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* Update Support Matrix page * Add page for algorithms * Add page for example usage * Remove support matrix from README
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| # Integration Algorithms | ||
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| ## Gauss-Kronrod | ||
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| ```@docs | ||
| MeshIntegrals.GaussKronrod | ||
| ``` | ||
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| ## Gauss-Legendre | ||
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| ```@docs | ||
| MeshIntegrals.GaussLegendre | ||
| ``` | ||
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| ## H-Adaptive Cubature | ||
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| ```@docs | ||
| MeshIntegrals.HAdaptiveCubature | ||
| ``` |
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| # Support Matrix | ||
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| | Symbol | Meaning | | ||
| While this library aims to support all possible integration algorithms and **Meshes.jl** | ||
| geometry types, some combinations are ill-suited and some others are simplu not yet | ||
| implemented. The following Support Matrix aims to capture the current development state of | ||
| all geometry/algorithm combinations. Entries with a green check mark are fully supported | ||
| and have passing unit tests that provide some confidence they produce accurate results. | ||
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| In general, Gauss-Kronrod integration rules are recommended (and the default) for geometries | ||
| with one parametric dimension, e.g.: `Segment`, `BezierCurve`, and `Rope`. Gauss-Kronrod | ||
| rules can also be applied to some geometries with more dimensions by nesting multiple | ||
| integration solves, but this is inefficient. These Gauss-Kronrod rules are supported (but | ||
| not recommended) for surface-like geometries, but not for volume-like geometries. For | ||
| geometries with more than one parametric dimension, e.g. surfaces and volumes, H-Adaptive | ||
| Cubature integration rules are recommended (and the default). | ||
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| | Symbol | Support Level | | ||
| |--------|---------| | ||
| | :white_check_mark: | Implemented, passes tests | | ||
| | :x: | Not yet supported | | ||
| | :stop_sign: | Not supported | | ||
| | ✅ | Supported, passes unit tests | | ||
| | 🎗️ | Planned to support in the future | | ||
| | 🛑 | Not supported | | ||
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| ### Integral | ||
| | Geometry | Gauss-Legendre | Gauss-Kronrod | H-Adaptive Cubature | | ||
| | `Meshes.Geometry` | Gauss-Legendre | Gauss-Kronrod | H-Adaptive Cubature | | ||
| |----------|----------------|---------------|---------------------| | ||
| | `Ball` in `𝔼{2}` | :white_check_mark: | :white_check_mark: | :white_check_mark: | | ||
| | `Ball` in `𝔼{3}` | :white_check_mark: | :stop_sign: | :white_check_mark: | | ||
| | `BezierCurve` | :white_check_mark: | :white_check_mark: | :white_check_mark: | | ||
| | `Box` in `𝔼{1}` | :white_check_mark: | :white_check_mark: | :white_check_mark: | | ||
| | `Box` in `𝔼{2}` | :white_check_mark: | :white_check_mark: | :white_check_mark: | | ||
| | `Box` in `𝔼{3}` | :white_check_mark: | :stop_sign: | :white_check_mark: | | ||
| | `Circle` | :white_check_mark: | :white_check_mark: | :white_check_mark: | | ||
| | `Cone` | :white_check_mark: | :white_check_mark: | :white_check_mark: | | ||
| | `ConeSurface` | :white_check_mark: | :white_check_mark: | :white_check_mark: | | ||
| | `Cylinder` | :white_check_mark: | :stop_sign: | :white_check_mark: | | ||
