Struct Vector3d

Represents a 3D vector using three double-precision floating-point numbers.

Implements

IEquatable<Vector3d>

IFormattable

Inherited Members

object.Equals(object, object)

object.GetType()

object.ReferenceEquals(object, object)

Namespace: OpenTK.Mathematics

Assembly: OpenTK.Mathematics.dll

Syntax

[Serializable]
public struct Vector3d : IEquatable<Vector3d>, IFormattable

Constructors

Vector3d(Vector2d, double)

Initializes a new instance of the Vector3d struct.

Declaration

public Vector3d(Vector2d xy, double z = 0)

Parameters

Type	Name	Description
Vector2d	xy	The x and y components of the Vector3d.
double	z	The z component of the Vector3d.

Vector3d(double)

Initializes a new instance of the Vector3d struct.

Declaration

public Vector3d(double value)

Parameters

Type	Name	Description
double	value	The value that will initialize this instance.

Vector3d(double, double, double)

Initializes a new instance of the Vector3d struct.

Declaration

public Vector3d(double x, double y, double z)

Parameters

Type	Name	Description
double	x	The x component of the Vector3d.
double	y	The y component of the Vector3d.
double	z	The z component of the Vector3d.

Fields

NegativeInfinity

Defines an instance with all components set to negative infinity.

Declaration

public static readonly Vector3d NegativeInfinity

Field Value

Type	Description
Vector3d

One

Defines an instance with all components set to 1.

Declaration

public static readonly Vector3d One

Field Value

Type	Description
Vector3d

PositiveInfinity

Defines an instance with all components set to positive infinity.

Declaration

public static readonly Vector3d PositiveInfinity

Field Value

Type	Description
Vector3d

SizeInBytes

Defines the size of the Vector3d struct in bytes.

Declaration

public static readonly int SizeInBytes

Field Value

Type	Description
int

UnitX

Defines a unit-length Vector3d that points towards the X-axis.

Declaration

public static readonly Vector3d UnitX

Field Value

Type	Description
Vector3d

UnitY

Defines a unit-length Vector3d that points towards the Y-axis.

Declaration

public static readonly Vector3d UnitY

Field Value

Type	Description
Vector3d

UnitZ

Defines a unit-length Vector3d that points towards the Z-axis.

Declaration

public static readonly Vector3d UnitZ

Field Value

Type	Description
Vector3d

X

The X component of the Vector3.

Declaration

public double X

Field Value

Type	Description
double

Y

The Y component of the Vector3.

Declaration

public double Y

Field Value

Type	Description
double

Z

The Z component of the Vector3.

Declaration

public double Z

Field Value

Type	Description
double

Zero

Defines an instance with all components set to 0.

Declaration

public static readonly Vector3d Zero

Field Value

Type	Description
Vector3d

Properties

this[int]

Gets or sets the value at the index of the Vector.

Declaration

public double this[int index] { readonly get; set; }

Parameters

Type	Name	Description
int	index	The index of the component from the Vector.

Property Value

Type	Description
double

Exceptions

Type	Condition
IndexOutOfRangeException	Thrown if the index is less than 0 or greater than 2.

Length

Gets the length (magnitude) of the vector.

Declaration

public readonly double Length { get; }

Property Value

Type	Description
double

See Also

LengthSquared

LengthFast

Gets an approximation of the vector length (magnitude).

Declaration

public readonly double LengthFast { get; }

Property Value

Type	Description
double

Remarks

This property uses an approximation of the square root function to calculate vector magnitude.

See Also

LengthSquared

LengthSquared

Gets the square of the vector length (magnitude).

Declaration

public readonly double LengthSquared { get; }

Property Value

Type	Description
double

Remarks

This property avoids the costly square root operation required by the Length property. This makes it more suitable for comparisons.

See Also

LengthFast

ReciprocalLengthFast

Gets an approximation of 1 over the length (magnitude) of the vector.

Declaration

public readonly double ReciprocalLengthFast { get; }

Property Value

Type	Description
double

Xy

Gets or sets an OpenTK.Vector2d with the X and Y components of this instance.

Declaration

public Vector2d Xy { get; set; }

Property Value

Type	Description
Vector2d

Xz

Gets or sets an OpenTK.Vector2d with the X and Z components of this instance.

Declaration

public Vector2d Xz { readonly get; set; }

Property Value

Type	Description
Vector2d

Xzy

Gets or sets an OpenTK.Vector3d with the X, Z, and Y components of this instance.

Declaration

public Vector3d Xzy { readonly get; set; }

Property Value

Type	Description
Vector3d

Yx

Gets or sets an OpenTK.Vector2d with the Y and X components of this instance.

Declaration

public Vector2d Yx { readonly get; set; }

Property Value

Type	Description
Vector2d

Yxz

Gets or sets an OpenTK.Vector3d with the Y, X, and Z components of this instance.

Declaration

public Vector3d Yxz { readonly get; set; }

Property Value

Type	Description
Vector3d

Yz

Gets or sets an OpenTK.Vector2d with the Y and Z components of this instance.

Declaration

public Vector2d Yz { readonly get; set; }

Property Value

Type	Description
Vector2d

Yzx

Gets or sets an OpenTK.Vector3d with the Y, Z, and X components of this instance.

