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

• Math documentation index

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

• float d

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.

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• Vector3 normal

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.

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• float x

Default

0.0

The X component of the plane's normal vector.

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• float y

Default

0.0

The Y component of the plane's normal vector.

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• float z

Default

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.

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• Plane Plane ( Plane from )

Constructs a Plane as a copy of the given Plane.

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• 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.

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• Plane Plane ( Vector3 normal )

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

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• Plane Plane ( Vector3 normal, float d )

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

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• Plane Plane ( Vector3 normal, Vector3 point )

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

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

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

Method Descriptions

• Vector3 center ( ) const

Returns the center of the plane.

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• 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.

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• 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.

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• 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.

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• 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.

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• 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.

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• 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.

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• bool is_point_over ( Vector3 point ) const

Returns true if point is located above the plane.

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• Plane normalized ( ) const

Returns a copy of the plane, normalized.

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• 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.

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• Plane operator * ( Transform3D right )

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

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• 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.

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• 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.

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• 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.