| | `CylinderSurface` | :white_check_mark: | :white_check_mark: | :white_check_mark: | | ||
| | `Disk` | :white_check_mark: | :white_check_mark: | :white_check_mark: | | ||
| | `Frustum` | :stop_sign: | :stop_sign: | :stop_sign: | | ||
| | `FrustumSurface` | :stop_sign: | :stop_sign: | :stop_sign: | | ||
| | `Line` | :white_check_mark: | :white_check_mark: | :white_check_mark: | | ||
| | `ParaboloidSurface` | :white_check_mark: | :white_check_mark: | :white_check_mark: | | ||
| | `Plane` | :white_check_mark: | :white_check_mark: | :white_check_mark: | | ||
| | `Ray` | :white_check_mark: | :white_check_mark: | :white_check_mark: | | ||
| | `Ring` | :white_check_mark: | :white_check_mark: | :white_check_mark: | | ||
| | `Rope` | :white_check_mark: | :white_check_mark: | :white_check_mark: | | ||
| | `Segment` | :white_check_mark: | :white_check_mark: | :white_check_mark: | | ||
| | `SimpleMesh` | :x: | :x: | :x: | | ||
| | `Sphere` in `𝔼{2}` | :white_check_mark: | :white_check_mark: | :white_check_mark: | | ||
| | `Sphere` in `𝔼{3}` | :white_check_mark: | :white_check_mark: | :white_check_mark: | | ||
| | `Tetrahedron` in `𝔼{3}` | :x: | :white_check_mark: | :x: | | ||
| | `Triangle` | :white_check_mark: | :white_check_mark: | :white_check_mark: | | ||
| | `Torus` | :white_check_mark: | :white_check_mark: | :white_check_mark: | | ||
| | `Ball` in `𝔼{2}` | ✅ | ✅ | ✅ | | ||
| | `Ball` in `𝔼{3}` | ✅ | 🛑 | ✅ | | ||
| | `BezierCurve` | ✅ | ✅ | ✅ | | ||
| | `Box` in `𝔼{1}` | ✅ | ✅ | ✅ | | ||
| | `Box` in `𝔼{2}` | ✅ | ✅ | ✅ | | ||
| | `Box` in `𝔼{3}` | ✅ | 🛑 | ✅ | | ||
| | `Circle` | ✅ | ✅ | ✅ | | ||
| | `Cone` | ✅ | ✅ | ✅ | | ||
| | `ConeSurface` | ✅ | ✅ | ✅ | | ||
| | `Cylinder` | ✅ | 🛑 | ✅ | | ||
| | `CylinderSurface` | ✅ | ✅ | ✅ | | ||
| | `Disk` | ✅ | ✅ | ✅ | | ||
| | `Frustum` | 🛑 | 🛑 | 🛑 | | ||
| | `FrustumSurface` | 🛑 | 🛑 | 🛑 | | ||
| | `Line` | ✅ | ✅ | ✅ | | ||
| | `ParaboloidSurface` | ✅ | ✅ | ✅ | | ||
| | `Plane` | ✅ | ✅ | ✅ | | ||
| | `Ray` | ✅ | ✅ | ✅ | | ||
| | `Ring` | ✅ | ✅ | ✅ | | ||
| | `Rope` | ✅ | ✅ | ✅ | | ||
| | `Segment` | ✅ | ✅ | ✅ | | ||
| | `SimpleMesh` | 🎗️ | 🎗️ | 🎗️ | | ||
| | `Sphere` in `𝔼{2}` | ✅ | ✅ | ✅ | | ||
| | `Sphere` in `𝔼{3}` | ✅ | ✅ | ✅ | | ||
| | `Tetrahedron` in `𝔼{3}` | 🎗️ | ✅ | 🎗️ | | ||
| | `Triangle` | ✅ | ✅ | ✅ | | ||
| | `Torus` | ✅ | ✅ | ✅ | |
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| # Example Usage | ||
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| ## Integrating along a Bezier curve | ||
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| ```julia | ||
| using Meshes | ||
| using MeshIntegrals | ||
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| # Define a unit circle on the xy-plane | ||
| origin = Point(0,0,0) | ||
| ẑ = Vec(0,0,1) | ||
| xy_plane = Plane(origin,ẑ) | ||
| unit_circle_xy = Circle(xy_plane, 1.0) | ||
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| # Approximate unit_circle_xy with a high-order Bezier curve | ||
| unit_circle_bz = BezierCurve( | ||
| [Point(cos(t), sin(t), 0.0) for t in range(0,2pi,length=361)] | ||
| ) | ||
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| # A Real-valued function | ||
| f(x, y, z) = abs(x + y) | ||
| f(p) = f(to(p)...) | ||
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| integral(f, unit_circle_xy, GaussKronrod()) | ||
| # 0.000170 seconds (5.00 k allocations: 213.531 KiB) | ||
| # ans == 5.656854249525293 m^2 | ||
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| integral(f, unit_circle_bz, GaussKronrod()) | ||
| # 0.017122 seconds (18.93 k allocations: 78.402 MiB) | ||
| # ans = 5.551055333711397 m^2 | ||
| ``` |