Struct Vector3

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

Implements

IEquatable<Vector3>

IFormattable

Inherited Members

object.Equals(object, object)

object.GetType()

object.ReferenceEquals(object, object)

Namespace: OpenTK.Mathematics

Assembly: OpenTK.Mathematics.dll

Syntax

[Serializable]
public struct Vector3 : IEquatable<Vector3>, IFormattable

Remarks

The Vector3 structure is suitable for interoperation with unmanaged code requiring three consecutive floats.

Constructors

Vector3(Vector2, float)

Initializes a new instance of the Vector3 struct.

Declaration

public Vector3(Vector2 xy, float z = 0)

Parameters

Type	Name	Description
Vector2	xy	The x and y components of the Vector3.
float	z	The z component of the Vector3.

Vector3(float)

Initializes a new instance of the Vector3 struct.

Declaration

public Vector3(float value)

Parameters

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

Vector3(float, float, float)

Initializes a new instance of the Vector3 struct.

Declaration

public Vector3(float x, float y, float z)

Parameters

Type	Name	Description
float	x	The x component of the Vector3.
float	y	The y component of the Vector3.
float	z	The z component of the Vector3.

Fields

NegativeInfinity

Defines an instance with all components set to negative infinity.

Declaration

public static readonly Vector3 NegativeInfinity

Field Value

Type	Description
Vector3

One

Defines an instance with all components set to 1.

Declaration

public static readonly Vector3 One

Field Value

Type	Description
Vector3

PositiveInfinity

Defines an instance with all components set to positive infinity.

Declaration

public static readonly Vector3 PositiveInfinity

Field Value

Type	Description
Vector3

SizeInBytes

Defines the size of the Vector3 struct in bytes.

Declaration

public static readonly int SizeInBytes

Field Value

Type	Description
int

UnitX

Defines a unit-length Vector3 that points towards the X-axis.

Declaration

public static readonly Vector3 UnitX

Field Value

Type	Description
Vector3

UnitY

Defines a unit-length Vector3 that points towards the Y-axis.

Declaration

public static readonly Vector3 UnitY

Field Value

Type	Description
Vector3

UnitZ

Defines a unit-length Vector3 that points towards the Z-axis.

Declaration

public static readonly Vector3 UnitZ

Field Value

Type	Description
Vector3

X

The X component of the Vector3.

Declaration

public float X

Field Value

Type	Description
float

Y

The Y component of the Vector3.

Declaration

public float Y

Field Value

Type	Description
float

Z

The Z component of the Vector3.

Declaration

public float Z

Field Value

Type	Description
float

Zero

Defines an instance with all components set to 0.

Declaration

public static readonly Vector3 Zero

Field Value

Type	Description
Vector3

Properties

this[int]

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

Declaration

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

Parameters

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

Property Value

Type	Description
float

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 float Length { get; }

Property Value

Type	Description
float

See Also

LengthSquared

LengthFast

Gets an approximation of the vector length (magnitude).

Declaration

public readonly float LengthFast { get; }

Property Value

Type	Description
float

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 float LengthSquared { get; }

Property Value

Type	Description
float

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 float ReciprocalLengthFast { get; }

Property Value

Type	Description
float

Xy

Gets or sets an OpenTK.Vector2 with the X and Y components of this instance.

Declaration

public Vector2 Xy { get; set; }

Property Value

Type	Description
Vector2

Xz

Gets or sets an OpenTK.Vector2 with the X and Z components of this instance.

Declaration

public Vector2 Xz { readonly get; set; }

Property Value

Type	Description
Vector2

Xzy

Gets or sets an OpenTK.Vector3 with the X, Z, and Y components of this instance.

Declaration

public Vector3 Xzy { readonly get; set; }

Property Value

Type	Description
Vector3

Yx

Gets or sets an OpenTK.Vector2 with the Y and X components of this instance.

Declaration

public Vector2 Yx { readonly get; set; }

Property Value

Type	Description
Vector2

Yxz

Gets or sets an OpenTK.Vector3 with the Y, X, and Z components of this instance.

Declaration

public Vector3 Yxz { readonly get; set; }

Property Value

Type	Description
Vector3

Yz

Gets or sets an OpenTK.Vector2 with the Y and Z components of this instance.

Declaration

public Vector2 Yz { readonly get; set; }

Property Value

Type	Description
Vector2

Yzx

Gets or sets an OpenTK.Vector3 with the Y, Z, and X components of this instance.