Declaration

public Vector3d Yzx { readonly get; set; }

Property Value

Type	Description
Vector3d

Zx

Gets or sets an OpenTK.Vector2d with the Z and X components of this instance.

Declaration

public Vector2d Zx { readonly get; set; }

Property Value

Type	Description
Vector2d

Zxy

Gets or sets an OpenTK.Vector3d with the Z, X, and Y components of this instance.

Declaration

public Vector3d Zxy { readonly get; set; }

Property Value

Type	Description
Vector3d

Zy

Gets or sets an OpenTK.Vector2d with the Z and Y components of this instance.

Declaration

public Vector2d Zy { readonly get; set; }

Property Value

Type	Description
Vector2d

Zyx

Gets or sets an OpenTK.Vector3d with the Z, Y, and X components of this instance.

Declaration

public Vector3d Zyx { readonly get; set; }

Property Value

Type	Description
Vector3d

Methods

Abs()

Returns a new vector that is the component-wise absolute value of the vector.

Declaration

public readonly Vector3d Abs()

Returns

Type	Description
Vector3d	The component-wise absolute value vector.

Abs(Vector3d)

Take the component-wise absolute value of a vector.

Declaration

public static Vector3d Abs(Vector3d vec)

Parameters

Type	Name	Description
Vector3d	vec	The vector to apply component-wise absolute value to.

Returns

Type	Description
Vector3d	The component-wise absolute value vector.

Abs(in Vector3d, out Vector3d)

Take the component-wise absolute value of a vector.

Declaration

public static void Abs(in Vector3d vec, out Vector3d result)

Parameters

Type	Name	Description
Vector3d	vec	The vector to apply component-wise absolute value to.
Vector3d	result	The component-wise absolute value vector.

Add(Vector3d, Vector3d)

Adds two vectors.

Declaration

[Pure]
public static Vector3d Add(Vector3d a, Vector3d b)

Parameters

Type	Name	Description
Vector3d	a	Left operand.
Vector3d	b	Right operand.

Returns

Type	Description
Vector3d	Result of operation.

Add(in Vector3d, in Vector3d, out Vector3d)

Adds two vectors.

Declaration

public static void Add(in Vector3d a, in Vector3d b, out Vector3d result)

Parameters

Type	Name	Description
Vector3d	a	Left operand.
Vector3d	b	Right operand.
Vector3d	result	Result of operation.

BaryCentric(Vector3d, Vector3d, Vector3d, double, double)

Interpolate 3 Vectors using Barycentric coordinates.

Declaration

[Pure]
public static Vector3d BaryCentric(Vector3d a, Vector3d b, Vector3d c, double u, double v)

Parameters

Type	Name	Description
Vector3d	a	First input Vector.
Vector3d	b	Second input Vector.
Vector3d	c	Third input Vector.
double	u	First Barycentric Coordinate.
double	v	Second Barycentric Coordinate.

Returns

Type	Description
Vector3d	a when u=v=0, b when u=1,v=0, c when u=0,v=1, and a linear combination of a,b,c otherwise.

BaryCentric(in Vector3d, in Vector3d, in Vector3d, double, double, out Vector3d)

Interpolate 3 Vectors using Barycentric coordinates.

Declaration

[Pure]
public static void BaryCentric(in Vector3d a, in Vector3d b, in Vector3d c, double u, double v, out Vector3d result)

Parameters

Type	Name	Description
Vector3d	a	First input Vector.
Vector3d	b	Second input Vector.
Vector3d	c	Third input Vector.
double	u	First Barycentric Coordinate.
double	v	Second Barycentric Coordinate.
Vector3d	result	Output Vector. a when u=v=0, b when u=1,v=0, c when u=0,v=1, and a linear combination of a,b,c otherwise.

CalculateAngle(Vector3d, Vector3d)

Calculates the angle (in radians) between two vectors.

Declaration

[Pure]
public static double CalculateAngle(Vector3d first, Vector3d second)

Parameters

Type	Name	Description
Vector3d	first	The first vector.
Vector3d	second	The second vector.

Returns

Type	Description
double	Angle (in radians) between the vectors.

Remarks

Note that the returned angle is never bigger than the constant Pi.

CalculateAngle(in Vector3d, in Vector3d, out double)

Calculates the angle (in radians) between two vectors.

Declaration

public static void CalculateAngle(in Vector3d first, in Vector3d second, out double result)

Parameters

Type	Name	Description
Vector3d	first	The first vector.
Vector3d	second	The second vector.
double	result	Angle (in radians) between the vectors.

Remarks

Note that the returned angle is never bigger than the constant Pi.

Clamp(Vector3d, Vector3d, Vector3d)

Clamp a vector to the given minimum and maximum vectors.

Declaration

[Pure]
public static Vector3d Clamp(Vector3d vec, Vector3d min, Vector3d max)

Parameters

Type	Name	Description
Vector3d	vec	Input vector.
Vector3d	min	Minimum vector.
Vector3d	max	Maximum vector.

Returns

Type	Description
Vector3d	The clamped vector.

