Struct Plane

Namespace

Misaki.HighPerformance.Mathematics.Geometry

Assembly

Misaki.HighPerformance.Mathematics.dll

A plane represented by a normal vector and a distance along the normal from the origin.

public struct Plane

Inherited Members

ValueType.Equals(object)

ValueType.GetHashCode()

ValueType.ToString()

object.Equals(object, object)

object.GetType()

object.ReferenceEquals(object, object)

Remarks

A plane splits the 3D space in half. The normal vector points to the positive half and the other half is considered negative.

Constructors

Plane(float3, float3)

Constructs a plane with a normal vector and a point that lies in the plane.

public Plane(float3 normal, float3 pointInPlane)

Parameters

normal float3

A non-zero vector that is perpendicular to the plane. It may be any length.

pointInPlane float3

A point that lies in the plane.

Remarks

The constructed plane will be the normalized form of the plane specified by the inputs.

Plane(float3, float3, float3)

Constructs a plane with two vectors and a point that all lie in the plane.

public Plane(float3 vector1InPlane, float3 vector2InPlane, float3 pointInPlane)

Parameters

vector1InPlane float3

A non-zero vector that lies in the plane. It may be any length.

vector2InPlane float3

A non-zero vector that lies in the plane. It may be any length and must not be a scalar multiple of vector1InPlane.

pointInPlane float3

A point that lies in the plane.

Remarks

The constructed plane will be the normalized form of the plane specified by the inputs.

Plane(float3, float)

Constructs a plane with a normal vector and distance from the origin.

public Plane(float3 normal, float distance)

Parameters

normal float3

A non-zero vector that is perpendicular to the plane. It may be any length.

distance float

Distance from the origin along the normal. A negative value moves the plane in the same direction as the normal while a positive value moves it in the opposite direction.

Remarks

The constructed plane will be the normalized form of the plane specified by the inputs.

Plane(float, float, float, float)

Constructs a Plane from arbitrary coefficients A, B, C, D of the plane equation Ax + By + Cz + Dw = 0.

public Plane(float coefficientA, float coefficientB, float coefficientC, float coefficientD)

Parameters

coefficientA float

Coefficient A from plane equation.

coefficientB float

Coefficient B from plane equation.

coefficientC float

Coefficient C from plane equation.

coefficientD float

Coefficient D from plane equation.

Remarks

The constructed plane will be the normalized form of the plane specified by the given coefficients.

Fields

normalAndDistance

A plane in the form Ax + By + Cz + Dw = 0.

public float4 normalAndDistance

Field Value

float4

Remarks

Stores the plane coefficients A, B, C, D where (A, B, C) is a unit normal vector and D is the distance from the origin. A plane stored with a unit normal vector is called a normalized plane.

Properties

Distance

Get/set the distance of the plane from the origin. May be a negative value.

public float Distance { get; set; }

Property Value

float

Remarks

It is assumed that the normal is unit length. If you set a new plane such that Ax + By + Cz + Dw = 0 but (A, B, C) is not unit length, then you must normalize the plane by calling Normalize(Plane).

Flipped

Flips the plane so the normal points in the opposite direction.

public Plane Flipped { get; }

Property Value

Plane

Normal

Get/set the normal vector of the plane.

public float3 Normal { get; set; }

Property Value

float3

Remarks

It is assumed that the normal is unit length. If you set a new plane such that Ax + By + Cz + Dw = 0 but (A, B, C) is not unit length, then you must normalize the plane by calling Normalize(Plane).

Methods

CreateFromUnitNormalAndDistance(float3, float)

Creates a normalized Plane directly without normalization cost.

public static Plane CreateFromUnitNormalAndDistance(float3 unitNormal, float distance)

Parameters

unitNormal float3

A non-zero vector that is perpendicular to the plane. It must be unit length.

distance float

Distance from the origin along the normal. A negative value moves the plane in the same direction as the normal while a positive value moves it in the opposite direction.

Returns

Plane

Normalized Plane constructed from given inputs.

Remarks

If you have a unit length normal vector, you can create a Plane faster than using one of its constructors by calling this function.

CreateFromUnitNormalAndPointInPlane(float3, float3)

Creates a normalized Plane without normalization cost.

public static Plane CreateFromUnitNormalAndPointInPlane(float3 unitNormal, float3 pointInPlane)

Parameters

unitNormal float3

A non-zero vector that is perpendicular to the plane. It must be unit length.

pointInPlane float3

A point that lies in the plane.

Returns

Plane

Normalized Plane constructed from given inputs.

Remarks

If you have a unit length normal vector, you can create a Plane faster than using one of its constructors by calling this function.

Normalize(Plane)

Normalizes the given Plane.

public static Plane Normalize(Plane plane)

Parameters

plane Plane

Plane to normalize.

Returns

Plane

Normalized Plane.

Normalize(float4)

Normalizes the plane represented by the given plane coefficients.

public static float4 Normalize(float4 planeCoefficients)

Parameters

planeCoefficients float4

Plane coefficients A, B, C, D stored in x, y, z, w (respectively).

Returns

float4

Normalized plane coefficients.

Remarks

The plane coefficients are A, B, C, D and stored in that order in the float4.

Projection(float3)

Projects the given point onto the plane.

public float3 Projection(float3 point)

Parameters

point float3

Point to project onto the plane.

Returns

float3

Projected point that's inside the plane.

Remarks

Plane must be normalized prior to calling this function. The result is the position closest to the point that still lies in the plane.

SignedDistanceToPoint(float3)

Get the signed distance from the point to the plane.

public float SignedDistanceToPoint(float3 point)

Parameters

point float3

Point to find the signed distance with.

Returns

float

Signed distance of the point from the plane.

Remarks

Plane must be normalized prior to calling this function. Distance is positive if point is on side of the plane the normal points to, negative if on the opposite side and zero if the point lies in the plane. Avoid comparing equality with 0.0f when testing if a point lies exactly in the plane and use an approximate comparison instead.

Operators

implicit operator float4(Plane)

Implicitly converts a Plane to float4.

public static implicit operator float4(Plane plane)

Parameters

plane Plane

Plane to convert.

Returns

float4

A float4 representing the plane.