Generation and Iterator Expressions

Streams of topological and geometric data can be generated from primitives like cubes and spheres using iterator expressions. Primitives emit topological structures like Triangles or Quads, which contain arbitrary geometric data in their vertices. These can be transformed and decomposed into other topologies and geometric data via triangulation, tesselation, and other operations.

```rust use nalgebra::Point3; use plexus::buffer::MeshBuffer; use plexus::generate::sphere; use plexus::prelude::*;

// Example module in the local crate that provides basic rendering. use render::{self, Color, Vertex};

// Construct a buffer of index and vertex data from a sphere primitive. let buffer = sphere::UvSphere::new(16, 16) .polygonswithposition() .mapvertices(|position| -> Point3 { position.into() }) .mapvertices(|position| position * 10.0) .mapvertices(|position| Vertex::new(position, Color::white())) .collect::>(); render::draw(buffer.asindexslice(), buffer.asvertex_slice()); ```

For an example of rendering, see the viewer example.

Half-Edge Graph Meshes

Generators produce an ephemeral stream of topology and vertex geometry. A Mesh, represented as a half-edge graph, supports arbitrary geometry for vertices, edges, and faces. The graph can also be traversed and manipulated in ways that generators and iterator expressions cannot, such as circulation, extrusion, merging, and joining.

```rust use nalgebra::Point3; use plexus::generate::sphere; use plexus::graph::Mesh; use plexus::prelude::*;

// Construct a mesh from a sphere primitive. The vertex geometry is convertible // to Point3 via the FromGeometry trait in this example. let mut mesh = sphere::UvSphere::new(8, 8) .polygonswithposition() .collect::>>(); // Extrude a face in the mesh. let key = mesh.faces().nth(0).unwrap().key(); let face = mesh.face_mut(key).unwrap().extrude(1.0).unwrap(); ```

Plexus avoids exposing very basic topological operations like inserting individual vertices, because they can easily be done incorrectly and lead to invalid topologies. Instead, meshes are manipulated with higher-level operations like extrusion and joining.

Geometric Traits

Meshes support arbitrary geometry for vertices, edges, and faces (including no geometry at all) via optional traits. Implementing these traits enables more operations and features, but only two basic traits are required: Geometry and Attribute.

```rust use nalgebra::{Point3, Vector3}; use plexus::geometry::{Attribute, Geometry}; use plexus::geometry::convert::AsPosition;

[derive(Clone, Copy)]

pub struct VertexGeometry { pub position: Point3, pub normal: Vector3, }

impl Attribute for VertexGeometry {}

impl Geometry for VertexGeometry { type Vertex = Self; type Edge = (); type Face = (); }

impl AsPosition for VertexGeometry { type Target = Point3;

fn as_position(&self) -> &Self::Target {
    &self.position
}

fn as_position_mut(&mut self) -> &mut Self::Target {
    &mut self.position
}

} ```

Geometric traits are optionally implemented for types in the nalgebra and cgmath crates so that common types can be used right away for vertex geometry. See the geometry-cgmath and geometry-nalgebra (enabled by default) crate features. Both 2D and 3D geometry are supported by mesh operations.

Hashing Floating-Point Values

When collecting an iterator expression into a graph or buffer, an indexer is used to transform the geometry into raw buffers. HashIndexer is fast and reliable, and is used by collect (which can be overridden via collect_with_indexer). However, geometry often contains floating point values, which do not implement Hash. An LruIndexer can also be used, but may be slower and requires a sufficient capacity to work correctly.

The decorum crate is used to ease this problem. Hashable types like NotNan, Finite, R32, etc. can be used as geometric data and are emitted by primitive generators like UvSphere and Cube. Decorum can also be used to more easily make custom geometric data hashable.