Clamp(in Vector3d, in Vector3d, in Vector3d, out Vector3d)

Clamp a vector to the given minimum and maximum vectors.

Declaration

public static void Clamp(in Vector3d vec, in Vector3d min, in Vector3d max, out Vector3d result)

Parameters

Type	Name	Description
Vector3d	vec	Input vector.
Vector3d	min	Minimum vector.
Vector3d	max	Maximum vector.
Vector3d	result	The clamped vector.

ComponentMax(Vector3d, Vector3d)

Returns a vector created from the largest of the corresponding components of the given vectors.

Declaration

[Pure]
public static Vector3d ComponentMax(Vector3d a, Vector3d b)

Parameters

Type	Name	Description
Vector3d	a	First operand.
Vector3d	b	Second operand.

Returns

Type	Description
Vector3d	The component-wise maximum.

ComponentMax(in Vector3d, in Vector3d, out Vector3d)

Returns a vector created from the largest of the corresponding components of the given vectors.

Declaration

public static void ComponentMax(in Vector3d a, in Vector3d b, out Vector3d result)

Parameters

Type	Name	Description
Vector3d	a	First operand.
Vector3d	b	Second operand.
Vector3d	result	The component-wise maximum.

ComponentMin(Vector3d, Vector3d)

Returns a vector created from the smallest of the corresponding components of the given vectors.

Declaration

[Pure]
public static Vector3d ComponentMin(Vector3d a, Vector3d b)

Parameters

Type	Name	Description
Vector3d	a	First operand.
Vector3d	b	Second operand.

Returns

Type	Description
Vector3d	The component-wise minimum.

ComponentMin(in Vector3d, in Vector3d, out Vector3d)

Returns a vector created from the smallest of the corresponding components of the given vectors.

Declaration

public static void ComponentMin(in Vector3d a, in Vector3d b, out Vector3d result)

Parameters

Type	Name	Description
Vector3d	a	First operand.
Vector3d	b	Second operand.
Vector3d	result	The component-wise minimum.

Cross(Vector3d, Vector3d)

Caclulate the cross (vector) product of two vectors.

Declaration

[Pure]
public static Vector3d Cross(Vector3d left, Vector3d right)

Parameters

Type	Name	Description
Vector3d	left	First operand.
Vector3d	right	Second operand.

Returns

Type	Description
Vector3d	The cross product of the two inputs.

Cross(in Vector3d, in Vector3d, out Vector3d)

Caclulate the cross (vector) product of two vectors.

Declaration

public static void Cross(in Vector3d left, in Vector3d right, out Vector3d result)

Parameters

Type	Name	Description
Vector3d	left	First operand.
Vector3d	right	Second operand.
Vector3d	result	The cross product of the two inputs.

Deconstruct(out double, out double, out double)

Deconstructs the vector into it's individual components.

Declaration

[Pure]
public readonly void Deconstruct(out double x, out double y, out double z)

Parameters

Type	Name	Description
double	x	The X component of the vector.
double	y	The Y component of the vector.
double	z	The Z component of the vector.

Distance(Vector3d, Vector3d)

Compute the euclidean distance between two vectors.

Declaration

[Pure]
public static double Distance(Vector3d vec1, Vector3d vec2)

Parameters

Type	Name	Description
Vector3d	vec1	The first vector.
Vector3d	vec2	The second vector.

Returns

Type	Description
double	The distance.

Distance(in Vector3d, in Vector3d, out double)

Compute the euclidean distance between two vectors.

Declaration

public static void Distance(in Vector3d vec1, in Vector3d vec2, out double result)

Parameters

Type	Name	Description
Vector3d	vec1	The first vector.
Vector3d	vec2	The second vector.
double	result	The distance.

DistanceSquared(Vector3d, Vector3d)

Compute the squared euclidean distance between two vectors.

Declaration

[Pure]
public static double DistanceSquared(Vector3d vec1, Vector3d vec2)

Parameters

Type	Name	Description
Vector3d	vec1	The first vector.
Vector3d	vec2	The second vector.

Returns

Type	Description
double	The squared distance.

DistanceSquared(in Vector3d, in Vector3d, out double)

Compute the squared euclidean distance between two vectors.

Declaration

public static void DistanceSquared(in Vector3d vec1, in Vector3d vec2, out double result)

Parameters

Type	Name	Description
Vector3d	vec1	The first vector.
Vector3d	vec2	The second vector.
double	result	The squared distance.

Divide(Vector3d, Vector3d)

Divides a vector by the components of a vector (scale).

Declaration

[Pure]
public static Vector3d Divide(Vector3d vector, Vector3d scale)

Parameters

Type	Name	Description
Vector3d	vector	Left operand.
Vector3d	scale	Right operand.

Returns

Type	Description
Vector3d	Result of the operation.

Divide(Vector3d, double)

Divides a vector by a scalar.

Declaration

[Pure]
public static Vector3d Divide(Vector3d vector, double scale)

Parameters

Type	Name	Description
Vector3d	vector	Left operand.
double	scale	Right operand.

Returns

Type	Description
Vector3d	Result of the operation.

Divide(in Vector3d, in Vector3d, out Vector3d)

Divide a vector by the components of a vector (scale).

