the right scalar multiplication of a Vector with a number.

Declaration
public static Vector operator *(Vector operand, double factor)
Parameters
Type Name Description
Vector operand

Vector to multiply.
Double factor

number.
Returns
Type Description
Vector

The new Vector resulting from the scalar multiplication.
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Multiply(Double, Vector)

Computes the left scalar multiplication of a Vector with a number.

Declaration
public static Vector operator *(double factor, Vector operand)
Parameters
Type Name Description
Double factor

number.
Vector operand

Vector to multiply.
Returns
Type Description
Vector

The new Vector resulting from the scalar multiplication.
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Subtraction(Vector, Point)

Computes right the subtraction of a Vector with a Point.

Declaration
public static Vector operator -(Vector left, Point right)
Parameters
Type Name Description
Vector left

Vector to subtract.
Point right

Point to subtract with.
Returns
Type Description
Vector

The new Vector resulting from the subtraction.
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Subtraction(Vector, Vector)

Computes the subtraction of two Vector.

Declaration
public static Vector operator -(Vector left, Vector right)
Parameters
Type Name Description
Vector left

Vector to subtract.
Vector right

Vector to subtract with.
Returns
Type Description
Vector

The new Vector resulting from the subtraction.
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UnaryNegation(Vector)

Computes the opposite of the given Vector.

Declaration
public static Vector operator -(Vector operand)
Parameters
Type Name Description
Vector operand

Vector to be opposed.
Returns
Type Description
Vector

The new Vector, opposite of the initial one.

Explicit Interface Implementations

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IDotProduct<Vector, Double>.DotProduct(Vector)

Computes the dot product of this element with another element.

Declaration
double IDotProduct<Vector, double>.DotProduct(Vector other)
Parameters
Type Name Description
Vector other
Returns
Type Description
Double

The value of the dot product of the two elements.
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IMetric<Vector>.DistanceTo(Vector)

Computes the distance of this element to another element.

Declaration
double IMetric<Vector>.DistanceTo(Vector other)
Parameters
Type Name Description
Vector other
Returns
Type Description
Double

The value of the distance between the two elements.
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INorm<Vector>.Norm()

Computes the norm of this element.

Declaration
double INorm<Vector>.Norm()
Returns
Type Description
Double

The value of the norm.
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IGroupAction<Vector, Double>.Divide(Double)

Computes the right scalar division of the current element.

Declaration
Vector IGroupAction<Vector, double>.Divide(double divisor)
Parameters
Type Name Description
Double divisor
Returns
Type Description
Vector

The new element resulting from the scalar dividion.
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IGroupAction<Vector, Double>.Multiply(Double)

Computes the right scalar multiplication of the current element.

Declaration
Vector IGroupAction<Vector, double>.Multiply(double factor)
Parameters
Type Name Description
Double factor
Returns
Type Description
Vector

The new element resulting from the scalar multiplication.

Implements

IEquatable<>