Struct Vector3

Namespace

Stride.Core.Mathematics

Assembly

Stride.Core.Mathematics.dll

Represents a three dimensional mathematical vector.

[DataContract("float3")]
[DataStyle(DataStyle.Compact)]
public struct Vector3 : IEquatable<Vector3>, IFormattable

Implements

IEquatable<Vector3>

IFormattable

Extension Methods

VectorExtensions.XY(Vector3)

VectorExtensions.XZ(Vector3)

VectorExtensions.YZ(Vector3)

Constructors

Vector3(Vector2, float)

Initializes a new instance of the Vector3 struct.

public Vector3(Vector2 value, float z)

Parameters

value Vector2

A vector containing the values with which to initialize the X and Y components.

z float

Initial value for the Z component of the vector.

Vector3(float)

Initializes a new instance of the Vector3 struct.

public Vector3(float value)

Parameters

value float

The value that will be assigned to all components.

Vector3(float, float, float)

Initializes a new instance of the Vector3 struct.

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

Parameters

x float

Initial value for the X component of the vector.

y float

Initial value for the Y component of the vector.

z float

Initial value for the Z component of the vector.

Vector3(float[])

Initializes a new instance of the Vector3 struct.

public Vector3(float[] values)

Parameters

values float[]

The values to assign to the X, Y, and Z components of the vector. This must be an array with three elements.

Exceptions

ArgumentNullException

Thrown when values is null.

ArgumentOutOfRangeException

Thrown when values contains more or less than three elements.

Fields

One

A Vector3 with all of its components set to one.

public static readonly Vector3 One

Field Value

Vector3

SizeInBytes

The size of the Vector3 type, in bytes.

public static readonly int SizeInBytes

Field Value

int

UnitX

The X unit Vector3 (1, 0, 0).

public static readonly Vector3 UnitX

Field Value

Vector3

UnitY

The Y unit Vector3 (0, 1, 0).

public static readonly Vector3 UnitY

Field Value

Vector3

UnitZ

The Z unit Vector3 (0, 0, 1).

public static readonly Vector3 UnitZ

Field Value

Vector3

X

The X component of the vector.

[DataMember(0)]
public float X

Field Value

float

Y

The Y component of the vector.

[DataMember(1)]
public float Y

Field Value

float

Z

The Z component of the vector.

[DataMember(2)]
public float Z

Field Value

float

Zero

A Vector3 with all of its components set to zero.

public static readonly Vector3 Zero

Field Value

Vector3

Properties

IsNormalized

Gets a value indicting whether this instance is normalized.

public readonly bool IsNormalized { get; }

Property Value

bool

this[int]

Gets or sets the component at the specified index.

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

Parameters

index int

The index of the component to access. Use 0 for the X component, 1 for the Y component, and 2 for the Z component.

Property Value

float

The value of the X, Y, or Z component, depending on the index.

Exceptions

ArgumentOutOfRangeException

Thrown when the index is out of the range [0, 2].

Methods

Add(Vector3, Vector3)

Adds two vectors.

public static Vector3 Add(Vector3 left, Vector3 right)

Parameters

left Vector3

The first vector to add.

right Vector3

The second vector to add.

Returns

Vector3

The sum of the two vectors.

Add(ref readonly Vector3, ref readonly Vector3, out Vector3)

Adds two vectors.

public static void Add(ref readonly Vector3 left, ref readonly Vector3 right, out Vector3 result)

Parameters

left Vector3

The first vector to add.

right Vector3

The second vector to add.

result Vector3

When the method completes, contains the sum of the two vectors.

Barycentric(Vector3, Vector3, Vector3, float, float)

Returns a Vector3 containing the 3D Cartesian coordinates of a point specified in Barycentric coordinates relative to a 3D triangle.

public static Vector3 Barycentric(Vector3 value1, Vector3 value2, Vector3 value3, float amount1, float amount2)

Parameters

value1 Vector3

A Vector3 containing the 3D Cartesian coordinates of vertex 1 of the triangle.

value2 Vector3

A Vector3 containing the 3D Cartesian coordinates of vertex 2 of the triangle.

value3 Vector3

A Vector3 containing the 3D Cartesian coordinates of vertex 3 of the triangle.

amount1 float

Barycentric coordinate b2, which expresses the weighting factor toward vertex 2 (specified in value2).

amount2 float

Barycentric coordinate b3, which expresses the weighting factor toward vertex 3 (specified in value3).

Returns

Vector3

A new Vector3 containing the 3D Cartesian coordinates of the specified point.

Barycentric(ref readonly Vector3, ref readonly Vector3, ref readonly Vector3, float, float, out Vector3)

Returns a Vector3 containing the 3D Cartesian coordinates of a point specified in Barycentric coordinates relative to a 3D triangle.

public static void Barycentric(ref readonly Vector3 value1, ref readonly Vector3 value2, ref readonly Vector3 value3, float amount1, float amount2, out Vector3 result)

Parameters

value1 Vector3

A Vector3 containing the 3D Cartesian coordinates of vertex 1 of the triangle.

value2 Vector3

A Vector3 containing the 3D Cartesian coordinates of vertex 2 of the triangle.

value3 Vector3

A Vector3 containing the 3D Cartesian coordinates of vertex 3 of the triangle.

amount1 float

Barycentric coordinate b2, which expresses the weighting factor toward vertex 2 (specified in value2).

amount2 float

Barycentric coordinate b3, which expresses the weighting factor toward vertex 3 (specified in value3).

result Vector3

When the method completes, contains the 3D Cartesian coordinates of the specified point.