Declaration

public static void Divide(in Vector3d vector, in Vector3d scale, out Vector3d result)

Parameters

Type	Name	Description
Vector3d	vector	Left operand.
Vector3d	scale	Right operand.
Vector3d	result	Result of the operation.

Divide(in Vector3d, double, out Vector3d)

Divides a vector by a scalar.

Declaration

public static void Divide(in Vector3d vector, double scale, out Vector3d result)

Parameters

Type	Name	Description
Vector3d	vector	Left operand.
double	scale	Right operand.
Vector3d	result	Result of the operation.

Dot(Vector3d, Vector3d)

Calculate the dot (scalar) product of two vectors.

Declaration

[Pure]
public static double Dot(Vector3d left, Vector3d right)

Parameters

Type	Name	Description
Vector3d	left	First operand.
Vector3d	right	Second operand.

Returns

Type	Description
double	The dot product of the two inputs.

Dot(in Vector3d, in Vector3d, out double)

Calculate the dot (scalar) product of two vectors.

Declaration

public static void Dot(in Vector3d left, in Vector3d right, out double result)

Parameters

Type	Name	Description
Vector3d	left	First operand.
Vector3d	right	Second operand.
double	result	The dot product of the two inputs.

Elerp(Vector3d, Vector3d, double)

Returns a new vector that is the exponential interpolation of the two vectors. Equivalent to a * pow(b/a, t).

Declaration

public static Vector3d Elerp(Vector3d a, Vector3d b, double t)

Parameters

Type	Name	Description
Vector3d	a	The starting value. Must be non-negative.
Vector3d	b	The end value. Must be non-negative.
double	t	The blend factor.

Returns

Type	Description
Vector3d	The exponential interpolation between a and b.

See Also

Elerp(double, double, double)

Elerp(in Vector3d, in Vector3d, double, out Vector3d)

Returns a new vector that is the exponential interpolation of the two vectors. Equivalent to a * pow(b/a, t).

Declaration

public static void Elerp(in Vector3d a, in Vector3d b, double t, out Vector3d result)

Parameters

Type	Name	Description
Vector3d	a	The starting value. Must be non-negative.
Vector3d	b	The end value. Must be non-negative.
double	t	The blend factor.
Vector3d	result	The exponential interpolation between a and b.

See Also

Elerp(double, double, double)

Equals(Vector3d)

Indicates whether the current object is equal to another object of the same type.

Declaration

public readonly bool Equals(Vector3d other)

Parameters

Type	Name	Description
Vector3d	other	An object to compare with this object.

Returns

Type	Description
bool	true if the current object is equal to the other parameter; otherwise, false.

Equals(object)

Indicates whether this instance and a specified object are equal.

Declaration

public override bool Equals(object obj)

Parameters

Type	Name	Description
object	obj	The object to compare with the current instance.

Returns

Type	Description
bool	true if obj and this instance are the same type and represent the same value; otherwise, false.

Overrides

ValueType.Equals(object)

GetHashCode()

Returns the hash code for this instance.

Declaration

public override readonly int GetHashCode()

Returns

Type	Description
int	A 32-bit signed integer that is the hash code for this instance.

Overrides

ValueType.GetHashCode()

Lerp(Vector3d, Vector3d, Vector3d)

Returns a new vector that is the component-wise linear blend of the 2 given vectors.

Declaration

[Pure]
public static Vector3d Lerp(Vector3d a, Vector3d b, Vector3d blend)

Parameters

Type	Name	Description
Vector3d	a	First input vector.
Vector3d	b	Second input vector.
Vector3d	blend	The blend factor.

Returns

Type	Description
Vector3d	a when blend=0, b when blend=1, and a component-wise linear combination otherwise.

Lerp(Vector3d, Vector3d, double)

Returns a new vector that is the linear blend of the 2 given vectors.

Declaration

[Pure]
public static Vector3d Lerp(Vector3d a, Vector3d b, double blend)

Parameters

Type	Name	Description
Vector3d	a	First input vector.
Vector3d	b	Second input vector.
double	blend	The blend factor.

Returns

Type	Description
Vector3d	a when blend=0, b when blend=1, and a linear combination otherwise.

Lerp(in Vector3d, in Vector3d, Vector3d, out Vector3d)

Returns a new vector that is the component-wise linear blend of the 2 given vectors.

Declaration

public static void Lerp(in Vector3d a, in Vector3d b, Vector3d blend, out Vector3d result)

Parameters

Type	Name	Description
Vector3d	a	First input vector.
Vector3d	b	Second input vector.
Vector3d	blend	The blend factor.
Vector3d	result	a when blend=0, b when blend=1, and a component-wise linear combination otherwise.

Lerp(in Vector3d, in Vector3d, double, out Vector3d)

Returns a new vector that is the linear blend of the 2 given vectors.

Declaration

public static void Lerp(in Vector3d a, in Vector3d b, double blend, out Vector3d result)

Parameters

Type	Name	Description
Vector3d	a	First input vector.
Vector3d	b	Second input vector.
double	blend	The blend factor.
Vector3d	result	a when blend=0, b when blend=1, and a linear combination otherwise.

