pub struct HalfSpace { /* private fields */ }
Expand description

A region of 3D space, specifically an open set whose border is a bisecting 2D plane. This bisecting plane partitions 3D space into two infinite regions, the half-space is one of those regions and excludes the bisecting plane.

Each instance of this type is characterized by:

  • the bisecting plane’s unit normal, normalized and pointing “inside” the half-space,
  • the signed distance along the normal from the bisecting plane to the origin of 3D space.

The distance can also be seen as:

  • the distance along the inverse of the normal from the origin of 3D space to the bisecting plane,
  • the opposite of the distance along the normal from the origin of 3D space to the bisecting plane.

Any point p is considered to be within the HalfSpace when the length of the projection of p on the normal is greater or equal than the opposite of the distance, meaning: if the equation normal.dot(p) + distance > 0. is satisfied.

For example, the half-space containing all the points with a z-coordinate lesser or equal than 8.0 would be defined by: HalfSpace::new(Vec3::NEG_Z.extend(-8.0)). It includes all the points from the bisecting plane towards NEG_Z, and the distance from the plane to the origin is -8.0 along NEG_Z.

It is used to define a Frustum, but is also a useful mathematical primitive for rendering tasks such as light computation.

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impl HalfSpace

pub fn new(normal_d: Vec4) -> HalfSpace

Constructs a HalfSpace from a 4D vector whose first 3 components represent the bisecting plane’s unit normal, and the last component is the signed distance along the normal from the plane to the origin. The constructor ensures the normal vector is normalized and the distance is appropriately scaled.

pub fn normal(&self) -> Vec3A

Returns the unit normal vector of the bisecting plane that characterizes the HalfSpace.

pub fn d(&self) -> f32

Returns the signed distance from the bisecting plane to the origin along the plane’s unit normal vector.

pub fn normal_d(&self) -> Vec4

Returns the bisecting plane’s unit normal vector and the signed distance from the plane to the origin.

Trait Implementations§

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impl Clone for HalfSpace

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fn clone(&self) -> HalfSpace

Returns a copy of the value. Read more
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fn clone_from(&mut self, source: &Self)

Performs copy-assignment from source. Read more
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impl Debug for HalfSpace

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fn fmt(&self, f: &mut Formatter<'_>) -> Result<(), Error>

Formats the value using the given formatter. Read more
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impl Default for HalfSpace

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fn default() -> HalfSpace

Returns the “default value” for a type. Read more
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impl Copy for HalfSpace

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