Declaration

public Vector3 Yzx { readonly get; set; }

Property Value

Type	Description
Vector3

Zx

Gets or sets an OpenTK.Vector2 with the Z and X components of this instance.

Declaration

public Vector2 Zx { readonly get; set; }

Property Value

Type	Description
Vector2

Zxy

Gets or sets an OpenTK.Vector3 with the Z, X, and Y components of this instance.

Declaration

public Vector3 Zxy { readonly get; set; }

Property Value

Type	Description
Vector3

Zy

Gets or sets an OpenTK.Vector2 with the Z and Y components of this instance.

Declaration

public Vector2 Zy { readonly get; set; }

Property Value

Type	Description
Vector2

Zyx

Gets or sets an OpenTK.Vector3 with the Z, Y, and X components of this instance.

Declaration

public Vector3 Zyx { readonly get; set; }

Property Value

Type	Description
Vector3

Methods

Abs()

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

Declaration

public readonly Vector3 Abs()

Returns

Type	Description
Vector3	The component-wise absolute value vector.

Abs(Vector3)

Take the component-wise absolute value of a vector.

Declaration

public static Vector3 Abs(Vector3 vec)

Parameters

Type	Name	Description
Vector3	vec	The vector to apply component-wise absolute value to.

Returns

Type	Description
Vector3	The component-wise absolute value vector.

Abs(in Vector3, out Vector3)

Take the component-wise absolute value of a vector.

Declaration

public static void Abs(in Vector3 vec, out Vector3 result)

Parameters

Type	Name	Description
Vector3	vec	The vector to apply component-wise absolute value to.
Vector3	result	The component-wise absolute value vector.

Add(Vector3, Vector3)

Adds two vectors.

Declaration

[Pure]
public static Vector3 Add(Vector3 a, Vector3 b)

Parameters

Type	Name	Description
Vector3	a	Left operand.
Vector3	b	Right operand.

Returns

Type	Description
Vector3	Result of operation.

Add(in Vector3, in Vector3, out Vector3)

Adds two vectors.

Declaration

public static void Add(in Vector3 a, in Vector3 b, out Vector3 result)

Parameters

Type	Name	Description
Vector3	a	Left operand.
Vector3	b	Right operand.
Vector3	result	Result of operation.

BaryCentric(Vector3, Vector3, Vector3, float, float)

Interpolate 3 Vectors using Barycentric coordinates.

Declaration

[Pure]
public static Vector3 BaryCentric(Vector3 a, Vector3 b, Vector3 c, float u, float v)

Parameters

Type	Name	Description
Vector3	a	First input Vector.
Vector3	b	Second input Vector.
Vector3	c	Third input Vector.
float	u	First Barycentric Coordinate.
float	v	Second Barycentric Coordinate.

Returns

Type	Description
Vector3	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 Vector3, in Vector3, in Vector3, float, float, out Vector3)

Interpolate 3 Vectors using Barycentric coordinates.

Declaration

[Pure]
public static void BaryCentric(in Vector3 a, in Vector3 b, in Vector3 c, float u, float v, out Vector3 result)

Parameters

Type	Name	Description
Vector3	a	First input Vector.
Vector3	b	Second input Vector.
Vector3	c	Third input Vector.
float	u	First Barycentric Coordinate.
float	v	Second Barycentric Coordinate.
Vector3	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(Vector3, Vector3)

Calculates the angle (in radians) between two vectors.

Declaration

[Pure]
public static float CalculateAngle(Vector3 first, Vector3 second)

Parameters

Type	Name	Description
Vector3	first	The first vector.
Vector3	second	The second vector.

Returns

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

Remarks

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

CalculateAngle(in Vector3, in Vector3, out float)

Calculates the angle (in radians) between two vectors.

Declaration

public static void CalculateAngle(in Vector3 first, in Vector3 second, out float result)

Parameters

Type	Name	Description
Vector3	first	The first vector.
Vector3	second	The second vector.
float	result	Angle (in radians) between the vectors.

Remarks

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

Clamp(Vector3, Vector3, Vector3)

Clamp a vector to the given minimum and maximum vectors.

Declaration

[Pure]
public static Vector3 Clamp(Vector3 vec, Vector3 min, Vector3 max)

Parameters

Type	Name	Description
Vector3	vec	Input vector.
Vector3	min	Minimum vector.
Vector3	max	Maximum vector.

Returns

Type	Description
Vector3	The clamped vector.

Clamp(in Vector3, in Vector3, in Vector3, out Vector3)

Clamp a vector to the given minimum and maximum vectors.