MagnitudeMax(Vector3d, Vector3d)

Returns the Vector3d with the minimum magnitude.

Declaration

[Pure]
public static Vector3d MagnitudeMax(Vector3d left, Vector3d right)

Parameters

Type	Name	Description
Vector3d	left	Left operand.
Vector3d	right	Right operand.

Returns

Type	Description
Vector3d	The minimum Vector3d.

MagnitudeMax(in Vector3d, in Vector3d, out Vector3d)

Returns the Vector3d with the maximum magnitude.

Declaration

public static void MagnitudeMax(in Vector3d left, in Vector3d right, out Vector3d result)

Parameters

Type	Name	Description
Vector3d	left	Left operand.
Vector3d	right	Right operand.
Vector3d	result	The magnitude-wise maximum.

MagnitudeMin(Vector3d, Vector3d)

Returns the Vector3d with the minimum magnitude.

Declaration

[Pure]
public static Vector3d MagnitudeMin(Vector3d left, Vector3d right)

Parameters

Type	Name	Description
Vector3d	left	Left operand.
Vector3d	right	Right operand.

Returns

Type	Description
Vector3d	The minimum Vector3d.

MagnitudeMin(in Vector3d, in Vector3d, out Vector3d)

Returns the Vector3d with the minimum magnitude.

Declaration

public static void MagnitudeMin(in Vector3d left, in Vector3d right, out Vector3d result)

Parameters

Type	Name	Description
Vector3d	left	Left operand.
Vector3d	right	Right operand.
Vector3d	result	The magnitude-wise minimum.

Multiply(Vector3d, Vector3d)

Multiplies a vector by the components a vector (scale).

Declaration

[Pure]
public static Vector3d Multiply(Vector3d vector, Vector3d scale)

Parameters

Type	Name	Description
Vector3d	vector	Left operand.
Vector3d	scale	Right operand.

Returns

Type	Description
Vector3d	Result of the operation.

Multiply(Vector3d, double)

Multiplies a vector by a scalar.

Declaration

[Pure]
public static Vector3d Multiply(Vector3d vector, double scale)

Parameters

Type	Name	Description
Vector3d	vector	Left operand.
double	scale	Right operand.

Returns

Type	Description
Vector3d	Result of the operation.

Multiply(in Vector3d, in Vector3d, out Vector3d)

Multiplies a vector by the components of a vector (scale).

Declaration

public static void Multiply(in Vector3d vector, in Vector3d scale, out Vector3d result)

Parameters

Type	Name	Description
Vector3d	vector	Left operand.
Vector3d	scale	Right operand.
Vector3d	result	Result of the operation.

Multiply(in Vector3d, double, out Vector3d)

Multiplies a vector by a scalar.

Declaration

public static void Multiply(in Vector3d vector, double scale, out Vector3d result)

Parameters

Type	Name	Description
Vector3d	vector	Left operand.
double	scale	Right operand.
Vector3d	result	Result of the operation.

Normalize()

Scales the Vector3d to unit length.

Declaration

public void Normalize()

Normalize(Vector3d)

Scale a vector to unit length.

Declaration

[Pure]
public static Vector3d Normalize(Vector3d vec)

Parameters

Type	Name	Description
Vector3d	vec	The input vector.

Returns

Type	Description
Vector3d	The normalized copy.

Normalize(in Vector3d, out Vector3d)

Scale a vector to unit length.

Declaration

public static void Normalize(in Vector3d vec, out Vector3d result)

Parameters

Type	Name	Description
Vector3d	vec	The input vector.
Vector3d	result	The normalized vector.

NormalizeFast()

Scales the Vector3d to approximately unit length.

Declaration

public void NormalizeFast()

NormalizeFast(Vector3d)

Scale a vector to approximately unit length.

Declaration

[Pure]
public static Vector3d NormalizeFast(Vector3d vec)

Parameters

Type	Name	Description
Vector3d	vec	The input vector.

Returns

Type	Description
Vector3d	The normalized copy.

NormalizeFast(in Vector3d, out Vector3d)

Scale a vector to approximately unit length.

Declaration

public static void NormalizeFast(in Vector3d vec, out Vector3d result)

Parameters

Type	Name	Description
Vector3d	vec	The input vector.
Vector3d	result	The normalized vector.

Normalized()

Returns a copy of the Vector3d scaled to unit length.

Declaration

public readonly Vector3d Normalized()

Returns

Type	Description
Vector3d	The normalized copy.

Slerp(Vector3d, Vector3d, double)

Returns a new vector that is the spherical interpolation of the two given vectors. a and b need to be normalized for this function to work properly.

Declaration

[Pure]
public static Vector3d Slerp(Vector3d a, Vector3d b, double t)

Parameters

Type	Name	Description
Vector3d	a	Unit vector start point.
Vector3d	b	Unit vector end point.
double	t	The blend factor.

Returns

Type	Description
Vector3d	a when t=0, b when t=1, and a spherical interpolation between the vectors otherwise.

Slerp(in Vector3d, in Vector3d, double, out Vector3d)

Returns a new vector that is the spherical interpolation of the two given vectors. a and b need to be normalized for this function to work properly.