CatmullRom(Vector3, Vector3, Vector3, Vector3, float)

Performs a Catmull-Rom interpolation using the specified positions.

public static Vector3 CatmullRom(Vector3 value1, Vector3 value2, Vector3 value3, Vector3 value4, float amount)

Parameters

value1 Vector3

The first position in the interpolation.

value2 Vector3

The second position in the interpolation.

value3 Vector3

The third position in the interpolation.

value4 Vector3

The fourth position in the interpolation.

amount float

Weighting factor.

Returns

Vector3

A vector that is the result of the Catmull-Rom interpolation.

CatmullRom(ref readonly Vector3, ref readonly Vector3, ref readonly Vector3, ref readonly Vector3, float, out Vector3)

Performs a Catmull-Rom interpolation using the specified positions.

public static void CatmullRom(ref readonly Vector3 value1, ref readonly Vector3 value2, ref readonly Vector3 value3, ref readonly Vector3 value4, float amount, out Vector3 result)

Parameters

value1 Vector3

The first position in the interpolation.

value2 Vector3

The second position in the interpolation.

value3 Vector3

The third position in the interpolation.

value4 Vector3

The fourth position in the interpolation.

amount float

Weighting factor.

result Vector3

When the method completes, contains the result of the Catmull-Rom interpolation.

Clamp(Vector3, Vector3, Vector3)

Restricts a value to be within a specified range.

public static Vector3 Clamp(Vector3 value, Vector3 min, Vector3 max)

Parameters

value Vector3

The value to clamp.

min Vector3

The minimum value.

max Vector3

The maximum value.

Returns

Vector3

The clamped value.

Clamp(ref readonly Vector3, ref readonly Vector3, ref readonly Vector3, out Vector3)

Restricts a value to be within a specified range.

public static void Clamp(ref readonly Vector3 value, ref readonly Vector3 min, ref readonly Vector3 max, out Vector3 result)

Parameters

value Vector3

The value to clamp.

min Vector3

The minimum value.

max Vector3

The maximum value.

result Vector3

When the method completes, contains the clamped value.

Cross(in Vector3, in Vector3)

Calculates the cross product of two vectors.

public static Vector3 Cross(in Vector3 left, in Vector3 right)

Parameters

left Vector3

First source vector.

right Vector3

Second source vector.

Returns

Vector3

The cross product of the two vectors.

Cross(ref readonly Vector3, ref readonly Vector3, out Vector3)

Calculates the cross product of two vectors.

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

Parameters

left Vector3

First source vector.

right Vector3

Second source vector.

result Vector3

When the method completes, contains he cross product of the two vectors.

Deconstruct(out float, out float, out float)

Deconstructs the vector's components into named variables.

public void Deconstruct(out float x, out float y, out float z)

Parameters

x float

The X component

y float

The Y component

z float

The Z component

Demodulate(Vector3, Vector3)

Demodulates a vector with another by performing component-wise division.

public static Vector3 Demodulate(Vector3 left, Vector3 right)

Parameters

left Vector3

The first vector to demodulate.

right Vector3

The second vector to demodulate.

Returns

Vector3

The demodulated vector.

Demodulate(ref readonly Vector3, ref readonly Vector3, out Vector3)

Demodulates a vector with another by performing component-wise division.

public static void Demodulate(ref readonly Vector3 left, ref readonly Vector3 right, out Vector3 result)

Parameters

left Vector3

The first vector to demodulate.

right Vector3

The second vector to demodulate.

result Vector3

When the method completes, contains the demodulated vector.

Distance(Vector3, Vector3)

Calculates the distance between two vectors.

public static float Distance(Vector3 value1, Vector3 value2)

Parameters

value1 Vector3

The first vector.

value2 Vector3

The second vector.

Returns

float

The distance between the two vectors.

Remarks

DistanceSquared(Vector3, Vector3) may be preferred when only the relative distance is needed and speed is of the essence.

Distance(ref readonly Vector3, ref readonly Vector3, out float)

Calculates the distance between two vectors.

public static void Distance(ref readonly Vector3 value1, ref readonly Vector3 value2, out float result)

Parameters

value1 Vector3

The first vector.

value2 Vector3

The second vector.

result float

When the method completes, contains the distance between the two vectors.

Remarks

DistanceSquared(ref readonly Vector3, ref readonly Vector3, out float) may be preferred when only the relative distance is needed and speed is of the essence.

DistanceSquared(Vector3, Vector3)

Calculates the squared distance between two vectors.

public static float DistanceSquared(Vector3 value1, Vector3 value2)

Parameters

value1 Vector3

The first vector.

value2 Vector3

The second vector.

Returns

float

The squared distance between the two vectors.