Declaration

public static void Clamp(in Vector3 vec, in Vector3 min, in Vector3 max, out Vector3 result)

Parameters

Type	Name	Description
Vector3	vec	Input vector.
Vector3	min	Minimum vector.
Vector3	max	Maximum vector.
Vector3	result	The clamped vector.

ComponentMax(Vector3, Vector3)

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

Declaration

[Pure]
public static Vector3 ComponentMax(Vector3 a, Vector3 b)

Parameters

Type	Name	Description
Vector3	a	First operand.
Vector3	b	Second operand.

Returns

Type	Description
Vector3	The component-wise maximum.

ComponentMax(in Vector3, in Vector3, out Vector3)

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

Declaration

public static void ComponentMax(in Vector3 a, in Vector3 b, out Vector3 result)

Parameters

Type	Name	Description
Vector3	a	First operand.
Vector3	b	Second operand.
Vector3	result	The component-wise maximum.

ComponentMin(Vector3, Vector3)

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

Declaration

[Pure]
public static Vector3 ComponentMin(Vector3 a, Vector3 b)

Parameters

Type	Name	Description
Vector3	a	First operand.
Vector3	b	Second operand.

Returns

Type	Description
Vector3	The component-wise minimum.

ComponentMin(in Vector3, in Vector3, out Vector3)

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

Declaration

public static void ComponentMin(in Vector3 a, in Vector3 b, out Vector3 result)

Parameters

Type	Name	Description
Vector3	a	First operand.
Vector3	b	Second operand.
Vector3	result	The component-wise minimum.

Cross(Vector3, Vector3)

Caclulate the cross (vector) product of two vectors.

Declaration

[Pure]
public static Vector3 Cross(Vector3 left, Vector3 right)

Parameters

Type	Name	Description
Vector3	left	First operand.
Vector3	right	Second operand.

Returns

Type	Description
Vector3	The cross product of the two inputs.

Cross(in Vector3, in Vector3, out Vector3)

Caclulate the cross (vector) product of two vectors.

Declaration

public static void Cross(in Vector3 left, in Vector3 right, out Vector3 result)

Parameters

Type	Name	Description
Vector3	left	First operand.
Vector3	right	Second operand.
Vector3	result	The cross product of the two inputs.

Deconstruct(out float, out float, out float)

Deconstructs the vector into it's individual components.

Declaration

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

Parameters

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

Distance(Vector3, Vector3)

Compute the euclidean distance between two vectors.

Declaration

[Pure]
public static float Distance(Vector3 vec1, Vector3 vec2)

Parameters

Type	Name	Description
Vector3	vec1	The first vector.
Vector3	vec2	The second vector.

Returns

Type	Description
float	The distance.

Distance(in Vector3, in Vector3, out float)

Compute the euclidean distance between two vectors.

Declaration

public static void Distance(in Vector3 vec1, in Vector3 vec2, out float result)

Parameters

Type	Name	Description
Vector3	vec1	The first vector.
Vector3	vec2	The second vector.
float	result	The distance.

DistanceSquared(Vector3, Vector3)

Compute the squared euclidean distance between two vectors.

Declaration

[Pure]
public static float DistanceSquared(Vector3 vec1, Vector3 vec2)

Parameters

Type	Name	Description
Vector3	vec1	The first vector.
Vector3	vec2	The second vector.

Returns

Type	Description
float	The squared distance.

DistanceSquared(in Vector3, in Vector3, out float)

Compute the squared euclidean distance between two vectors.

Declaration

public static void DistanceSquared(in Vector3 vec1, in Vector3 vec2, out float result)

Parameters

Type	Name	Description
Vector3	vec1	The first vector.
Vector3	vec2	The second vector.
float	result	The squared distance.

Divide(Vector3, Vector3)

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

Declaration

[Pure]
public static Vector3 Divide(Vector3 vector, Vector3 scale)

Parameters

Type	Name	Description
Vector3	vector	Left operand.
Vector3	scale	Right operand.

Returns

Type	Description
Vector3	Result of the operation.

Divide(Vector3, float)

Divides a vector by a scalar.

Declaration

[Pure]
public static Vector3 Divide(Vector3 vector, float scale)

Parameters

Type	Name	Description
Vector3	vector	Left operand.
float	scale	Right operand.

Returns

Type	Description
Vector3	Result of the operation.

