1 unstable release
0.1.0  May 6, 2021 

#24 in #2dgraphics
45 downloads per month
Used in bevy_more_shapes
145KB
3K
SLoC
triangulate
Subdivides a set of nonselfintersecting polygons into a set of nonoverlapping triangles. Inputs and outputs can be customized to use your required formats to avoid unnecessary conversions.
Usage
// A hollow square shape
// ________
//  ____ 
//    
//  ____ 
// ________
let polygons: Vec<Vec<MyVert>> = vec![
vec![(0., 0.).into(), (0., 1.).into(), (1., 1.).into(), (1., 0.).into()],
vec![(0.05, 0.05).into(), (0.05, 0.95).into(), (0.95, 0.95).into(), (0.95, 0.05).into()]
];
// `output` is an arbitrary triangulation of polygons in a format determined by the type parameter (in this case, a `Vec` of triangle fans represented by a `Vec` of the `MyVert` vertices).
let output: Vec<Vec<MyVert>> = polygons.triangulate_default::<builders::VecVecFanBuilder<_>>().unwrap();
Input traits

VertexIndex
Any type which isEq
andClone
. 
Vertex
A twodimensional point. The coordinate type must implementnum_traits::real::Real
, reexported astriangulate::Real
. 
PolygonList
A collection of zero or more polygons which can iterate values convertable toenum PolygonVertex<T: VertexIndex>
.
PolygonVertex::ContinuePolygon
provides the next index in the current polygon andPolygonVertex::NewPolygon
indicates the end of the current polygon, and subsequent indices belong to a separate polygon. Indices must be ordered by adjacency, but either clockwise or counterclockwise ordering is accepted.
Preimplemented forVec<Vec<T>>
(multiple polygons) andVec<T>
(single polygon). WrappersIndexWithU16
,IndexWithU16U16
,IndexWithU32
andIndexWithU32U32
are also provided to convertPolygonList
implementations that useusize
and(usize, usize)
as indices to useu16
/(u16, u16)
andu32
/(u32, u32)
for performance reasons when the list of vertices is small enough.
Output traits
FanBuilder
Streams the resulting triangulation into the desired output format.
Triangles are provided as fans, where a callback toextend_fan
adds a new vertex (and correspondingly a new triangle) to the existing fan, whileextend_fan
begins a new fan. These callbacks provideVertexIndex
s, so if the output requiresVertex
s, the builder is responsible for indexing into thePolygonList
.
Since triangle fans are not useful for most applications, also included is theFanToListAdapter
, which allows you to use aListBuilder
as aFanBuilder
. Like the name implies,ListBuilder
works with triangle lists, where each included triangle is specified by all 3 vertex indices.
The output of the included builders is described below:VecVecIndexedFanBuilder
A vector of vectors of indices. Each inner vector is a single triangle fan, with the first element being the 'central' vertex.
let output: Vec<Vec<usize>> = vec![
vec![0, 1, 2, 3, 4],
vec![2, 3, 5]
];
VecVecFanBuilder
A vector of vectors of vertices. LikeVecVecIndexedFanBuilder
, but the indices have been used to clone the vertices' values.
let output: Vec<Vec<Vec2>> = vec![
vec![Vec2::new(0., 0.), Vec2::new(1., 0.), Vec2::new(1., 0.5), Vec2::new(0.5, 1.), Vec2::new(0., 1.)],
vec![Vec2::new(0., 0.), Vec2::new(0., 1.), Vec2::new(1., 2.)]
];
VecDelimitedIndexedFanBuilder
A flat vector of indices, where fans are delimited by a given sentinel value.
let sentinel: usize = usize::MAX;
let output: Vec<usize> = vec![0, 1, 2, 3, 4, sentinel, 2, 3, 5];
VecIndexedListBuilder
A flat vector of indices. Each chunk of 3 vertices represents 1 triangle.
let output: Vec<usize> = vec![0, 1, 2, 0, 2, 3, 1, 3, 4];
VecListBuilder
LikeVecIndexedListBuilder
, but with vertices deindexed.
let output: Vec<Vec2> = vec![Vec2::new(0., 0.), Vec2::new(1., 0.), Vec2::new(1., 1.), Vec2::new(0., 0.), Vec2::new(1., 1.), Vec2::new(0., 1.), Vec2::new(0., 0.), Vec2::new(0., 1.), Vec2::new(1., 2.)];
Preconditions
 No edge can cross any other edge, whether it is on the same polygon or not.
 Each vertex must be part of exactly two edges. Polygons cannot 'share' vertices with each other.
 Each vertex must be distinct  no vertex can have x and y coordinates that both compare equal to another vertex's.
These preconditions are not explicitly checked, but an invalid polygon set will likely yield
TriangulationError::InternalError
.
Results
Because the algorithm involves random ordering, the exact triangulation is not guaranteed to be same between invocations.
Algorithm
This library is based on Raimund Seidel's randomized algorithm for triangulating polygons. The expected runtime for each polygon or hole with n vertices is O(n log* n), a nearlinear runtime.
Dependencies
~4.5MB
~91K SLoC