Remarks

Distance squared is the value before taking the square root. Distance squared can often be used in place of distance if relative comparisons are being made. For example, consider three points A, B, and C. To determine whether B or C is further from A, compare the distance between A and B to the distance between A and C. Calculating the two distances involves two square roots, which are computationally expensive. However, using distance squared provides the same information and avoids calculating two square roots.

DistanceSquared(ref readonly Vector3, ref readonly Vector3, out float)

Calculates the squared distance between two vectors.

public static void DistanceSquared(ref readonly Vector3 value1, ref readonly Vector3 value2, out float result)

Parameters

value1 Vector3

The first vector.

value2 Vector3

The second vector.

result float

When the method completes, contains the squared distance between the two vectors.

Remarks

Distance squared is the value before taking the square root. Distance squared can often be used in place of distance if relative comparisons are being made. For example, consider three points A, B, and C. To determine whether B or C is further from A, compare the distance between A and B to the distance between A and C. Calculating the two distances involves two square roots, which are computationally expensive. However, using distance squared provides the same information and avoids calculating two square roots.

Divide(Vector3, float)

Scales a vector by the given value.

public static Vector3 Divide(Vector3 value, float scale)

Parameters

value Vector3

The vector to scale.

scale float

The amount by which to scale the vector.

Returns

Vector3

The scaled vector.

Divide(ref readonly Vector3, float, out Vector3)

Scales a vector by the given value.

public static void Divide(ref readonly Vector3 value, float scale, out Vector3 result)

Parameters

value Vector3

The vector to scale.

scale float

The amount by which to scale the vector.

result Vector3

When the method completes, contains the scaled vector.

Dot(Vector3, Vector3)

Calculates the dot product of two vectors.

public static float Dot(Vector3 left, Vector3 right)

Parameters

left Vector3

First source vector.

right Vector3

Second source vector.

Returns

float

The dot product of the two vectors.

Dot(ref readonly Vector3, ref readonly Vector3, out float)

Calculates the dot product of two vectors.

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

Parameters

left Vector3

First source vector.

right Vector3

Second source vector.

result float

When the method completes, contains the dot product of the two vectors.

Equals(Vector3)

Determines whether the specified Vector3 is equal to this instance.

public bool Equals(Vector3 other)

Parameters

other Vector3

The Vector3 to compare with this instance.

Returns

bool

true if the specified Vector3 is equal to this instance; otherwise, false.

Equals(object)

Determines whether the specified object is equal to this instance.

public override bool Equals(object value)

Parameters

value object

The object to compare with this instance.

Returns

bool

true if the specified object is equal to this instance; otherwise, false.

GetHashCode()

Returns a hash code for this instance.

public override int GetHashCode()

Returns

int

A hash code for this instance, suitable for use in hashing algorithms and data structures like a hash table.

Hermite(Vector3, Vector3, Vector3, Vector3, float)

Performs a Hermite spline interpolation.

public static Vector3 Hermite(Vector3 value1, Vector3 tangent1, Vector3 value2, Vector3 tangent2, float amount)

Parameters

value1 Vector3

First source position vector.

tangent1 Vector3

First source tangent vector.

value2 Vector3

Second source position vector.

tangent2 Vector3

Second source tangent vector.

amount float

Weighting factor.

Returns

Vector3

The result of the Hermite spline interpolation.

Hermite(ref readonly Vector3, ref readonly Vector3, ref readonly Vector3, ref readonly Vector3, float, out Vector3)

Performs a Hermite spline interpolation.

public static void Hermite(ref readonly Vector3 value1, ref readonly Vector3 tangent1, ref readonly Vector3 value2, ref readonly Vector3 tangent2, float amount, out Vector3 result)

Parameters

value1 Vector3

First source position vector.

tangent1 Vector3

First source tangent vector.

value2 Vector3

Second source position vector.

tangent2 Vector3

Second source tangent vector.

amount float

Weighting factor.

result Vector3

When the method completes, contains the result of the Hermite spline interpolation.

Length()

Calculates the length of the vector.

public readonly float Length()

Returns

float

The length of the vector.

Remarks

LengthSquared() may be preferred when only the relative length is needed and speed is of the essence.

LengthSquared()

Calculates the squared length of the vector.

public readonly float LengthSquared()

Returns

float

The squared length of the vector.

Remarks

This method may be preferred to Length() when only a relative length is needed and speed is of the essence.

Lerp(Vector3, Vector3, float)

Performs a linear interpolation between two vectors.

public static Vector3 Lerp(Vector3 start, Vector3 end, float amount)

Parameters

start Vector3

Start vector.

end Vector3

End vector.

amount float

Value between 0 and 1 indicating the weight of end.

Returns

Vector3

The linear interpolation of the two vectors.

Remarks

This method performs the linear interpolation based on the following formula.

start + (end - start) * amount

Passing amount a value of 0 will cause start to be returned; a value of 1 will cause end to be returned.

Lerp(ref readonly Vector3, ref readonly Vector3, float, out Vector3)

Performs a linear interpolation between two vectors.

public static void Lerp(ref readonly Vector3 start, ref readonly Vector3 end, float amount, out Vector3 result)

Parameters

start Vector3

Start vector.

end Vector3

End vector.

amount float

Value between 0 and 1 indicating the weight of end.

result Vector3

When the method completes, contains the linear interpolation of the two vectors.