Declaration

public static void Slerp(in Vector3d a, in Vector3d b, double t, out Vector3d result)

Parameters

Type	Name	Description
Vector3d	a	Unit vector start point.
Vector3d	b	Unit vector end point.
double	t	The blend factor.
Vector3d	result	Is a when t=0, b when t=1, and a spherical interpolation between the vectors otherwise.

Subtract(Vector3d, Vector3d)

Subtract one Vector from another.

Declaration

[Pure]
public static Vector3d Subtract(Vector3d a, Vector3d b)

Parameters

Type	Name	Description
Vector3d	a	First operand.
Vector3d	b	Second operand.

Returns

Type	Description
Vector3d	Result of subtraction.

Subtract(in Vector3d, in Vector3d, out Vector3d)

Subtract one Vector from another.

Declaration

public static void Subtract(in Vector3d a, in Vector3d b, out Vector3d result)

Parameters

Type	Name	Description
Vector3d	a	First operand.
Vector3d	b	Second operand.
Vector3d	result	Result of subtraction.

ToString()

Returns the fully qualified type name of this instance.

Declaration

public override string ToString()

Returns

Type	Description
string	The fully qualified type name.

Overrides

ValueType.ToString()

ToString(IFormatProvider)

Formats the value of the current instance using the specified format.

Declaration

public string ToString(IFormatProvider formatProvider)

Parameters

Type	Name	Description
IFormatProvider	formatProvider	The provider to use to format the value. -or- A null reference (Nothing in Visual Basic) to obtain the numeric format information from the current locale setting of the operating system.

Returns

Type	Description
string	The value of the current instance in the specified format.

ToString(string)

Formats the value of the current instance using the specified format.

Declaration

public string ToString(string format)

Parameters

Type	Name	Description
string	format	The format to use. -or- A null reference (Nothing in Visual Basic) to use the default format defined for the type of the IFormattable implementation.

Returns

Type	Description
string	The value of the current instance in the specified format.

ToString(string, IFormatProvider)

Formats the value of the current instance using the specified format.

Declaration

public readonly string ToString(string format, IFormatProvider formatProvider)

Parameters

Type	Name	Description
string	format	The format to use. -or- A null reference (Nothing in Visual Basic) to use the default format defined for the type of the IFormattable implementation.
IFormatProvider	formatProvider	The provider to use to format the value. -or- A null reference (Nothing in Visual Basic) to obtain the numeric format information from the current locale setting of the operating system.

Returns

Type	Description
string	The value of the current instance in the specified format.

Transform(Vector3d, Quaterniond)

Transforms a vector by a quaternion rotation.

Declaration

[Pure]
public static Vector3d Transform(Vector3d vec, Quaterniond quat)

Parameters

Type	Name	Description
Vector3d	vec	The vector to transform.
Quaterniond	quat	The quaternion to rotate the vector by.

Returns

Type	Description
Vector3d	The result of the operation.

Transform(in Vector3d, in Quaterniond, out Vector3d)

Transforms a vector by a quaternion rotation.

Declaration

public static void Transform(in Vector3d vec, in Quaterniond quat, out Vector3d result)

Parameters

Type	Name	Description
Vector3d	vec	The vector to transform.
Quaterniond	quat	The quaternion to rotate the vector by.
Vector3d	result	The result of the operation.

TransformColumn(Matrix3d, Vector3d)

Transform a Vector by the given Matrix using right-handed notation.

Declaration

[Pure]
public static Vector3d TransformColumn(Matrix3d mat, Vector3d vec)

Parameters

Type	Name	Description
Matrix3d	mat	The desired transformation.
Vector3d	vec	The vector to transform.

Returns

Type	Description
Vector3d	The transformed vector.

TransformColumn(in Matrix3d, in Vector3d, out Vector3d)

Transform a Vector by the given Matrix using right-handed notation.

Declaration

public static void TransformColumn(in Matrix3d mat, in Vector3d vec, out Vector3d result)

Parameters

Type	Name	Description
Matrix3d	mat	The desired transformation.
Vector3d	vec	The vector to transform.
Vector3d	result	The transformed vector.

TransformNormal(Vector3d, Matrix4d)

Transform a Normal by the given Matrix.

Declaration

[Pure]
public static Vector3d TransformNormal(Vector3d norm, Matrix4d mat)

Parameters

Type	Name	Description
Vector3d	norm	The normal to transform.
Matrix4d	mat	The desired transformation.

Returns

Type	Description
Vector3d	The transformed normal.

Remarks

This calculates the inverse of the given matrix, use TransformNormalInverse if you already have the inverse to avoid this extra calculation.

TransformNormal(in Vector3d, in Matrix4d, out Vector3d)

Transform a Normal by the given Matrix.

Declaration

public static void TransformNormal(in Vector3d norm, in Matrix4d mat, out Vector3d result)

Parameters

Type	Name	Description
Vector3d	norm	The normal to transform.
Matrix4d	mat	The desired transformation.
Vector3d	result	The transformed normal.

Remarks

This calculates the inverse of the given matrix, use TransformNormalInverse if you already have the inverse to avoid this extra calculation.

