Struct g3::Branch

pub struct Branch(_);

The Branch both a line through the origin and also the principal branch of the logarithm of a rotor.

The rotor branch will be most commonly constructed by taking the logarithm of a normalized rotor. The branch may then be linearily scaled to adjust the “strength” of the rotor, and subsequently re-exponentiated to create the adjusted rotor.

Implementations

impl Branch

pub const fn new(a: f32, b: f32, c: f32) -> Branch

Construct the branch as the following multivector:

$$a \mathbf{e}{23} + b\mathbf{e}{31} + c\mathbf{e}_{12}$$

To convince yourself this is a line through the origin, remember that such a line can be generated using the geometric product of two planes through the origin.

pub fn squared_norm(self) -> f32

If a line is constructed as the regressive product (join) of two points, the squared norm provided here is the squared distance between the two points (provided the points are normalized). Returns $d^2 + e^2 + f^2$.

pub fn norm(self) -> f32

Returns the square root of the quantity produced by squared_norm.

pub fn normalized(self) -> Branch

pub fn inverse(self) -> Branch

pub fn exp(self) -> Rotor

Exponentiate a branch to produce a rotor.

pub fn sqrt(self) -> Rotor

pub fn reverse(self) -> Branch

Reversion

pub fn e12(&self) -> f32

pub fn e21(&self) -> f32

pub fn z(&self) -> f32

pub fn e31(&self) -> f32

pub fn e13(&self) -> f32

pub fn y(&self) -> f32

pub fn e23(&self) -> f32

pub fn e32(&self) -> f32

pub fn x(&self) -> f32

Trait Implementations

impl Add<Branch> for Branch

type Output = Branch

The resulting type after applying the + operator.

fn add(self, b: Branch) -> Branch

Performs the + operation.

impl AddAssign<Branch> for Branch

fn add_assign(&mut self, b: Self)

Performs the += operation.

impl BitAnd<Branch> for Point

type Output = Plane

The resulting type after applying the & operator.

fn bitand(self, b: Branch) -> Plane

Performs the & operation.

impl BitAnd<Point> for Branch

type Output = Plane

The resulting type after applying the & operator.

fn bitand(self, a: Point) -> Plane

Performs the & operation.

impl BitXor<Branch> for Horizon

type Output = Dual

The resulting type after applying the ^ operator.

fn bitxor(self, b: Branch) -> Dual

Performs the ^ operation.

impl BitXor<Branch> for Line

type Output = Dual

The resulting type after applying the ^ operator.

fn bitxor(self, b: Branch) -> Dual

Performs the ^ operation.

impl BitXor<Branch> for Plane

type Output = Point

The resulting type after applying the ^ operator.

fn bitxor(self, b: Branch) -> Point

Performs the ^ operation.

impl BitXor<Horizon> for Branch

type Output = Dual

The resulting type after applying the ^ operator.

fn bitxor(self, l: Horizon) -> Dual

Performs the ^ operation.

impl BitXor<Line> for Branch

type Output = Dual

The resulting type after applying the ^ operator.

fn bitxor(self, l: Line) -> Dual

Performs the ^ operation.

impl BitXor<Plane> for Branch

type Output = Point

The resulting type after applying the ^ operator.

fn bitxor(self, p: Plane) -> Point

Performs the ^ operation.

impl Clone for Branch

fn clone(&self) -> Branch

Returns a copy of the value.

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

Performs copy-assignment from source.

impl Debug for Branch

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

Formats the value using the given formatter.

impl Default for Branch

fn default() -> Branch

Returns the “default value” for a type.

impl Div<Branch> for Branch

type Output = Rotor

The resulting type after applying the / operator.

fn div(self, b: Branch) -> Rotor

Performs the / operation.

impl Div<f32> for Branch

type Output = Branch

The resulting type after applying the / operator.

fn div(self, s: f32) -> Branch

Performs the / operation.

impl DivAssign<f32> for Branch

fn div_assign(&mut self, s: f32)

Performs the /= operation.

impl From<&Line> for Branch

fn from(l: &Line) -> Self

Converts to this type from the input type.

impl From<Branch> for Line

fn from(b: Branch) -> Self

Converts to this type from the input type.

impl From<Line> for Branch

fn from(l: Line) -> Self

Converts to this type from the input type.

impl Mul<Branch> for Branch

type Output = Rotor

The resulting type after applying the * operator.

fn mul(self, b: Branch) -> Rotor

Performs the * operation.

impl Mul<f32> for Branch

type Output = Branch

The resulting type after applying the * operator.

fn mul(self, s: f32) -> Branch

Performs the * operation.

impl MulAssign<f32> for Branch

fn mul_assign(&mut self, s: f32)

Performs the *= operation.

impl Neg for Branch

type Output = Branch

The resulting type after applying the - operator.

fn neg(self) -> Branch

Performs the unary - operation.

impl Not for Branch

type Output = Horizon

The resulting type after applying the ! operator.

fn not(self) -> Horizon

Performs the unary ! operation.

impl PartialEq<Branch> for Branch

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

This method tests for self and other values to be equal, and is used by ==.

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

This method tests for !=. The default implementation is almost always sufficient, and should not be overridden without very good reason.

impl Sub<Branch> for Branch

type Output = Branch

The resulting type after applying the - operator.

fn sub(self, b: Branch) -> Branch

Performs the - operation.

impl SubAssign<Branch> for Branch

fn sub_assign(&mut self, b: Self)

Performs the -= operation.

impl Copy for Branch

impl StructuralPartialEq for Branch