Remarks

This method performs the linear interpolation based on the following formula.

start + (end - start) * amount

Passing amount a value of 0 will cause start to be returned; a value of 1 will cause end to be returned.

Max(Vector3, Vector3)

Returns a vector containing the largest components of the specified vectors.

public static Vector3 Max(Vector3 left, Vector3 right)

Parameters

left Vector3

The first source vector.

right Vector3

The second source vector.

Returns

Vector3

A vector containing the largest components of the source vectors.

Max(ref readonly Vector3, ref readonly Vector3, out Vector3)

Returns a vector containing the largest components of the specified vectors.

public static void Max(ref readonly Vector3 left, ref readonly Vector3 right, out Vector3 result)

Parameters

left Vector3

The first source vector.

right Vector3

The second source vector.

result Vector3

When the method completes, contains an new vector composed of the largest components of the source vectors.

Min(Vector3, Vector3)

Returns a vector containing the smallest components of the specified vectors.

public static Vector3 Min(Vector3 left, Vector3 right)

Parameters

left Vector3

The first source vector.

right Vector3

The second source vector.

Returns

Vector3

A vector containing the smallest components of the source vectors.

Min(ref readonly Vector3, ref readonly Vector3, out Vector3)

Returns a vector containing the smallest components of the specified vectors.

public static void Min(ref readonly Vector3 left, ref readonly Vector3 right, out Vector3 result)

Parameters

left Vector3

The first source vector.

right Vector3

The second source vector.

result Vector3

When the method completes, contains an new vector composed of the smallest components of the source vectors.

Mod(Vector3, Vector3)

Performs mathematical modulo component-wise (see MathUtil.Mod).

public static Vector3 Mod(Vector3 left, Vector3 right)

Parameters

left Vector3

The first source vector.

right Vector3

The second source vector.

Returns

Vector3

When the method completes, contains an new vector composed of each component's modulo.

Mod(ref readonly Vector3, ref readonly Vector3, out Vector3)

Performs mathematical modulo component-wise (see MathUtil.Mod).

public static void Mod(ref readonly Vector3 left, ref readonly Vector3 right, out Vector3 result)

Parameters

left Vector3

The first source vector.

right Vector3

The second source vector.

result Vector3

When the method completes, contains an new vector composed of each component's modulo.

Modulate(Vector3, Vector3)

Modulates a vector with another by performing component-wise multiplication.

public static Vector3 Modulate(Vector3 left, Vector3 right)

Parameters

left Vector3

The first vector to modulate.

right Vector3

The second vector to modulate.

Returns

Vector3

The modulated vector.

Modulate(ref readonly Vector3, ref readonly Vector3, out Vector3)

Modulates a vector with another by performing component-wise multiplication.

public static void Modulate(ref readonly Vector3 left, ref readonly Vector3 right, out Vector3 result)

Parameters

left Vector3

The first vector to modulate.

right Vector3

The second vector to modulate.

result Vector3

When the method completes, contains the modulated vector.

MoveTo(in Vector3, in Vector3, float)

Moves the first vector3 to the second one in a straight line.

public static Vector3 MoveTo(in Vector3 from, in Vector3 to, float maxTravelDistance)

Parameters

from Vector3

The first point.

to Vector3

The second point.

maxTravelDistance float

The rate at which the first point is going to move towards the second point.

Returns

Vector3

Multiply(Vector3, float)

Scales a vector by the given value.

public static Vector3 Multiply(Vector3 value, float scale)

Parameters

value Vector3

The vector to scale.

scale float

The amount by which to scale the vector.

Returns

Vector3

The scaled vector.

Multiply(ref readonly Vector3, float, out Vector3)

Scales a vector by the given value.

public static void Multiply(ref readonly Vector3 value, float scale, out Vector3 result)

Parameters

value Vector3

The vector to scale.

scale float

The amount by which to scale the vector.

result Vector3

When the method completes, contains the scaled vector.

NearEqual(ref readonly Vector3, ref readonly Vector3, ref readonly Vector3)

Tests whether one 3D vector is near another 3D vector.

public static bool NearEqual(ref readonly Vector3 left, ref readonly Vector3 right, ref readonly Vector3 epsilon)

Parameters

left Vector3

The left vector.

right Vector3

The right vector.

epsilon Vector3

The epsilon.

Returns

bool

true if left and right are near another 3D, false otherwise

Negate(Vector3)

Reverses the direction of a given vector.

public static Vector3 Negate(Vector3 value)

Parameters

value Vector3

The vector to negate.

Returns

Vector3

A vector facing in the opposite direction.

Negate(ref readonly Vector3, out Vector3)

Reverses the direction of a given vector.

public static void Negate(ref readonly Vector3 value, out Vector3 result)

Parameters

value Vector3

The vector to negate.

result Vector3

When the method completes, contains a vector facing in the opposite direction.

Normalize()

Converts the vector into a unit vector.

public void Normalize()

Normalize(Vector3)

Converts the vector into a unit vector.

public static Vector3 Normalize(Vector3 value)

Parameters

value Vector3

The vector to normalize.

Returns

Vector3

The normalized vector.