TransformNormalInverse(Vector3d, Matrix4d)

Transform a Normal by the (transpose of the) given Matrix.

Declaration

[Pure]
public static Vector3d TransformNormalInverse(Vector3d norm, Matrix4d invMat)

Parameters

Type	Name	Description
Vector3d	norm	The normal to transform.
Matrix4d	invMat	The inverse of the desired transformation.

Returns

Type	Description
Vector3d	The transformed normal.

Remarks

This version doesn't calculate the inverse matrix. Use this version if you already have the inverse of the desired transform to hand.

TransformNormalInverse(in Vector3d, in Matrix4d, out Vector3d)

Transform a Normal by the (transpose of the) given Matrix.

Declaration

public static void TransformNormalInverse(in Vector3d norm, in Matrix4d invMat, out Vector3d result)

Parameters

Type	Name	Description
Vector3d	norm	The normal to transform.
Matrix4d	invMat	The inverse of the desired transformation.
Vector3d	result	The transformed normal.

Remarks

This version doesn't calculate the inverse matrix. Use this version if you already have the inverse of the desired transform to hand.

TransformPerspective(Vector3d, Matrix4d)

Transform a Vector3d by the given Matrix, and project the resulting Vector4 back to a Vector3.

Declaration

[Pure]
public static Vector3d TransformPerspective(Vector3d vec, Matrix4d mat)

Parameters

Type	Name	Description
Vector3d	vec	The vector to transform.
Matrix4d	mat	The desired transformation.

Returns

Type	Description
Vector3d	The transformed vector.

TransformPerspective(in Vector3d, in Matrix4d, out Vector3d)

Transform a Vector3d by the given Matrix, and project the resulting Vector4d back to a Vector3d.

Declaration

public static void TransformPerspective(in Vector3d vec, in Matrix4d mat, out Vector3d result)

Parameters

Type	Name	Description
Vector3d	vec	The vector to transform.
Matrix4d	mat	The desired transformation.
Vector3d	result	The transformed vector.

TransformPosition(Vector3d, Matrix4d)

Transform a Position by the given Matrix.

Declaration

[Pure]
public static Vector3d TransformPosition(Vector3d pos, Matrix4d mat)

Parameters

Type	Name	Description
Vector3d	pos	The position to transform.
Matrix4d	mat	The desired transformation.

Returns

Type	Description
Vector3d	The transformed position.

TransformPosition(in Vector3d, in Matrix4d, out Vector3d)

Transform a Position by the given Matrix.

Declaration

public static void TransformPosition(in Vector3d pos, in Matrix4d mat, out Vector3d result)

Parameters

Type	Name	Description
Vector3d	pos	The position to transform.
Matrix4d	mat	The desired transformation.
Vector3d	result	The transformed position.

TransformRow(Vector3d, Matrix3d)

Transform a Vector by the given Matrix.

Declaration

[Pure]
public static Vector3d TransformRow(Vector3d vec, Matrix3d mat)

Parameters

Type	Name	Description
Vector3d	vec	The vector to transform.
Matrix3d	mat	The desired transformation.

Returns

Type	Description
Vector3d	The transformed vector.

TransformRow(in Vector3d, in Matrix3d, out Vector3d)

Transform a Vector by the given Matrix.

Declaration

public static void TransformRow(in Vector3d vec, in Matrix3d mat, out Vector3d result)

Parameters

Type	Name	Description
Vector3d	vec	The vector to transform.
Matrix3d	mat	The desired transformation.
Vector3d	result	The transformed vector.

TransformVector(Vector3d, Matrix4d)

Transform a direction vector by the given Matrix. Assumes the matrix has a bottom row of (0,0,0,1), that is the translation part is ignored.

Declaration

[Pure]
public static Vector3d TransformVector(Vector3d vec, Matrix4d mat)

Parameters

Type	Name	Description
Vector3d	vec	The vector to transform.
Matrix4d	mat	The desired transformation.

Returns

Type	Description
Vector3d	The transformed vector.

TransformVector(in Vector3d, in Matrix4d, out Vector3d)

Transform a direction vector by the given Matrix. Assumes the matrix has a bottom row of (0,0,0,1), that is the translation part is ignored.

Declaration

public static void TransformVector(in Vector3d vec, in Matrix4d mat, out Vector3d result)

Parameters

Type	Name	Description
Vector3d	vec	The vector to transform.
Matrix4d	mat	The desired transformation.
Vector3d	result	The transformed vector.

Operators

operator +(Vector3d, Vector3d)

Adds two instances.

Declaration

[Pure]
public static Vector3d operator +(Vector3d left, Vector3d right)

Parameters

Type	Name	Description
Vector3d	left	The first instance.
Vector3d	right	The second instance.

Returns

Type	Description
Vector3d	The result of the calculation.

operator /(Vector3d, Vector3d)

Component-wise division between the specified instance by a scale vector.

Declaration

[Pure]
public static Vector3d operator /(Vector3d vec, Vector3d scale)

Parameters

Type	Name	Description
Vector3d	vec	Left operand.
Vector3d	scale	Right operand.

Returns

Type	Description
Vector3d	Result of the division.

operator /(Vector3d, double)

Divides an instance by a scalar.