Divide(in Vector3, in Vector3, out Vector3)

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

Declaration

public static void Divide(in Vector3 vector, in Vector3 scale, out Vector3 result)

Parameters

Type	Name	Description
Vector3	vector	Left operand.
Vector3	scale	Right operand.
Vector3	result	Result of the operation.

Divide(in Vector3, float, out Vector3)

Divides a vector by a scalar.

Declaration

public static void Divide(in Vector3 vector, float scale, out Vector3 result)

Parameters

Type	Name	Description
Vector3	vector	Left operand.
float	scale	Right operand.
Vector3	result	Result of the operation.

Dot(Vector3, Vector3)

Calculate the dot (scalar) product of two vectors.

Declaration

[Pure]
public static float Dot(Vector3 left, Vector3 right)

Parameters

Type	Name	Description
Vector3	left	First operand.
Vector3	right	Second operand.

Returns

Type	Description
float	The dot product of the two inputs.

Dot(in Vector3, in Vector3, out float)

Calculate the dot (scalar) product of two vectors.

Declaration

public static void Dot(in Vector3 left, in Vector3 right, out float result)

Parameters

Type	Name	Description
Vector3	left	First operand.
Vector3	right	Second operand.
float	result	The dot product of the two inputs.

Elerp(Vector3, Vector3, float)

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

Declaration

public static Vector3 Elerp(Vector3 a, Vector3 b, float t)

Parameters

Type	Name	Description
Vector3	a	The starting value. Must be non-negative.
Vector3	b	The end value. Must be non-negative.
float	t	The blend factor.

Returns

Type	Description
Vector3	The exponential interpolation between a and b.

See Also

Elerp(float, float, float)

Elerp(in Vector3, in Vector3, float, out Vector3)

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 Vector3 a, in Vector3 b, float t, out Vector3 result)

Parameters

Type	Name	Description
Vector3	a	The starting value. Must be non-negative.
Vector3	b	The end value. Must be non-negative.
float	t	The blend factor.
Vector3	result	The exponential interpolation between a and b.

See Also

Elerp(float, float, float)

Equals(Vector3)

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

Declaration

public readonly bool Equals(Vector3 other)

Parameters

Type	Name	Description
Vector3	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 readonly 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(Vector3, Vector3, Vector3)

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

Declaration

[Pure]
public static Vector3 Lerp(Vector3 a, Vector3 b, Vector3 blend)

Parameters

Type	Name	Description
Vector3	a	First input vector.
Vector3	b	Second input vector.
Vector3	blend	The blend factor.

Returns

Type	Description
Vector3	a when blend=0, b when blend=1, and a component-wise linear combination otherwise.

Lerp(Vector3, Vector3, float)

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

Declaration

[Pure]
public static Vector3 Lerp(Vector3 a, Vector3 b, float blend)

Parameters

Type	Name	Description
Vector3	a	First input vector.
Vector3	b	Second input vector.
float	blend	The blend factor.

Returns

Type	Description
Vector3	a when blend=0, b when blend=1, and a linear combination otherwise.

Lerp(in Vector3, in Vector3, Vector3, out Vector3)

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

Declaration

public static void Lerp(in Vector3 a, in Vector3 b, Vector3 blend, out Vector3 result)

Parameters

Type	Name	Description
Vector3	a	First input vector.
Vector3	b	Second input vector.
Vector3	blend	The blend factor.
Vector3	result	a when blend=0, b when blend=1, and a component-wise linear combination otherwise.

Lerp(in Vector3, in Vector3, float, out Vector3)

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

Declaration

public static void Lerp(in Vector3 a, in Vector3 b, float blend, out Vector3 result)

Parameters

Type	Name	Description
Vector3	a	First input vector.
Vector3	b	Second input vector.
float	blend	The blend factor.
Vector3	result	a when blend=0, b when blend=1, and a linear combination otherwise.

MagnitudeMax(Vector3, Vector3)

Returns the Vector3 with the maximum magnitude. If the magnitudes are equal, the first vector is selected.

Declaration

[Pure]
public static Vector3 MagnitudeMax(Vector3 left, Vector3 right)

Parameters

Type	Name	Description
Vector3	left	Left operand.
Vector3	right	Right operand.

Returns

Type	Description
Vector3	The maximum Vector3.

MagnitudeMax(in Vector3, in Vector3, out Vector3)

Returns the Vector3 with the maximum magnitude. If the magnitudes are equal, the first vector is selected.

Declaration

public static void MagnitudeMax(in Vector3 left, in Vector3 right, out Vector3 result)

Parameters

Type	Name	Description
Vector3	left	Left operand.
Vector3	right	Right operand.
Vector3	result	The magnitude-wise maximum.