Normalize(ref readonly Vector3, out Vector3)

Converts the vector into a unit vector.

public static void Normalize(ref readonly Vector3 value, out Vector3 result)

Parameters

value Vector3

The vector to normalize.

result Vector3

When the method completes, contains the normalized vector.

Orthogonalize(Vector3[], params Vector3[])

Orthogonalizes a list of vectors.

public static void Orthogonalize(Vector3[] destination, params Vector3[] source)

Parameters

destination Vector3[]

The list of orthogonalized vectors.

source Vector3[]

The list of vectors to orthogonalize.

Remarks

Orthogonalization is the process of making all vectors orthogonal to each other. This means that any given vector in the list will be orthogonal to any other given vector in the list.

Because this method uses the modified Gram-Schmidt process, the resulting vectors tend to be numerically unstable. The numeric stability decreases according to the vectors position in the list so that the first vector is the most stable and the last vector is the least stable.

Exceptions

ArgumentNullException

Thrown when source or destination is null.

ArgumentOutOfRangeException

Thrown when destination is shorter in length than source.

Orthonormalize(Vector3[], params Vector3[])

Orthonormalizes a list of vectors.

public static void Orthonormalize(Vector3[] destination, params Vector3[] source)

Parameters

destination Vector3[]

The list of orthonormalized vectors.

source Vector3[]

The list of vectors to orthonormalize.

Remarks

Orthonormalization is the process of making all vectors orthogonal to each other and making all vectors of unit length. This means that any given vector will be orthogonal to any other given vector in the list.

Because this method uses the modified Gram-Schmidt process, the resulting vectors tend to be numerically unstable. The numeric stability decreases according to the vectors position in the list so that the first vector is the most stable and the last vector is the least stable.

Exceptions

ArgumentNullException

Thrown when source or destination is null.

ArgumentOutOfRangeException

Thrown when destination is shorter in length than source.

Pow(float)

Raises the exponent for each components.

public void Pow(float exponent)

Parameters

exponent float

The exponent.

Project(Vector3, float, float, float, float, float, float, Matrix)

Projects a 3D vector from object space into screen space.

public static Vector3 Project(Vector3 vector, float x, float y, float width, float height, float minZ, float maxZ, Matrix worldViewProjection)

Parameters

vector Vector3

The vector to project.

x float

The X position of the viewport.

y float

The Y position of the viewport.

width float

The width of the viewport.

height float

The height of the viewport.

minZ float

The minimum depth of the viewport.

maxZ float

The maximum depth of the viewport.

worldViewProjection Matrix

The combined world-view-projection matrix.

Returns

Vector3

The vector in screen space.

Project(ref readonly Vector3, float, float, float, float, float, float, ref readonly Matrix, out Vector3)

Projects a 3D vector from object space into screen space.

public static void Project(ref readonly Vector3 vector, float x, float y, float width, float height, float minZ, float maxZ, ref readonly Matrix worldViewProjection, out Vector3 result)

Parameters

vector Vector3

The vector to project.

x float

The X position of the viewport.

y float

The Y position of the viewport.

width float

The width of the viewport.

height float

The height of the viewport.

minZ float

The minimum depth of the viewport.

maxZ float

The maximum depth of the viewport.

worldViewProjection Matrix

The combined world-view-projection matrix.

result Vector3

When the method completes, contains the vector in screen space.

Reflect(Vector3, Vector3)

Returns the reflection of a vector off a surface that has the specified normal.

public static Vector3 Reflect(Vector3 vector, Vector3 normal)

Parameters

vector Vector3

The source vector.

normal Vector3

Normal of the surface.

Returns

Vector3

The reflected vector.

Remarks

Reflect only gives the direction of a reflection off a surface, it does not determine whether the original vector was close enough to the surface to hit it.

Reflect(ref readonly Vector3, ref readonly Vector3, out Vector3)

Returns the reflection of a vector off a surface that has the specified normal.

public static void Reflect(ref readonly Vector3 vector, ref readonly Vector3 normal, out Vector3 result)

Parameters

vector Vector3

The source vector.

normal Vector3

Normal of the surface.

result Vector3

When the method completes, contains the reflected vector.

Remarks

Reflect only gives the direction of a reflection off a surface, it does not determine whether the original vector was close enough to the surface to hit it.

RotateAround(in Vector3, in Vector3, in Vector3, float)

Rotates the source around the target by the rotation angle around the supplied axis.

public static Vector3 RotateAround(in Vector3 source, in Vector3 target, in Vector3 axis, float angle)

Parameters

source Vector3

The position to rotate.

target Vector3

The point to rotate around.

axis Vector3

The axis of rotation.

angle float

The angle to rotate by in radians.

Returns

Vector3

The rotated vector.

