Struct CgaVector5D 

#[repr(C, align(32))]
pub struct CgaVector5D {
    pub x: f32,
    pub y: f32,
    pub z: f32,
    pub no: f32,
    pub ni: f32,
    pub _pad0: f32,
    pub _pad1: f32,
    pub _pad2: f32,
}

5D Conformal Null-Basis Vector in Cl(4, 1). Basis: e1, e2, e3 (Euclidean, e_i^2 = +1), no (origin), ni (infinity). Metric properties:

• no^2 = 0, ni^2 = 0
• no . ni = -1 Alignment: 32 bytes (8 floats: x, y, z, no, ni, plus 3 padding floats).

Fields

x: f32

y: f32

z: f32

no: f32

ni: f32

_pad0: f32

_pad1: f32

_pad2: f32

Implementations

impl CgaVector5D

pub const fn zero() -> Self

Zero vector.

pub const fn origin() -> Self

Origin point n_o (0, 0, 0, 1, 0).

pub const fn infinity() -> Self

Infinity point n_\infty (0, 0, 0, 0, 1).

pub fn point(x: f32, y: f32, z: f32) -> Self

Embeds a 3D Euclidean point x = (x, y, z) into CGA: P = x + 0.5 * ||x||^2 * n_\infty + n_o.

pub fn sphere(cx: f32, cy: f32, cz: f32, radius: f32) -> Self

Embeds a 3D sphere with center c = (cx, cy, cz) and radius r: S = c + 0.5 * (||c||^2 - r^2) * n_\infty + n_o.

pub fn plane(nx: f32, ny: f32, nz: f32, d: f32) -> Self

Embeds a 3D plane with unit normal n = (nx, ny, nz) and signed distance d: \pi = n + d * n_\infty (with no = 0).

pub fn inner_product(&self, other: &Self) -> f32

Computes the Lorentzian inner product: U . V = (uxvx + uyvy + uz*vz) - (u_no * v_ni + u_ni * v_no).

pub fn to_euclidean(&self) -> [f32; 3]

Extracts Euclidean coordinates [x/no, y/no, z/no].

pub fn squared_distance(&self, other: &Self) -> f32

Computes squared Euclidean distance between two conformal points: ||p1 - p2||^2 = -2 * (P1 . P2) / (P1_no * P2_no).

pub fn distance(&self, other: &Self) -> f32

Euclidean distance between two conformal points.

pub fn sphere_radius(&self) -> Option<f32>

If this vector represents a sphere, extracts its radius: r = sqrt(S . S).

pub fn invert_in_sphere(&self, sphere: &Self) -> Self

Reflects this conformal point across a sphere via 1-versor sandwich: P’ = S * P * S / ||S||^2. This is the classical spherical inversion!

pub fn translate(&self, dx: f32, dy: f32, dz: f32) -> Self

Applies a conformal translation by vector d = (dx, dy, dz).

pub fn dilate(&self, lambda: f32) -> Self

Applies a conformal dilation / uniform scale with factor lambda > 0.

Trait Implementations

impl Add for CgaVector5D

type Output = CgaVector5D

The resulting type after applying the + operator.

fn add(self, rhs: Self) -> Self

Performs the + operation.

impl Clone for CgaVector5D

fn clone(&self) -> Self

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl Copy for CgaVector5D

impl Debug for CgaVector5D

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

Formats the value using the given formatter.

impl Default for CgaVector5D

fn default() -> Self

Returns the “default value” for a type.

impl Div<f32> for CgaVector5D

type Output = CgaVector5D

The resulting type after applying the / operator.

fn div(self, rhs: f32) -> Self

Performs the / operation.

impl Mul<f32> for CgaVector5D

type Output = CgaVector5D

The resulting type after applying the * operator.

fn mul(self, rhs: f32) -> Self

Performs the * operation.

impl Neg for CgaVector5D

type Output = CgaVector5D

The resulting type after applying the - operator.

fn neg(self) -> Self

Performs the unary - operation.

impl PartialEq for CgaVector5D

fn eq(&self, other: &Self) -> bool

Equality operator ==.

fn ne(&self, other: &Rhs) -> bool

Inequality operator !=.

impl StructuralPartialEq for CgaVector5D

impl Sub for CgaVector5D

type Output = CgaVector5D

The resulting type after applying the - operator.

fn sub(self, rhs: Self) -> Self

Performs the - operation.