MagnitudeMin(Vector3, Vector3)

Returns the Vector3 with the minimum magnitude. If the magnitudes are equal, the second vector is selected.

Declaration

[Pure]
public static Vector3 MagnitudeMin(Vector3 left, Vector3 right)

Parameters

Type	Name	Description
Vector3	left	Left operand.
Vector3	right	Right operand.

Returns

Type	Description
Vector3	The minimum Vector3.

MagnitudeMin(in Vector3, in Vector3, out Vector3)

Returns the Vector3 with the minimum magnitude. If the magnitudes are equal, the second vector is selected.

Declaration

public static void MagnitudeMin(in Vector3 left, in Vector3 right, out Vector3 result)

Parameters

Type	Name	Description
Vector3	left	Left operand.
Vector3	right	Right operand.
Vector3	result	The magnitude-wise minimum.

Multiply(Vector3, Vector3)

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

Declaration

[Pure]
public static Vector3 Multiply(Vector3 vector, Vector3 scale)

Parameters

Type	Name	Description
Vector3	vector	Left operand.
Vector3	scale	Right operand.

Returns

Type	Description
Vector3	Result of the operation.

Multiply(Vector3, float)

Multiplies a vector by a scalar.

Declaration

[Pure]
public static Vector3 Multiply(Vector3 vector, float scale)

Parameters

Type	Name	Description
Vector3	vector	Left operand.
float	scale	Right operand.

Returns

Type	Description
Vector3	Result of the operation.

Multiply(in Vector3, in Vector3, out Vector3)

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

Declaration

public static void Multiply(in Vector3 vector, in Vector3 scale, out Vector3 result)

Parameters

Type	Name	Description
Vector3	vector	Left operand.
Vector3	scale	Right operand.
Vector3	result	Result of the operation.

Multiply(in Vector3, float, out Vector3)

Multiplies a vector by a scalar.

Declaration

public static void Multiply(in Vector3 vector, float scale, out Vector3 result)

Parameters

Type	Name	Description
Vector3	vector	Left operand.
float	scale	Right operand.
Vector3	result	Result of the operation.

Normalize()

Scales the Vector3 to unit length.

Declaration

public void Normalize()

Normalize(Vector3)

Scale a vector to unit length.

Declaration

[Pure]
public static Vector3 Normalize(Vector3 vec)

Parameters

Type	Name	Description
Vector3	vec	The input vector.

Returns

Type	Description
Vector3	The normalized copy.

Normalize(in Vector3, out Vector3)

Scale a vector to unit length.

Declaration

public static void Normalize(in Vector3 vec, out Vector3 result)

Parameters

Type	Name	Description
Vector3	vec	The input vector.
Vector3	result	The normalized vector.

NormalizeFast()

Scales the Vector3 to approximately unit length.

Declaration

public void NormalizeFast()

NormalizeFast(Vector3)

Scale a vector to approximately unit length.

Declaration

[Pure]
public static Vector3 NormalizeFast(Vector3 vec)

Parameters

Type	Name	Description
Vector3	vec	The input vector.

Returns

Type	Description
Vector3	The normalized copy.

NormalizeFast(in Vector3, out Vector3)

Scale a vector to approximately unit length.

Declaration

public static void NormalizeFast(in Vector3 vec, out Vector3 result)

Parameters

Type	Name	Description
Vector3	vec	The input vector.
Vector3	result	The normalized vector.

Normalized()

Returns a copy of the Vector3 scaled to unit length.

Declaration

public readonly Vector3 Normalized()

Returns

Type	Description
Vector3	The normalized copy.

Project(Vector3, float, float, float, float, float, float, Matrix4)

Projects a vector from object space into screen space.

Declaration

[Pure]
public static Vector3 Project(Vector3 vector, float x, float y, float width, float height, float minZ, float maxZ, Matrix4 worldViewProjection)

Parameters

Type	Name	Description
Vector3	vector	The vector to project.
float	x	The X coordinate of the viewport.
float	y	The Y coordinate of the viewport.
float	width	The width of the viewport.
float	height	The height of the viewport.
float	minZ	The minimum depth of the viewport.
float	maxZ	The maximum depth of the viewport.
Matrix4	worldViewProjection	The world-view-projection matrix.

Returns

Type	Description
Vector3	The vector in screen space.

Remarks

To project to normalized device coordinates (NDC) use the following parameters: Project(vector, -1, -1, 2, 2, -1, 1, worldViewProjection).