RotationYawPitchRoll(Quaternion)

Calculate the yaw/pitch/roll rotation equivalent to the provided quaterion.

public static Vector3 RotationYawPitchRoll(Quaternion quaternion)

Parameters

quaternion Quaternion

The input rotation as quaternion

Returns

Vector3

The equivation yaw/pitch/roll rotation

RotationYawPitchRoll(ref readonly Quaternion, out Vector3)

Calculate the yaw/pitch/roll rotation equivalent to the provided quaterion.

public static void RotationYawPitchRoll(ref readonly Quaternion quaternion, out Vector3 yawPitchRoll)

Parameters

quaternion Quaternion

The input rotation as quaternion

yawPitchRoll Vector3

The equivation yaw/pitch/roll rotation

SmoothStep(Vector3, Vector3, float)

Performs a cubic interpolation between two vectors.

public static Vector3 SmoothStep(Vector3 start, Vector3 end, float amount)

Parameters

start Vector3

Start vector.

end Vector3

End vector.

amount float

Value between 0 and 1 indicating the weight of end.

Returns

Vector3

The cubic interpolation of the two vectors.

SmoothStep(ref readonly Vector3, ref readonly Vector3, float, out Vector3)

Performs a cubic interpolation between two vectors.

public static void SmoothStep(ref readonly Vector3 start, ref readonly Vector3 end, float amount, out Vector3 result)

Parameters

start Vector3

Start vector.

end Vector3

End vector.

amount float

Value between 0 and 1 indicating the weight of end.

result Vector3

When the method completes, contains the cubic interpolation of the two vectors.

Subtract(in Vector3, in Vector3)

Subtracts two vectors.

public static Vector3 Subtract(in Vector3 left, in Vector3 right)

Parameters

left Vector3

The first vector to subtract.

right Vector3

The second vector to subtract.

Returns

Vector3

The difference of the two vectors.

Subtract(ref readonly Vector3, ref readonly Vector3, out Vector3)

Subtracts two vectors.

public static void Subtract(ref readonly Vector3 left, ref readonly Vector3 right, out Vector3 result)

Parameters

left Vector3

The first vector to subtract.

right Vector3

The second vector to subtract.

result Vector3

When the method completes, contains the difference of the two vectors.

ToArray()

Creates an array containing the elements of the vector.

public float[] ToArray()

Returns

float[]

A three-element array containing the components of the vector.

ToString()

Returns a string that represents this instance.

public override string ToString()

Returns

string

A string that represents this instance.

ToString(IFormatProvider)

Returns a string that represents this instance.

public string ToString(IFormatProvider formatProvider)

Parameters

formatProvider IFormatProvider

The format provider.

Returns

string

A string that represents this instance.

ToString(string)

Returns a string that represents this instance.

public string ToString(string format)

Parameters

format string

The format.

Returns

string

A string that represents this instance.

ToString(string, IFormatProvider)

Returns a string that represents this instance.

public string ToString(string format, IFormatProvider formatProvider)

Parameters

format string

The format.

formatProvider IFormatProvider

The format provider.

Returns

string

A string that represents this instance.

Transform(Vector3, Matrix)

Transforms a 3D vector by the given Matrix.

public static Vector4 Transform(Vector3 vector, Matrix transform)

Parameters

vector Vector3

The source vector.

transform Matrix

The transformation Matrix.

Returns

Vector4

The transformed Vector4.

Transform(Vector3, Quaternion)

Transforms a 3D vector by the given Quaternion rotation.

public static Vector3 Transform(Vector3 vector, Quaternion rotation)

Parameters

vector Vector3

The vector to rotate.

rotation Quaternion

The Quaternion rotation to apply.

Returns

Vector3

The transformed Vector4.

Transform(ref readonly Vector3, ref readonly Matrix, out Vector3)

Transforms a 3D vector by the given Matrix.

public static void Transform(ref readonly Vector3 vector, ref readonly Matrix transform, out Vector3 result)

Parameters

vector Vector3

The source vector.

transform Matrix

The transformation Matrix.

result Vector3

When the method completes, contains the transformed Vector3.

Transform(ref readonly Vector3, ref readonly Matrix, out Vector4)

Transforms a 3D vector by the given Matrix.

public static void Transform(ref readonly Vector3 vector, ref readonly Matrix transform, out Vector4 result)

Parameters

vector Vector3

The source vector.

transform Matrix

The transformation Matrix.

result Vector4

When the method completes, contains the transformed Vector4.

Transform(ref readonly Vector3, ref readonly Quaternion, out Vector3)

Transforms a 3D vector by the given Quaternion rotation.

public static void Transform(ref readonly Vector3 vector, ref readonly Quaternion rotation, out Vector3 result)

Parameters

vector Vector3

The vector to rotate.

rotation Quaternion

The Quaternion rotation to apply.

result Vector3

When the method completes, contains the transformed Vector4.

Transform(Vector3[], ref readonly Matrix, Vector4[])

Transforms an array of 3D vectors by the given Matrix.

public static void Transform(Vector3[] source, ref readonly Matrix transform, Vector4[] destination)

Parameters

source Vector3[]

The array of vectors to transform.

transform Matrix

The transformation Matrix.

destination Vector4[]

The array for which the transformed vectors are stored.

Exceptions

ArgumentNullException

Thrown when source or destination is null.

ArgumentOutOfRangeException

Thrown when destination is shorter in length than source.

Transform(Vector3[], ref readonly Quaternion, Vector3[])

Transforms an array of vectors by the given Quaternion rotation.

public static void Transform(Vector3[] source, ref readonly Quaternion rotation, Vector3[] destination)

Parameters

source Vector3[]

The array of vectors to transform.

rotation Quaternion

The Quaternion rotation to apply.

destination Vector3[]

The array for which the transformed vectors are stored. This array may be the same array as source.

