Struct Projection 

pub struct Projection {
    pub p: Vec4,
    pub local_x: Vec4,
    pub local_y: Vec4,
    pub local_z: Vec4,
    pub matrix_inverse: Mat4,
}

A 4D -> 3D stereographic projection from S3 -> R3.

Fields

p: Vec4

Center of projection

local_x: Vec4

Three elements of the orthonormal basis for the tangent plane of a point – plane is centered at 0 rather than p.

local_y: Vec4

local_z: Vec4

matrix_inverse: Mat4

Inverse matrix, used when projecting to strip a dimension out.

Implementations

impl Projection

pub const UNIT_PROJECTION: Projection

The unit projection uses Vec4::W as the center of projection.

pub fn new(p: Vec4) -> Self

Creates a new projection with p as the center.

Picks an arbitrary orthonormal basis for local_x, local_y, and local_z.

pub fn from_orthonormal_basis(p: Vec4, q: Vec4, r: Vec4, s: Vec4) -> Self

Constructs a projection from an existing orthonormal basis.

pub fn project(self, point: Vec4) -> Vec3

Projects a point according to the stereographic projection described by self.

pub fn project_normal(self, at: Vec4, normal: Vec4) -> Vec3

Projects a tangent vector to a point in an angle-preserving way.

If:

• normal is tangent to the hypersphere at at, ie normal.dot(at) == 0
• at is part of some shape K which lives on the surface of the hypersphere
• K' is the projection of K
• at' is the projection of at
• x(t) = (at + t * normal).normalize() is a spherical line segment for t > 0
• x(t) intersects K at an angle alpha
• n' is self.project_normal(at, normal)

Then:

• y(t) = at' + t * n' intersects K' at an angle alpha.

This is meaningful because it means that normal vectors remain normal vectors.

Trait Implementations

impl Clone for Projection

fn clone(&self) -> Projection

Returns a duplicate of the value.

fn clone_from(&mut self, source: &Self)

Performs copy-assignment from source.

impl Debug for Projection

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

Formats the value using the given formatter.

impl Copy for Projection