Slerp(Vector3, Vector3, float)

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 Vector3 Slerp(Vector3 a, Vector3 b, float t)

Parameters

Type	Name	Description
Vector3	a	Unit vector start point.
Vector3	b	Unit vector end point.
float	t	The blend factor.

Returns

Type	Description
Vector3	a when t=0, b when t=1, and a spherical interpolation between the vectors otherwise.

Slerp(in Vector3, in Vector3, float, out Vector3)

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 Vector3 a, in Vector3 b, float t, out Vector3 result)

Parameters

Type	Name	Description
Vector3	a	Unit vector start point.
Vector3	b	Unit vector end point.
float	t	The blend factor.
Vector3	result	Is a when t=0, b when t=1, and a spherical interpolation between the vectors otherwise.

Subtract(Vector3, Vector3)

Subtract one Vector from another.

Declaration

[Pure]
public static Vector3 Subtract(Vector3 a, Vector3 b)

Parameters

Type	Name	Description
Vector3	a	First operand.
Vector3	b	Second operand.

Returns

Type	Description
Vector3	Result of subtraction.

Subtract(in Vector3, in Vector3, out Vector3)

Subtract one Vector from another.

Declaration

public static void Subtract(in Vector3 a, in Vector3 b, out Vector3 result)

Parameters

Type	Name	Description
Vector3	a	First operand.
Vector3	b	Second operand.
Vector3	result	Result of subtraction.

ToString()

Returns the fully qualified type name of this instance.

Declaration

public override readonly 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 readonly 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 readonly 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(Vector3, Quaternion)

Transforms a vector by a quaternion rotation.

Declaration

[Pure]
public static Vector3 Transform(Vector3 vec, Quaternion quat)

Parameters

Type	Name	Description
Vector3	vec	The vector to transform.
Quaternion	quat	The quaternion to rotate the vector by.

Returns

Type	Description
Vector3	The result of the operation.

Transform(in Vector3, in Quaternion, out Vector3)

Transforms a vector by a quaternion rotation.

Declaration

public static void Transform(in Vector3 vec, in Quaternion quat, out Vector3 result)

Parameters

Type	Name	Description
Vector3	vec	The vector to transform.
Quaternion	quat	The quaternion to rotate the vector by.
Vector3	result	The result of the operation.

TransformColumn(Matrix3, Vector3)

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

Declaration

[Pure]
public static Vector3 TransformColumn(Matrix3 mat, Vector3 vec)

Parameters

Type	Name	Description
Matrix3	mat	The desired transformation.
Vector3	vec	The vector to transform.

Returns

Type	Description
Vector3	The transformed vector.

TransformColumn(in Matrix3, in Vector3, out Vector3)

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

Declaration

public static void TransformColumn(in Matrix3 mat, in Vector3 vec, out Vector3 result)

Parameters

Type	Name	Description
Matrix3	mat	The desired transformation.
Vector3	vec	The vector to transform.
Vector3	result	The transformed vector.

TransformNormal(Vector3, Matrix4)

Transform a Normal by the given Matrix.

Declaration

[Pure]
public static Vector3 TransformNormal(Vector3 norm, Matrix4 mat)

Parameters

Type	Name	Description
Vector3	norm	The normal to transform.
Matrix4	mat	The desired transformation.

Returns

Type	Description
Vector3	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 Vector3, in Matrix4, out Vector3)

Transform a Normal by the given Matrix.

Declaration

public static void TransformNormal(in Vector3 norm, in Matrix4 mat, out Vector3 result)

Parameters

Type	Name	Description
Vector3	norm	The normal to transform.
Matrix4	mat	The desired transformation.
Vector3	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(Vector3, Matrix4)

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

Declaration

[Pure]
public static Vector3 TransformNormalInverse(Vector3 norm, Matrix4 invMat)

Parameters

Type	Name	Description
Vector3	norm	The normal to transform.
Matrix4	invMat	The inverse of the desired transformation.

Returns

Type	Description
Vector3	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 Vector3, in Matrix4, out Vector3)

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

Declaration

public static void TransformNormalInverse(in Vector3 norm, in Matrix4 invMat, out Vector3 result)

Parameters

Type	Name	Description
Vector3	norm	The normal to transform.
Matrix4	invMat	The inverse of the desired transformation.
Vector3	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(Vector3, Matrix4)

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

Declaration

[Pure]
public static Vector3 TransformPerspective(Vector3 vec, Matrix4 mat)

Parameters

Type	Name	Description
Vector3	vec	The vector to transform.
Matrix4	mat	The desired transformation.

