Documentation

# Geometry and Mesh

Define geometry and discretize it using triangular or tetrahedral mesh

Reconstruct a geometry from STL or mesh data:

• Import an STL file into MATLAB®by using `importGeometry`. The STL file format is very common and supported by most CAD software. In case of a planar STL geometry, the toolbox converts it to a 2-D geometry by mapping it to the X-Y plane.

• Reconstruct a geometry from a mesh by using `geometryFromMesh`. This function works with triangulated meshes, including planar, volume, and surface triangulation that bounds a closed volume.

Create a geometry:

• Stack or nest cubes, cylinders, or spheres to create a geometry for a 3-D problem.

• Use the constructive solid geometry (CSG) approach, write a geometry function, or by use the `polyshape` function to create a geometry for a 2-D problem. The CSG approach uses a set of solid building blocks (square, rectangle, circle, ellipse, and polygon) and combines them to define complex geometries.

• Use the PDE Modeler app to create complex 2-D geometries by drawing, overlapping, and rotating basic shapes, such as circles, polygons and so on.

Mesh a geometry by using the `generateMesh` function. The toolbox uses the finite element method (FEM) to solve PDEs. A PDE model stores the generated mesh as an `FEMesh` object in its `Mesh` property. For details, see Mesh Data.

## Functions

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#### Command Line

 `importGeometry` Import 2-D or 3-D geometry from STL data `geometryFromMesh` Create 2-D or 3-D geometry from mesh `geometryFromEdges` Create 2-D geometry from decomposed geometry matrix `decsg` Decompose constructive solid 2-D geometry into minimal regions `multicuboid` Create geometry formed by several cubic cells `multicylinder` Create geometry formed by several cylindrical cells `multisphere` Create geometry formed by several spherical cells `pdegplot` Plot PDE geometry `addVertex` Add a vertex on a geometry boundary `csgchk` Check validity of Geometry Description matrix `csgdel` Delete borders between minimal regions `pdearcl` Interpolation between parametric representation and arc length `wgeom` Write geometry specification function

#### PDE Modeler App

 `pdecirc` Draw circle in PDE Modeler app `pdeellip` Draw ellipse in PDE Modeler app `pdepoly` Draw polygon in PDE Modeler app `pderect` Draw rectangle in PDE Modeler app
 `generateMesh` Create triangular or tetrahedral mesh `meshQuality` Evaluate shape quality of mesh elements `findElements` Find mesh elements in specified region `findNodes` Find mesh nodes in specified region `area` Area of 2-D mesh elements `volume` Volume of 3-D mesh elements `pdemesh` Plot PDE mesh `pdeplot` Plot solution or mesh for 2-D problem `pdeplot3D` Plot solution or surface mesh for 3-D problem
 `adaptmesh` Adaptive 2-D mesh generation and PDE solution `initmesh` Create initial 2-D mesh `meshToPet` [p,e,t] representation of FEMesh data `jigglemesh` (Not recommended) Jiggle internal points of triangular mesh `refinemesh` Refine triangular mesh `pdeent` Indices of triangles neighboring given set of triangles `pdesde` Indices of points/edges/triangles in set of subdomains

## Properties

 AnalyticGeometry Properties Analytic 2-D geometry description DiscreteGeometry Properties Discrete 2-D or 3-D geometry description FEMesh Properties Mesh object

## Apps

 PDE Modeler Create complex 2-D geometries by drawing, overlapping, and rotating basic shapes

## Topics

### Geometry

STL File Import

Include a geometry into your PDE model by importing an STL file.

Geometry from Triangulated Mesh

Reconstruct a geometry from a tetrahedral mesh and from a planar multidomain mesh.

Geometry from polyshape

Reconstruct a geometry from a triangulated mesh created by the MATLAB `polyshape` function.

Geometry from alphaShape

Reconstruct a geometry from a triangulated surface mesh created by the MATLAB `alphaShape` function.

2-D Geometry Creation at Command Line

Use constructive solid geometry (CSG) modeling approach to combine basic shapes at the command line.

Parametrized Function for 2-D Geometry Creation

Create a 2-D geometry by using a parametrized function.

Cuboids, Cylinders, and Spheres

Create a 3-D geometry by stacking or nesting three basic volumes.

Multidomain Geometry Reconstructed from Mesh

Split a single-domain block geometry into two domains.

Sphere in Cube

Create a nested multidomain geometry consisting of a unit sphere and a cube.

### Mesh

Generate Mesh

Find Mesh Elements and Nodes by Location

Find mesh elements and nodes by their geometric location or proximity to a particular point or node.

Assess Quality of Mesh Elements

Evaluate the shape quality of mesh elements.

### Mesh Data Representation

Mesh Data

Recommended workflow uses `FEMesh` objects to represent meshes.

Mesh Data as [p,e,t] Triples

Legacy workflow uses [p,e,t] triples to represent meshes.

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