struct Plane in Tinman.Core.Math

Represents a plane in 3D space.

struct

Plane

Serialization

Serializer

The serialization helper object for values of Plane.

public static readonly field	Serializer
type	ITypeSerializer<Plane>

Public / Constants

XY

The XY-plane, having the positive Z-axis as normal vector.

public static readonly field	XY
type	Plane

XZ

The XZ-plane, having the positive Y-axis as normal vector.

public static readonly field	XZ
type	Plane

YZ

The YZ-plane, having the positive X-axis as normal vector.

public static readonly field	YZ
type	Plane

Zero

No plane.

public static readonly field	Zero
type	Plane

Public / Attributes

Coefficients

Returns the plane coefficients.

public property	Coefficients { get }
type	Vec4D
value		The coefficients vector.

Remarks:

This value refers to the general plane equation:

a*x + b*y + c*z + d = 0

where a, b, c and d are returned as the X, Y, Z and W components.

Distance

Distance of the plane to the coordinate origin.

public property	Distance { get }
type	float64
value		The distance value.

Remarks:

This value refers to the Hessian Normal Form:

n * X = -p

where n is the unit-length normal vector (see Normal) and p is the distance of the plane from the origin.

Normal

Unit-length plane normal vector.

public property	Normal { get }
type	Vec3D
value		The unit normal vector.

Remarks:

This value refers to the Hessian Normal Form:

n * X = -p

where n is the unit-length normal vector and p is the distance of the plane from the origin (see Distance).

Public / Constructors

FromEquation

Creates a new instance of Plane.

public static method	FromEquation (float64 a, float64 b, float64 c, float64 d)
type	Plane
params	a		First plane coefficient.
	b		Second plane coefficient.
	c		Third plane coefficient.
	d		Fourth plane coefficient.
returns			The plane.

Remarks:

The plane is computed using the following formula:

a*x + b*y + c*z + d = 0

FromHessian

Creates a new instance of Plane.

public static method	FromHessian (Vec3D normal, float64 distance)
type	Plane
params	normal		The plane normal vector (will be normalized if necessary).
	distance		Distance of the plane from the origin.
returns			The plane.

Remarks:

The plane is defined by the Hessian Normal Form:

n * X = -p

where n is the unit-length normal vector (see Normal) and p is the distance of the plane from the origin (see Distance).

FromPoint

Creates a new instance of Plane.

public static method	FromPoint (Vec3D p, Vec3D n)
type	Plane
params	p		The point in the plane.
	n		The plane normal vector.
returns			The plane.

Remarks:

The plane will contain the given point.

FromPoints

Creates a new instance of Plane.

public static method	FromPoints (Vec3D a, Vec3D b, Vec3D c)
type	Plane
params	a		First triangle vertex.
	b		Second triangle vertex.
	c		Third triangle vertex.
returns			The plane.

Remarks:

The plane will contain the given points, having a normal vector that points in the same direction as (b-a) x (c-a).

Public / Methods

ClipLineSegment

Clips the given line segment with the positive half-space of this plane.

[Pure]
public method	ClipLineSegment (ref Vec3D a, ref Vec3D b)
type	int32
params	a		First point of line segment.
	b		Second point of line segment.
returns			-1 if the line segment lies entirely within the negative half-space of the plane. 0 if the line segment lies entirely within the positive half-space of the plane. 1 if a has been updated to represent the clipped line segment. 2 if b has been updated to represent the clipped line segment.

DistanceToPoint

Computes the distance of the given point to the plane.

[Pure]
public method	DistanceToPoint (Vec3D point)
type	float64
params	point		The point.
returns			The distance to this plane.

---

Computes the distance of the given point to the plane.

[Pure]
public method	DistanceToPoint (float64 x, float64 y, float64 z)
type	float64
params	x		X-coordinate of point.
	y		Y-coordinate of point.
	z		Z-coordinate of point.
returns			The distance to this plane.

Flip

Flips the normal vector of this plane.

[Pure]
public method	Flip ()
type	Plane
returns			The resulting plane.

IntersectLineSegment

Intersects the given line segment with this plane.

[Pure]
public method	IntersectLineSegment (Vec3D a, Vec3D b)
type	Vec3D
params	a		First point of line segment.
	b		Second point of line segment.
returns			The intersection point or Undefined if there is no intersection.

IntersectRay

Intersects the given ray with this plane.

[Pure]
public method	IntersectRay (Vec3D p, Vec3D v)
type	Vec3D
params	p		The ray origin.
	v		The ray direction.
returns			The intersection point or Undefined if there is no intersection.

Offset

Applies a distance offset to this plane.

[Pure]
public method	Offset (float64 amount)
type	Plane
params	amount		The distance offset to apply.
returns			The resulting plane.

Remarks:

The plane offset is defined as follows:

plane.DistanceToPoint(point)
=
plane.Offset(amount).DistanceToPoint(point) + amount

Project

Projects the given point onto this plane.

[Pure]
public method	Project (Vec3D p)
type	Vec3D
params	p		The point to project.
returns			The projected point on this plane.

Transform

Transforms this plane.

[Pure]
public method	Transform (Mat4D matrix)
type	Plane
params	matrix		The transformation matrix, as would be used for normal vectors.
returns			The resulting plane.

Remarks:

Planes must be transformed using the inverse transpose of the matrix that is used to transform points, just like normal vectors.

Translate

Translates this plane.

[Pure]
public method	Translate (Vec3D offset)
type	Plane
params	offset		The translation offset.
returns			The resulting plane.