Returns

Type	Description
Vector3	The transformed vector.

TransformPerspective(in Vector3, in Matrix4, out Vector3)

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

Declaration

public static void TransformPerspective(in Vector3 vec, in Matrix4 mat, out Vector3 result)

Parameters

Type	Name	Description
Vector3	vec	The vector to transform.
Matrix4	mat	The desired transformation.
Vector3	result	The transformed vector.

TransformPosition(Vector3, Matrix4)

Transform a Position by the given Matrix.

Declaration

[Pure]
public static Vector3 TransformPosition(Vector3 pos, Matrix4 mat)

Parameters

Type	Name	Description
Vector3	pos	The position to transform.
Matrix4	mat	The desired transformation.

Returns

Type	Description
Vector3	The transformed position.

TransformPosition(in Vector3, in Matrix4, out Vector3)

Transform a Position by the given Matrix.

Declaration

public static void TransformPosition(in Vector3 pos, in Matrix4 mat, out Vector3 result)

Parameters

Type	Name	Description
Vector3	pos	The position to transform.
Matrix4	mat	The desired transformation.
Vector3	result	The transformed position.

TransformRow(Vector3, Matrix3)

Transform a Vector by the given Matrix.

Declaration

[Pure]
public static Vector3 TransformRow(Vector3 vec, Matrix3 mat)

Parameters

Type	Name	Description
Vector3	vec	The vector to transform.
Matrix3	mat	The desired transformation.

Returns

Type	Description
Vector3	The transformed vector.

TransformRow(in Vector3, in Matrix3, out Vector3)

Transform a Vector by the given Matrix.

Declaration

public static void TransformRow(in Vector3 vec, in Matrix3 mat, out Vector3 result)

Parameters

Type	Name	Description
Vector3	vec	The vector to transform.
Matrix3	mat	The desired transformation.
Vector3	result	The transformed vector.

TransformVector(Vector3, Matrix4)

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 Vector3 TransformVector(Vector3 vec, Matrix4 mat)

Parameters

Type	Name	Description
Vector3	vec	The vector to transform.
Matrix4	mat	The desired transformation.

Returns

Type	Description
Vector3	The transformed vector.

TransformVector(in Vector3, in Matrix4, out Vector3)

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 Vector3 vec, in Matrix4 mat, out Vector3 result)

Parameters

Type	Name	Description
Vector3	vec	The vector to transform.
Matrix4	mat	The desired transformation.
Vector3	result	The transformed vector.

Unproject(Vector3, float, float, float, float, float, float, Matrix4)

Projects a vector from screen space into object space.

Declaration

[Pure]
public static Vector3 Unproject(Vector3 vector, float x, float y, float width, float height, float minZ, float maxZ, Matrix4 inverseWorldViewProjection)

Parameters

Type	Name	Description
Vector3	vector	The vector to project.
float	x	The X coordinate of the viewport.
float	y	The Y coordinate of the viewport.
float	width	The width of the viewport.
float	height	The height of the viewport.
float	minZ	The minimum depth of the viewport.
float	maxZ	The maximum depth of the viewport.
Matrix4	inverseWorldViewProjection	The inverse of the world-view-projection matrix.

Returns

Type	Description
Vector3	The vector in object space.

Remarks

To project from normalized device coordinates (NDC) use the following parameters: Project(vector, -1, -1, 2, 2, -1, 1, inverseWorldViewProjection).

Operators

operator +(Vector3, Vector3)

Adds two instances.

Declaration

[Pure]
public static Vector3 operator +(Vector3 left, Vector3 right)

Parameters

Type	Name	Description
Vector3	left	The first instance.
Vector3	right	The second instance.

Returns

Type	Description
Vector3	The result of the calculation.

operator /(Vector3, Vector3)

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

Declaration

[Pure]
public static Vector3 operator /(Vector3 vec, Vector3 scale)

Parameters

Type	Name	Description
Vector3	vec	Left operand.
Vector3	scale	Right operand.

Returns

Type	Description
Vector3	Result of the division.

operator /(Vector3, float)

Divides an instance by a scalar.

Declaration

[Pure]
public static Vector3 operator /(Vector3 vec, float scale)

Parameters

Type	Name	Description
Vector3	vec	The instance.
float	scale	The scalar.

Returns

Type	Description
Vector3	The result of the calculation.

operator ==(Vector3, Vector3)

Compares two instances for equality.