Exceptions

ArgumentNullException

Thrown when source or destination is null.

ArgumentOutOfRangeException

Thrown when destination is shorter in length than source.

TransformCoordinate(Vector3, Matrix)

Performs a coordinate transformation using the given Matrix.

public static Vector3 TransformCoordinate(Vector3 coordinate, Matrix transform)

Parameters

coordinate Vector3

The coordinate vector to transform.

transform Matrix

The transformation Matrix.

Returns

Vector3

The transformed coordinates.

Remarks

A coordinate transform performs the transformation with the assumption that the w component is one. The four dimensional vector obtained from the transformation operation has each component in the vector divided by the w component. This forces the wcomponent to be one and therefore makes the vector homogeneous. The homogeneous vector is often prefered when working with coordinates as the w component can safely be ignored.

TransformCoordinate(ref readonly Vector3, ref readonly Matrix, out Vector3)

Performs a coordinate transformation using the given Matrix.

public static void TransformCoordinate(ref readonly Vector3 coordinate, ref readonly Matrix transform, out Vector3 result)

Parameters

coordinate Vector3

The coordinate vector to transform.

transform Matrix

The transformation Matrix.

result Vector3

When the method completes, contains the transformed coordinates.

Remarks

A coordinate transform performs the transformation with the assumption that the w component is one. The four dimensional vector obtained from the transformation operation has each component in the vector divided by the w component. This forces the wcomponent to be one and therefore makes the vector homogeneous. The homogeneous vector is often prefered when working with coordinates as the w component can safely be ignored.

TransformCoordinate(Vector3[], ref readonly Matrix, Vector3[])

Performs a coordinate transformation on an array of vectors using the given Matrix.

public static void TransformCoordinate(Vector3[] source, ref readonly Matrix transform, Vector3[] destination)

Parameters

source Vector3[]

The array of coordinate vectors to trasnform.

transform Matrix

The transformation Matrix.

destination Vector3[]

The array for which the transformed vectors are stored. This array may be the same array as source.

Remarks

A coordinate transform performs the transformation with the assumption that the w component is one. The four dimensional vector obtained from the transformation operation has each component in the vector divided by the w component. This forces the wcomponent to be one and therefore makes the vector homogeneous. The homogeneous vector is often prefered when working with coordinates as the w component can safely be ignored.

Exceptions

ArgumentNullException

Thrown when source or destination is null.

ArgumentOutOfRangeException

Thrown when destination is shorter in length than source.

TransformNormal(Vector3, Matrix)

Performs a normal transformation using the given Matrix.

public static Vector3 TransformNormal(Vector3 normal, Matrix transform)

Parameters

normal Vector3

The normal vector to transform.

transform Matrix

The transformation Matrix.

Returns

Vector3

The transformed normal.

Remarks

A normal transform performs the transformation with the assumption that the w component is zero. This causes the fourth row and fourth collumn of the matrix to be unused. The end result is a vector that is not translated, but all other transformation properties apply. This is often prefered for normal vectors as normals purely represent direction rather than location because normal vectors should not be translated.

TransformNormal(ref readonly Vector3, ref readonly Matrix, out Vector3)

Performs a normal transformation using the given Matrix.

public static void TransformNormal(ref readonly Vector3 normal, ref readonly Matrix transform, out Vector3 result)

Parameters

normal Vector3

The normal vector to transform.

transform Matrix

The transformation Matrix.

result Vector3

When the method completes, contains the transformed normal.

Remarks

A normal transform performs the transformation with the assumption that the w component is zero. This causes the fourth row and fourth collumn of the matrix to be unused. The end result is a vector that is not translated, but all other transformation properties apply. This is often prefered for normal vectors as normals purely represent direction rather than location because normal vectors should not be translated.

TransformNormal(Vector3[], ref readonly Matrix, Vector3[])

Performs a normal transformation on an array of vectors using the given Matrix.

public static void TransformNormal(Vector3[] source, ref readonly Matrix transform, Vector3[] destination)

Parameters

source Vector3[]

The array of normal vectors to transform.

transform Matrix

The transformation Matrix.

destination Vector3[]

The array for which the transformed vectors are stored. This array may be the same array as source.

Remarks

A normal transform performs the transformation with the assumption that the w component is zero. This causes the fourth row and fourth collumn of the matrix to be unused. The end result is a vector that is not translated, but all other transformation properties apply. This is often prefered for normal vectors as normals purely represent direction rather than location because normal vectors should not be translated.

Exceptions

ArgumentNullException

Thrown when source or destination is null.

ArgumentOutOfRangeException

Thrown when destination is shorter in length than source.

Unproject(Vector3, float, float, float, float, float, float, Matrix)

Projects a 3D vector from screen space into object space.

public static Vector3 Unproject(Vector3 vector, float x, float y, float width, float height, float minZ, float maxZ, Matrix worldViewProjection)

Parameters

vector Vector3

The vector to project.

x float

The X position of the viewport.

y float

The Y position of the viewport.

width float

The width of the viewport.

height float

The height of the viewport.

minZ float

The minimum depth of the viewport.

maxZ float

The maximum depth of the viewport.

worldViewProjection Matrix

The combined world-view-projection matrix.

