Class Plane

A plane in Hessian normal form.

Plane

Remarks

Represents a normalized plane equation. normal is the normal of the plane (a, b, c normalized), and d is the distance from the origin to the plane (in the direction of "normal"). "Over" or "Above" the plane is considered the side of the plane towards where the normal is pointing.

See Also

Math documentation index

Constructors

Plane

Constructs a default-initialized Plane with all components set to 0.

Plane Plane

Plane(Plane)

Constructs a Plane as a copy of the given Plane.

Plane Plane(Plane from)

Parameters

from Plane

Plane(float, float, float, float)

Creates a plane from the four parameters. The three components of the resulting plane's normal are a, b and c, and the plane has a distance of d from the origin.

Plane Plane(float a, float b, float c, float d)

Parameters

a float

b float

c float

d float

Plane(Vector3)

Creates a plane from the normal vector. The plane will intersect the origin.

The normal of the plane must be a unit vector.

Plane Plane(Vector3 normal)

Parameters

normal Vector3

Plane(Vector3, float)

Creates a plane from the normal vector and the plane's distance from the origin.

The normal of the plane must be a unit vector.

Plane Plane(Vector3 normal, float d)

Parameters

normal Vector3

d float

Plane(Vector3, Vector3)

Creates a plane from the normal vector and a point on the plane.

The normal of the plane must be a unit vector.

Plane Plane(Vector3 normal, Vector3 point)

Parameters

normal Vector3

point Vector3

Plane(Vector3, Vector3, Vector3)

Creates a plane from the three points, given in clockwise order.

Plane Plane(Vector3 point1, Vector3 point2, Vector3 point3)

Parameters

point1 Vector3

point2 Vector3

point3 Vector3

Fields

PLANE_YZ

A plane that extends in the Y and Z axes (normal vector points +X).

const PLANE_YZ = Plane(1, 0, 0, 0)

PLANE_XZ

A plane that extends in the X and Z axes (normal vector points +Y).

const PLANE_XZ = Plane(0, 1, 0, 0)

PLANE_XY

A plane that extends in the X and Y axes (normal vector points +Z).

const PLANE_XY = Plane(0, 0, 1, 0)

Properties

d

The distance from the origin to the plane, expressed in terms of normal (according to its direction and magnitude). Actual absolute distance from the origin to the plane can be calculated as abs(d) / normal.length() (if normal has zero length then this Plane does not represent a valid plane).

In the scalar equation of the plane ax + by + cz = d, this is d, while the (a, b, c) coordinates are represented by the normal property.

var d : float = 0.0

Property Value

float

normal

The normal of the plane, typically a unit vector. Shouldn't be a zero vector as Plane with such normal does not represent a valid plane.

In the scalar equation of the plane ax + by + cz = d, this is the vector (a, b, c), where d is the d property.

var normal : Vector3 = Vector3(0, 0, 0)

Property Value

Vector3

x

The X component of the plane's normal vector.

var x : float = 0.0

Property Value

float

y

The Y component of the plane's normal vector.

var y : float = 0.0

Property Value

float

z

The Z component of the plane's normal vector.

var z : float = 0.0

Property Value

float

Methods

distance_to(Vector3)

Qualifiers: const

Returns the shortest distance from the plane to the position point. If the point is above the plane, the distance will be positive. If below, the distance will be negative.

float distance_to(Vector3 point)

Parameters

point Vector3

get_center

Qualifiers: const

Returns the center of the plane.

Vector3 get_center

has_point(Vector3, float)

Qualifiers: const

Returns true if point is inside the plane. Comparison uses a custom minimum tolerance threshold.

bool has_point(Vector3 point, float tolerance)

Parameters

point Vector3

tolerance float

intersect_3(Plane, Plane)

Qualifiers: const

Returns the intersection point of the three planes b, c and this plane. If no intersection is found, null is returned.

Variant intersect_3(Plane b, Plane c)

Parameters

b Plane

c Plane

intersects_ray(Vector3, Vector3)

Qualifiers: const

Returns the intersection point of a ray consisting of the position from and the direction normal dir with this plane. If no intersection is found, null is returned.

Variant intersects_ray(Vector3 from, Vector3 dir)

Parameters

from Vector3

dir Vector3

intersects_segment(Vector3, Vector3)

Qualifiers: const

Returns the intersection point of a segment from position from to position to with this plane. If no intersection is found, null is returned.

Variant intersects_segment(Vector3 from, Vector3 to)

Parameters

from Vector3

to Vector3

is_equal_approx(Plane)

Qualifiers: const

Returns true if this plane and to_plane are approximately equal, by running @GlobalScope.is_equal_approx on each component.

bool is_equal_approx(Plane to_plane)

Parameters

to_plane Plane

is_finite

Qualifiers: const

Returns true if this plane is finite, by calling @GlobalScope.is_finite on each component.

bool is_finite

is_point_over(Vector3)

Qualifiers: const

Returns true if point is located above the plane.

bool is_point_over(Vector3 point)

Parameters

point Vector3

normalized

Qualifiers: const

Returns a copy of the plane, with normalized normal (so it's a unit vector). Returns Plane(0, 0, 0, 0) if normal can't be normalized (it has zero length).

Plane normalized

project(Vector3)

Qualifiers: const

Returns the orthogonal projection of point into a point in the plane.

Vector3 project(Vector3 point)

Parameters

point Vector3

Operators

!= (Plane)

Returns true if the planes are not equal.

Note: Due to floating-point precision errors, consider using Plane.is_equal_approx instead, which is more reliable.

bool != (Plane right)

Parameters

right Plane

* (Transform3D)

Inversely transforms (multiplies) the Plane by the given Transform3D transformation matrix.

plane * transform is equivalent to transform.affine_inverse() * plane. See affine_inverse.

Plane * (Transform3D right)

Parameters

right Transform3D

== (Plane)

Returns true if the planes are exactly equal.

Note: Due to floating-point precision errors, consider using Plane.is_equal_approx instead, which is more reliable.

bool == (Plane right)

Parameters

right Plane

unary+

Returns the same value as if the + was not there. Unary + does nothing, but sometimes it can make your code more readable.

Plane unary+

unary-

Returns the negative value of the Plane. This is the same as writing Plane(-p.normal, -p.d). This operation flips the direction of the normal vector and also flips the distance value, resulting in a Plane that is in the same place, but facing the opposite direction.

Plane unary-