Declaration

public static bool operator ==(Vector3 left, Vector3 right)

Parameters

Type	Name	Description
Vector3	left	The first instance.
Vector3	right	The second instance.

Returns

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

explicit operator Vector3h(Vector3)

Converts OpenTK.Vector3 to OpenTK.Vector3h.

Declaration

[Pure]
public static explicit operator Vector3h(Vector3 vec)

Parameters

Type	Name	Description
Vector3	vec	The Vector3 to convert.

Returns

Type	Description
Vector3h	The resulting Vector3h.

explicit operator Vector3i(Vector3)

Converts OpenTK.Vector3 to OpenTK.Vector3i.

Declaration

[Pure]
public static explicit operator Vector3i(Vector3 vec)

Parameters

Type	Name	Description
Vector3	vec	The Vector3 to convert.

Returns

Type	Description
Vector3i	The resulting Vector3i.

implicit operator Vector3d(Vector3)

Converts OpenTK.Vector3 to OpenTK.Vector3d.

Declaration

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

Parameters

Type	Name	Description
Vector3	vec	The Vector3 to convert.

Returns

Type	Description
Vector3d	The resulting Vector3d.

implicit operator Vector3((float X, float Y, float Z))

Initializes a new instance of the Vector3 struct using a tuple containing the component values.

Declaration

[Pure]
public static implicit operator Vector3((float X, float Y, float Z) values)

Parameters

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

Returns

Type	Description
Vector3	A new instance of the Vector3 struct with the given component values.

operator !=(Vector3, Vector3)

Compares two instances for inequality.

Declaration

public static bool operator !=(Vector3 left, Vector3 right)

Parameters

Type	Name	Description
Vector3	left	The first instance.
Vector3	right	The second instance.

Returns

Type	Description
bool	True, if left does not equal right; false otherwise.

operator *(Matrix3, Vector3)

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

Declaration

[Pure]
public static Vector3 operator *(Matrix3 mat, Vector3 vec)

Parameters

Type	Name	Description
Matrix3	mat	The desired transformation.
Vector3	vec	The vector to transform.

Returns

Type	Description
Vector3	The transformed vector.

operator *(Quaternion, Vector3)

Transforms a vector by a quaternion rotation.

Declaration

[Pure]
public static Vector3 operator *(Quaternion quat, Vector3 vec)

Parameters

Type	Name	Description
Quaternion	quat	The quaternion to rotate the vector by.
Vector3	vec	The vector to transform.

Returns

Type	Description
Vector3	The multiplied vector.

operator *(Vector3, Matrix3)

Transform a Vector by the given Matrix.

Declaration

[Pure]
public static Vector3 operator *(Vector3 vec, Matrix3 mat)

Parameters

Type	Name	Description
Vector3	vec	The vector to transform.
Matrix3	mat	The desired transformation.

Returns

Type	Description
Vector3	The transformed vector.

operator *(Vector3, Vector3)

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

Declaration

[Pure]
public static Vector3 operator *(Vector3 vec, Vector3 scale)

Parameters

Type	Name	Description
Vector3	vec	Right operand.
Vector3	scale	Left operand.

Returns

Type	Description
Vector3	Result of multiplication.

operator *(Vector3, float)

Multiplies an instance by a scalar.

Declaration

[Pure]
public static Vector3 operator *(Vector3 vec, float scale)

Parameters

Type	Name	Description
Vector3	vec	The instance.
float	scale	The scalar.

Returns

Type	Description
Vector3	The result of the calculation.

operator *(float, Vector3)

Multiplies an instance by a scalar.

Declaration

[Pure]
public static Vector3 operator *(float scale, Vector3 vec)

Parameters

Type	Name	Description
float	scale	The scalar.
Vector3	vec	The instance.

Returns

Type	Description
Vector3	The result of the calculation.

operator -(Vector3, Vector3)

Subtracts two instances.

Declaration

[Pure]
public static Vector3 operator -(Vector3 left, Vector3 right)

Parameters

Type	Name	Description
Vector3	left	The first instance.
Vector3	right	The second instance.

Returns

Type	Description
Vector3	The result of the calculation.

operator -(Vector3)

Negates an instance.

Declaration

[Pure]
public static Vector3 operator -(Vector3 vec)

Parameters

Type	Name	Description
Vector3	vec	The instance.

Returns

Type	Description
Vector3	The result of the calculation.

Implements

IEquatable<T>

IFormattable