Struct Tessellation

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pub struct Tessellation { /* private fields */ }

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pub fn smooth_welded( &mut self, smoothing: Smoothing, ) -> Result<(), &'static str>

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impl Tessellation

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pub fn dual_background( &self, balancing: Balancing, scale: Scalar, ) -> Result<(Mesh<D>, Vec<Class>), &'static str>

Builds the dual of an octree fitted to this tessellation, with each cell classified against the surface.

The background for cut. balancing must be Strong(1) or Weak(1), which is what dualization requires.

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pub fn lattice_background( &self, spacing: Quantity<Length>, ) -> Result<(Mesh<D>, Vec<Class>), &'static str>

Builds a uniform lattice of cubes of the given edge length around this tessellation, with each cell classified against the surface.

The lattice spans the cells the surface passes through, those its interior encloses, and a single shell of cells beyond them, so it is a background to be cut, or trimmed and buffered, rather than a finished mesh.

Unlike dual_background the cells are all axis-aligned cubes, at the cost of the grading a tree provides, and the classes fall out of rasterizing rather than being found again.

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pub fn lattice_tet_background( &self, spacing: Quantity<Length>, ) -> Result<(Mesh<D>, Vec<Class>), &'static str>

Builds a uniform lattice around this tessellation and splits every cell into six tetrahedra, with each one classified against the surface.

The tetrahedral counterpart of lattice_background. The cells are still classified by rasterizing, so the six tetrahedra of a cell all take the class of the cell they came from.

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pub fn octree_background( &self, balancing: Balancing, scale: Scalar, ) -> Result<(Mesh<D>, Vec<Class>), &'static str>

Builds an octree fitted to this tessellation, with each cell classified against the surface.

The background for cut_polyhedral, taking the octree directly rather than its dual. This places no 2:1 requirement on balancing, since hanging nodes become extra vertices on a face rather than something to be dualized away. Weak(n) and Strong(n) for n > 1 are therefore available here, permitting coarser trees than dualization allows.

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pub fn octree_tet_background( &self, balancing: Balancing, pairing: Pairing, scale: Scalar, tolerance: Option<Quantity<Length>>, ) -> Result<(Mesh<D>, Vec<Class>), &'static str>

Builds an octree fitted to this tessellation and meshes it as tetrahedra, with each one classified against the surface.

The tetrahedral counterpart of octree_background, to be trimmed. balancing must be Strong(1): the templates filling a graded cell only span a one-level difference, and only a balance over edges and vertices as well as faces holds them to it. pairing need not be Regular; the tetrahedra conform under any pairing, and None yields a smaller background.

tolerance is the Dunyach chord-error tolerance for curvature-driven refinement; None disables it.

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pub fn cut( &self, mesh: Mesh<D>, classes: &[Class], ) -> Result<Mesh<D>, &'static str>

Cuts a classified background mesh to this tessellation, leaving hexahedra everywhere but at the boundary.

Snaps the nodes that nearly lie on the surface onto it, builds the crossing tables, and assembles the cut cells into polyhedra.

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pub fn cut_polyhedral( &self, mesh: Mesh<D>, classes: &[Class], ) -> Result<Mesh<D>, &'static str>

Cuts a classified background mesh to this tessellation, leaving polyhedra throughout.

The counterpart of cut for a background whose cells carry hanging nodes, such as an octree taken directly.

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impl Tessellation

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pub fn shape_diameter_function( &self, half_angle: Scalar, rings: usize, azimuthal: usize, ) -> QuantityVector<Length>

Estimates local thickness at each node via the shape diameter function.¹

L. Shapira, A. Shamir, and D. Cohen-Or, Visual Comp. 24, 249 (2008). ↩

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impl Tessellation

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pub fn trim(&self, mesh: &mut Mesh<D>) -> Result<(), &'static str>

Discards the cells of a background mesh lying outside this tessellation, leaving a mesh that covers the volume it encloses.

A cell survives when the signed distances at its nodes satisfy minimum + 0.1 * maximum >= 0, so the cells straddling the surface are kept for buffer to fit onto it.