Returns

Vector3

The vector in object space.

Unproject(ref readonly Vector3, float, float, float, float, float, float, ref readonly Matrix, out Vector3)

Projects a 3D vector from screen space into object space.

public static void Unproject(ref readonly Vector3 vector, float x, float y, float width, float height, float minZ, float maxZ, ref readonly Matrix worldViewProjection, out Vector3 result)

Parameters

vector Vector3

The vector to project.

x float

The X position of the viewport.

y float

The Y position of the viewport.

width float

The width of the viewport.

height float

The height of the viewport.

minZ float

The minimum depth of the viewport.

maxZ float

The maximum depth of the viewport.

worldViewProjection Matrix

The combined world-view-projection matrix.

result Vector3

When the method completes, contains the vector in object space.

Operators

operator +(in Vector3, in Vector3)

Adds two vectors.

public static Vector3 operator +(in Vector3 left, in Vector3 right)

Parameters

left Vector3

The first vector to add.

right Vector3

The second vector to add.

Returns

Vector3

The sum of the two vectors.

operator +(in Vector3, float)

Adds a vector with the given value.

public static Vector3 operator +(in Vector3 value, float scale)

Parameters

value Vector3

The vector to scale.

scale float

The amount by which to scale the vector.

Returns

Vector3

The vector offset.

operator /(in Vector3, in Vector3)

Divides a vector by the given vector, component-wise.

public static Vector3 operator /(in Vector3 value, in Vector3 by)

Parameters

value Vector3

The vector to scale.

by Vector3

The by.

Returns

Vector3

The scaled vector.

operator /(in Vector3, float)

Scales a vector by the given value.

public static Vector3 operator /(in Vector3 value, float scale)

Parameters

value Vector3

The vector to scale.

scale float

The amount by which to scale the vector.

Returns

Vector3

The scaled vector.

operator /(float, in Vector3)

Divides a numerator by a vector.

public static Vector3 operator /(float numerator, in Vector3 value)

Parameters

numerator float

The numerator.

value Vector3

The value.

Returns

Vector3

The scaled vector.

operator ==(Vector3, Vector3)

Tests for equality between two objects.

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

Parameters

left Vector3

The first value to compare.

right Vector3

The second value to compare.

Returns

bool

true if left has the same value as right; otherwise, false.

explicit operator Int3(in Vector3)

Performs an explicit conversion from Vector3 to Int3.

public static explicit operator Int3(in Vector3 value)

Parameters

value Vector3

The value.

Returns

Int3

The result of the conversion.

explicit operator Vector2(in Vector3)

Performs an explicit conversion from Vector3 to Vector2.

public static explicit operator Vector2(in Vector3 value)

Parameters

value Vector3

The value.

Returns

Vector2

The result of the conversion.

explicit operator Vector4(in Vector3)

Performs an explicit conversion from Vector3 to Vector4.

public static explicit operator Vector4(in Vector3 value)

Parameters

value Vector3

The value.

Returns

Vector4

The result of the conversion.

operator !=(Vector3, Vector3)

Tests for inequality between two objects.

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

Parameters

left Vector3

The first value to compare.

right Vector3

The second value to compare.

Returns

bool

true if left has a different value than right; otherwise, false.

operator *(in Vector3, in Vector3)

Modulates a vector with another by performing component-wise multiplication.

public static Vector3 operator *(in Vector3 left, in Vector3 right)

Parameters

left Vector3

The first vector to multiply.

right Vector3

The second vector to multiply.

Returns

Vector3

The multiplication of the two vectors.

operator *(in Vector3, float)

Scales a vector by the given value.

public static Vector3 operator *(in Vector3 value, float scale)

Parameters

value Vector3

The vector to scale.

scale float

The amount by which to scale the vector.

Returns

Vector3

The scaled vector.

operator *(float, in Vector3)

Scales a vector by the given value.

public static Vector3 operator *(float scale, in Vector3 value)

Parameters

scale float

The amount by which to scale the vector.

value Vector3

The vector to scale.

Returns

Vector3

The scaled vector.

operator -(in Vector3, in Vector3)

Subtracts two vectors.

public static Vector3 operator -(in Vector3 left, in Vector3 right)

Parameters

left Vector3

The first vector to subtract.

right Vector3

The second vector to subtract.

Returns

Vector3

The difference of the two vectors.

operator -(in Vector3, float)

Substracts a vector by the given value.

public static Vector3 operator -(in Vector3 value, float scale)

Parameters

value Vector3

The vector to scale.

scale float

The amount by which to scale the vector.

Returns

Vector3

The vector offset.

operator -(in Vector3)

Reverses the direction of a given vector.

public static Vector3 operator -(in Vector3 value)

Parameters

value Vector3

The vector to negate.

Returns

Vector3

A vector facing in the opposite direction.

operator +(in Vector3)

Assert a vector (return it unchanged).

public static Vector3 operator +(in Vector3 value)

Parameters

value Vector3

The vector to assert (unchange).

Returns

Vector3

The asserted (unchanged) vector.