Attention: Here be dragons

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# Plane¶

A plane in Hessian normal form.

## Description¶

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.

## 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¶

 float distance_to ( Vector3 point ) const Vector3 get_center ( ) 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_finite ( ) 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 Plane

## 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¶

float d = `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.

Vector3 normal = `Vector3(0, 0, 0)`

The normal of the plane, which must be a unit vector.

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

float x = `0.0`

The X component of the plane's normal vector.

float y = `0.0`

The Y component of the plane's normal vector.

float z = `0.0`

The Z component of the plane's normal vector.

## Constructor Descriptions¶

Plane Plane ( )

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

Plane Plane ( Plane from )

Constructs a Plane as a copy of the given Plane.

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

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 ( Vector3 normal )

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, float d )

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, Vector3 point )

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 point1, Vector3 point2, Vector3 point3 )

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

## Method Descriptions¶

float distance_to ( Vector3 point ) 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.

Vector3 get_center ( ) const

Returns the center of the plane.

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

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

Variant intersect_3 ( Plane b, Plane c ) const

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

Variant intersects_ray ( Vector3 from, Vector3 dir ) 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_segment ( Vector3 from, Vector3 to ) 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.

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.

bool is_finite ( ) const

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

bool is_point_over ( Vector3 point ) const

Returns `true` if `point` is located above the plane.

Plane normalized ( ) const

Returns a copy of the plane, normalized.

Vector3 project ( Vector3 point ) const

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

## Operator Descriptions¶

bool operator != ( Plane right )

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.

Plane operator * ( Transform3D right )

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

bool operator == ( Plane right )

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.