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.

Tutorials

• Math documentation index

Properties

Constructors

Methods

Operators

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, 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.

Vector3 normal = Vector3(0, 0, 0) 🔗

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.

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(from: Plane)

Constructs a Plane as a copy of the given Plane.

Plane Plane(a: float, b: float, c: float, d: 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(normal: 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(normal: Vector3, d: 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(normal: Vector3, point: 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(point1: Vector3, point2: Vector3, point3: Vector3)

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

Method Descriptions

float distance_to(point: Vector3) 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(point: Vector3, tolerance: float = 1e-05) const 🔗

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

Variant intersect_3(b: Plane, c: Plane) 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(from: Vector3, dir: Vector3) 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(from: Vector3, to: Vector3) 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(to_plane: 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(point: Vector3) const 🔗

Returns true if point is located above the plane.

Plane normalized() 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).

Vector3 project(point: Vector3) const 🔗

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

Operator Descriptions

bool operator !=(right: Plane) 🔗

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 *(right: Transform3D) 🔗

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

plane * transform is equivalent to transform.affine_inverse() * plane. See Transform3D.affine_inverse.

bool operator ==(right: Plane) 🔗

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.

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