logo

Trait plexus::primitive::Topological

source · [−]
pub trait Topological: Adjunct<Item = Self::Vertex> + AsMut<[Self::Vertex]> + AsRef<[Self::Vertex]> + DynamicArity<Dynamic = usize> + IntoIterator<Item = Self::Vertex> + Sized {
    type Vertex;

    fn try_from_slice<T>(vertices: T) -> Option<Self>
    where
        Self::Vertex: Copy,
        T: AsRef<[Self::Vertex]>;

    fn embed_into_e3_xy<P>(ngon: P, z: Scalar<Self::Vertex>) -> Self
    where
        Self::Vertex: EuclideanSpace + FiniteDimensional<N = U3>,
        P: Map<Self::Vertex, Output = Self> + Topological,
        P::Vertex: EuclideanSpace + FiniteDimensional<N = U2> + Extend<Self::Vertex>,
        Vector<P::Vertex>: VectorSpace<Scalar = Scalar<Self::Vertex>>,
    { ... }
    fn embed_into_e3_xy_with<P, F>(
        ngon: P, 
        z: Scalar<Position<Self::Vertex>>, 
        f: F
    ) -> Self
    where
        Self::Vertex: AsPosition,
        Position<Self::Vertex>: EuclideanSpace + FiniteDimensional<N = U3>,
        P: Map<Self::Vertex, Output = Self> + Topological,
        P::Vertex: EuclideanSpace + FiniteDimensional<N = U2> + Extend<Position<Self::Vertex>>,
        Vector<P::Vertex>: VectorSpace<Scalar = Scalar<Position<Self::Vertex>>>,
        F: FnMut(Position<Self::Vertex>) -> Self::Vertex,
    { ... }
    fn embed_into_e3_plane<P>(ngon: P, plane: Plane<Self::Vertex>) -> Self
    where
        Self::Vertex: EuclideanSpace + FiniteDimensional<N = U3>,
        P: Map<Self::Vertex, Output = Self> + Topological,
        P::Vertex: EuclideanSpace + FiniteDimensional<N = U2> + Extend<Self::Vertex>,
        Vector<P::Vertex>: VectorSpace<Scalar = Scalar<Self::Vertex>>,
    { ... }
    fn embed_into_e3_plane_with<P, F>(
        ngon: P, 
        _: Plane<Position<Self::Vertex>>, 
        f: F
    ) -> Self
    where
        Self::Vertex: AsPosition,
        Position<Self::Vertex>: EuclideanSpace + FiniteDimensional<N = U3>,
        P: Map<Self::Vertex, Output = Self> + Topological,
        P::Vertex: EuclideanSpace + FiniteDimensional<N = U2> + Extend<Position<Self::Vertex>>,
        Vector<P::Vertex>: VectorSpace<Scalar = Scalar<Position<Self::Vertex>>>,
        F: FnMut(Position<Self::Vertex>) -> Self::Vertex,
    { ... }
    fn project_into_plane(self, plane: Plane<Position<Self::Vertex>>) -> Self
    where
        Self::Vertex: AsPositionMut,
        Position<Self::Vertex>: EuclideanSpace + FiniteDimensional,
        <Position<Self::Vertex> as FiniteDimensional>::N: Cmp<U2, Output = Greater>,
    { ... }
    fn edges(&self) -> Vec<Edge<&Self::Vertex>> { ... }
}
Expand description

Topological structure.

Types implementing Topological provide some notion of adjacency between vertices of their Vertex type. These types typically represent cycle graphs and polygonal structures, but may also include degenerate forms like monogons.

Required Associated Types

Required Methods

Provided Methods

Embeds an $n$-gon from $\Reals^2$ into $\Reals^3$.

The scalar for the additional basis is normalized to the given value.

Examples

Embedding a triangle into the $xy$-plane at $z=1$:

use nalgebra::Point2;
use plexus::primitive::{Topological, Trigon};
use theon::space::EuclideanSpace;

type E2 = Point2<f64>;

let trigon = Trigon::embed_into_e3_xy(
    Trigon::from([
        E2::from_xy(-1.0, 0.0),
        E2::from_xy(0.0, 1.0),
        E2::from_xy(1.0, 0.0),
    ]),
    1.0,
);

Embeds an $n$-gon from $\Reals^2$ into $\Reals^3$.

The $n$-gon is rotated into the given plane about the origin.

Examples

Embedding a triangle into the $xy$-plane at $z=0$:

use nalgebra::{Point2, Point3};
use plexus::geometry::{Plane, Unit};
use plexus::primitive::{Topological, Trigon};
use theon::space::{Basis, EuclideanSpace};

type E2 = Point2<f64>;
type E3 = Point3<f64>;

let trigon = Trigon::embed_into_e3_plane(
    Trigon::from([
        E2::from_xy(-1.0, 0.0),
        E2::from_xy(0.0, 1.0),
        E2::from_xy(1.0, 0.0),
    ]),
    Plane::<E3> {
        origin: EuclideanSpace::origin(),
        normal: Unit::z(),
    },
);

Projects an $n$-gon into a plane.

The positions in each vertex of the $n$-gon are translated along the normal of the plane.

Implementors