Plane

Plane in hessian form.

Description

Plane represents a normalized plane equation. Basically, "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.

Tutorials

Properties

float

d

0.0

Vector3

normal

Vector3(0, 0, 0)

float

x

0.0

float

y

0.0

float

z

0.0

Constructors

Plane

Plane ( )

Plane

Plane ( Plane from )

Plane

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

Plane

Plane ( Vector3 normal )

Plane

Plane ( Vector3 normal, float d )

Plane

Plane ( Vector3 normal, Vector3 point )

Plane

Plane ( Vector3 point1, Vector3 point2, Vector3 point3 )

Methods

Vector3

center ( ) const

float

distance_to ( Vector3 point ) const

bool

has_point ( Vector3 point, float tolerance=1e-05 ) const

Variant

intersect_3 ( Plane b, Plane c ) const

Variant

intersects_ray ( Vector3 from, Vector3 dir ) const

Variant

intersects_segment ( Vector3 from, Vector3 to ) const

bool

is_equal_approx ( Plane to_plane ) const

bool

is_point_over ( Vector3 point ) const

Plane

normalized ( ) const

Vector3

project ( Vector3 point ) const

Operators

bool

operator != ( Plane right )

Plane

operator * ( Transform3D right )

bool

operator == ( Plane right )

Plane

operator unary+ ( )

Plane

operator unary- ( )

Constants

  • PLANE_YZ = Plane(1, 0, 0, 0) --- A plane that extends in the Y and Z axes (normal vector points +X).

  • PLANE_XZ = Plane(0, 1, 0, 0) --- A plane that extends in the X and Z axes (normal vector points +Y).

  • PLANE_XY = Plane(0, 0, 1, 0) --- A plane that extends in the X and Y axes (normal vector points +Z).

Property Descriptions

Default

0.0

The distance from the origin to the plane, in the direction of normal. This value is typically non-negative.

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.


Default

Vector3(0, 0, 0)

The normal of the plane, which must be normalized.

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


Default

0.0

The X component of the plane's normal vector.


Default

0.0

The Y component of the plane's normal vector.


Default

0.0

The Z component of the plane's normal vector.

Constructor Descriptions

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


Constructs a Plane as a copy of the given Plane.


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.


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


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


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


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

Method Descriptions

Returns the center of the plane.


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.


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


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


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.


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


  • bool is_equal_approx ( Plane to_plane ) const

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


Returns true if point is located above the plane.


  • Plane normalized ( ) const

Returns a copy of the plane, normalized.


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

Operator Descriptions

Returns true if the planes are not equal.

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


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


Returns true if the planes are exactly equal.

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


  • Plane operator unary+ ( )

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


  • Plane operator 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.