Declaration

[Pure]
public static Vector3d operator /(Vector3d vec, double scale)

Parameters

Type	Name	Description
Vector3d	vec	The instance.
double	scale	The scalar.

Returns

Type	Description
Vector3d	The result of the calculation.

operator ==(Vector3d, Vector3d)

Compares two instances for equality.

Declaration

public static bool operator ==(Vector3d left, Vector3d right)

Parameters

Type	Name	Description
Vector3d	left	The first instance.
Vector3d	right	The second instance.

Returns

Type	Description
bool	True, if left equals right; false otherwise.

explicit operator Vector3(Vector3d)

Converts OpenTK.Vector3d to OpenTK.Vector3.

Declaration

[Pure]
public static explicit operator Vector3(Vector3d vec)

Parameters

Type	Name	Description
Vector3d	vec	The Vector3d to convert.

Returns

Type	Description
Vector3	The resulting Vector3.

explicit operator Vector3h(Vector3d)

Converts OpenTK.Vector3d to OpenTK.Vector3h.

Declaration

[Pure]
public static explicit operator Vector3h(Vector3d vec)

Parameters

Type	Name	Description
Vector3d	vec	The Vector3d to convert.

Returns

Type	Description
Vector3h	The resulting Vector3h.

explicit operator Vector3i(Vector3d)

Converts OpenTK.Vector3d to OpenTK.Vector3i.

Declaration

[Pure]
public static explicit operator Vector3i(Vector3d vec)

Parameters

Type	Name	Description
Vector3d	vec	The Vector3d to convert.

Returns

Type	Description
Vector3i	The resulting Vector3i.

implicit operator Vector3d((double X, double Y, double Z))

Initializes a new instance of the Vector3d struct using a tuple containing the component values.

Declaration

[Pure]
public static implicit operator Vector3d((double X, double Y, double Z) values)

Parameters

Type	Name	Description
(double X, double Y, double Z)	values	A tuple containing the component values.

Returns

Type	Description
Vector3d	A new instance of the Vector3d struct with the given component values.

operator !=(Vector3d, Vector3d)

Compares two instances for inequality.

Declaration

public static bool operator !=(Vector3d left, Vector3d right)

Parameters

Type	Name	Description
Vector3d	left	The first instance.
Vector3d	right	The second instance.

Returns

Type	Description
bool	True, if left does not equa lright; false otherwise.

operator *(Matrix3d, Vector3d)

Transform a Vector by the given Matrix using right-handed notation.

Declaration

[Pure]
public static Vector3d operator *(Matrix3d mat, Vector3d vec)

Parameters

Type	Name	Description
Matrix3d	mat	The desired transformation.
Vector3d	vec	The vector to transform.

Returns

Type	Description
Vector3d	The transformed vector.

operator *(Quaterniond, Vector3d)

Transforms a vector by a quaternion rotation.

Declaration

[Pure]
public static Vector3d operator *(Quaterniond quat, Vector3d vec)

Parameters

Type	Name	Description
Quaterniond	quat	The quaternion to rotate the vector by.
Vector3d	vec	The vector to transform.

Returns

Type	Description
Vector3d	The transformed vector.

operator *(Vector3d, Matrix3d)

Transform a Vector by the given Matrix.

Declaration

[Pure]
public static Vector3d operator *(Vector3d vec, Matrix3d mat)

Parameters

Type	Name	Description
Vector3d	vec	The vector to transform.
Matrix3d	mat	The desired transformation.

Returns

Type	Description
Vector3d	The transformed vector.

operator *(Vector3d, Vector3d)

Component-wise multiplication between the specified instance by a scale vector.

Declaration

[Pure]
public static Vector3d operator *(Vector3d vec, Vector3d scale)

Parameters

Type	Name	Description
Vector3d	vec	Right operand.
Vector3d	scale	Left operand.

Returns

Type	Description
Vector3d	Result of multiplication.

operator *(Vector3d, double)

Multiplies an instance by a scalar.

Declaration

[Pure]
public static Vector3d operator *(Vector3d vec, double scale)

Parameters

Type	Name	Description
Vector3d	vec	The instance.
double	scale	The scalar.

Returns

Type	Description
Vector3d	The result of the calculation.

operator *(double, Vector3d)

Multiplies an instance by a scalar.

Declaration

[Pure]
public static Vector3d operator *(double scale, Vector3d vec)

Parameters

Type	Name	Description
double	scale	The scalar.
Vector3d	vec	The instance.

Returns

Type	Description
Vector3d	The result of the calculation.

operator -(Vector3d, Vector3d)

Subtracts two instances.

Declaration

[Pure]
public static Vector3d operator -(Vector3d left, Vector3d right)

Parameters

Type	Name	Description
Vector3d	left	The first instance.
Vector3d	right	The second instance.

Returns

Type	Description
Vector3d	The result of the calculation.

operator -(Vector3d)

Negates an instance.

Declaration

[Pure]
public static Vector3d operator -(Vector3d vec)

Parameters

Type	Name	Description
Vector3d	vec	The instance.

Returns

Type	Description
Vector3d	The result of the calculation.

Implements

IEquatable<T>

IFormattable