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| --- | ||
| uid: dynamic-triangulation-manual | ||
| --- | ||
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| # Dynamic triangulation | ||
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| Using the [`UnsafeTriangulator<T>`][unsafe-triangulator] API, you can perform dynamic triangulation. | ||
| This feature is especially useful in scenarios like path-finding in RTS games, where recalculating only a small portion of the mesh, instead of the entire mesh, can significantly improve efficiency. | ||
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| | Method | Implemented | | ||
| | :---------------------------------------- | :---: | | ||
| | [DynamicInsertPoint][dynamic-insert-point] | ✔️ | | ||
| | DynamicSplitHalfedge | ❌ | | ||
| | DynamicRemovePoint | ❌ | | ||
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| ## DynamicInsertPoint | ||
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| The [DynamicInsertPoint][dynamic-insert-point] method allows you to insert a point into a specified triangle using barycentric coordinates. This method only supports point insertion within the original triangulation domain and cannot be used to insert points outside the existing mesh. | ||
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| Inserting a point at specific `T2 p` coordinates can be computationally expensive since it requires locating the triangle that contains the point `p`. | ||
| This package does not include acceleration structures, as it assumes the user will implement this based on their specific requirements. | ||
| It is recommended to use structures such as bounding volume hierarchies, 2D trees, grids, or buckets for efficient point lookup (`p` $\to \triangle$). | ||
| The most suitable acceleration structure may vary depending on the use case. | ||
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| The [DynamicInsertPoint][dynamic-insert-point] method accepts the following parameters (in addition to `output` and `allocator`): | ||
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| - `tId` the index of the triangle where the point should be inserted. | ||
| - `bar` the barycentric coordinates of the point inside triangle `tId`. | ||
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| > [!IMPORTANT] | ||
| > All $\texttt{bar}$ coordinates must be valid barycentric coordinates *inside* the triangle, meaning | ||
| > | ||
| > - $\forall_i\,\,\texttt{bar}[i]\in(0, 1)$; | ||
| > - $\sum_i \, \texttt{bar}[i] = 1$. | ||
| Here is an example of how to use the API: | ||
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| ```csharp | ||
| var t = new UnsafeTriangulator<float2>(); | ||
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| using var positions = new NativeArray<float2>(..., Allocator.Persistent); | ||
| using var constraints = new NativeArray<int>(..., Allocator.Persistent); | ||
| var input = new InputData<float2> { Positions = positions, ConstraintEdges = constraints }; | ||
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| using var outputPositions = new NativeList<float2>(Allocator.Persistent); | ||
| using var triangles = new NativeList<int>(Allocator.Persistent); | ||
| using var halfedges = new NativeList<int>(Allocator.Persistent); | ||
| using var constrainedHalfedges = new NativeList<bool>(Allocator.Persistent); | ||
| var output = new OutputData<float2> { Positions = outputPositions, Triangles = triangles, Halfedges = halfedges, ConstrainedHalfedges = constrainedHalfedges }; | ||
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| t.Triangulate(input, output, args: Args.Default(autoHolesAndBoundary: true), Allocator.Persistent); | ||
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| // Insert a new point in triangle with index 42 at the center (barycentric coordinates: [⅓, ⅓, ⅓]). | ||
| t.DynamicInsertPoint(output, tId: 42, bar: 1f / 3, allocator: Allocator.Persistent); | ||
| ``` | ||
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| > [!NOTE] | ||
| > To quickly calculate the corresponding `bar` for a given `p` inside a triangle `(a, b, c)`, you can use the following utility function (not included in the package): | ||
| > | ||
| > ```csharp | ||
| > static float3 Bar(float2 p, float2 a, float2 b, float2 c) | ||
| > { | ||
| > float cross(float2 x, float2 y) => x.x * y.y - x.y * y.x; | ||
| > var (v0, v1, v2) = (b - a, c - a, p - a); | ||
| > var v = cross(v2, v1) / cross(v0, v1); | ||
| > var w = cross(v0, v2) / cross(v0, v1); | ||
| > var u = 1 - v - w; | ||
| > return math.float3(u, v, w); | ||
| > } | ||
| > ``` | ||
| ## DynamicSplitHalfedge | ||
| Not implemented. | ||
| ## DynamicRemovePoint | ||
| Not implemented. | ||
| [unsafe-triangulator]: xref:andywiecko.BurstTriangulator.LowLevel.Unsafe.UnsafeTriangulator`1 | ||
| [dynamic-insert-point]: xref:andywiecko.BurstTriangulator.LowLevel.Unsafe.Extensions.DynamicInsertPoint* |
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@@ -28,18 +28,34 @@ references: | |
| name: float2 | ||
| href: https://docs.unity3d.com/Packages/[email protected]/api/Unity.Mathematics.float2.html | ||
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| - uid: Unity.Mathematics.float3 | ||
| name: float3 | ||
| href: https://docs.unity3d.com/Packages/[email protected]/api/Unity.Mathematics.float3.html | ||
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| - uid: UnityEngine.Vector2 | ||
| name: Vector2 | ||
| href: https://docs.unity3d.com/ScriptReference/Vector2.html | ||
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| - uid: UnityEngine.Vector3 | ||
| name: Vector3 | ||
| href: https://docs.unity3d.com/ScriptReference/Vector3.html | ||
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| - uid: Unity.Mathematics.double2 | ||
| name: double2 | ||
| href: https://docs.unity3d.com/Packages/[email protected]/api/Unity.Mathematics.double2.html | ||
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| - uid: Unity.Mathematics.double3 | ||
| name: double3 | ||
| href: https://docs.unity3d.com/Packages/[email protected]/api/Unity.Mathematics.double3.html | ||
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| - uid: Unity.Mathematics.int2 | ||
| name: int2 | ||
| href: https://docs.unity3d.com/Packages/[email protected]/api/Unity.Mathematics.int2.html | ||
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| - uid: Unity.Mathematics.int3 | ||
| name: int3 | ||
| href: https://docs.unity3d.com/Packages/[email protected]/api/Unity.Mathematics.int3.html | ||
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| - uid: UnityEngine.MonoBehaviour | ||
| name: MonoBehaviour | ||
| href: https://docs.unity3d.com/ScriptReference/MonoBehaviour.html | ||